{"slug":"tmp1027.tmp1027.opp-lat1","id":"latin:ogl-pl:tmp1027.tmp1027.opp-lat1","title":"Posteriorum Analyticorum Aristotelis Libri Duo","title_source":"Posteriorum Analyticorum Aristotelis Libri Duo","author":"Boethius. Severinus","genre":"treatise","date":"","tradition":"latin","coverage":"not-located","coverage_claim":{"status":"not-located","text":"No English translation could be identified: a language model asked twice could not name one, though it could not rule one out either. That is not proof that none exists — translations in dissertations, recent books and other modern languages are easily missed."},"publication":{"status":"machine-draft","reviewed_by":null,"model":"deepseek/deepseek-v4.1-flash:floor","provider":"Baidu","generated":"2026-11-15T20:56:27Z","cost_usd":0.011007},"source":{"registry_id":"latin:ogl-pl:tmp1027.tmp1027.opp-lat1","work_id":"tmp1027.tmp1027.opp-lat1","edition":"ogl-pl","language":"","license":"Available under a Creative Commons Attribution-ShareAlike 4.0 International License","url":"https://github.com/OpenGreekAndLatin/patrologia_latina-dev/blob/master/data/tmp1027/tmp1027/tmp1027.tmp1027.opp-lat1.xml"},"stats":{"passages":119,"english_words":31582,"coptic_letters":0,"source_letters":114511,"commentary_units":0,"commentary_kinds":0,"derived_notes":5,"ambiguities":0,"work_notes":0,"external_links":0,"timeline":0},"summary":{},"links":[{"kind":"source","label":"Open Greek and Latin Patrologia Latina","url":"https://github.com/OpenGreekAndLatin/patrologia_latina-dev/blob/master/data/tmp1027/tmp1027/tmp1027.tmp1027.opp-lat1.xml"}],"checks":{"work":"tmp1027.tmp1027.opp-lat1","status":"pass","blocking":[],"warnings":[],"stats":{"passages":119,"translated":119,"commentary_passages":0,"commentary_units":0,"english_words":31582,"source_letters":114053,"commentary_kinds":0},"model":"deepseek/deepseek-v4.1-flash:floor"},"work_notes":[],"derived_work_notes":[{"kind":"coverage","severity":"info","text":"No English translation could be identified: a language model asked twice could not name one, though it could not rule one out either. That is not proof that none exists — translations in dissertations, recent books and other modern languages are easily missed."},{"kind":"limit","severity":"caution","text":"The English is a machine draft produced passage by passage from the transcribed Latin; no human has verified it. The commentary is model-written and cites only keys the pipeline could resolve."},{"kind":"register","severity":"info","text":"Register: treatise in Latin; the English keeps the liturgical formulae and the vocatives rather than normalising them."},{"kind":"structure","severity":"info","text":"Passages: 119 narrative."},{"kind":"caution","severity":"caution","text":"5 passage(s) are fragmentary in the source; the English bridges each break and says so in the note."},{"kind":"source","severity":"info","text":"Source edition: ogl-pl."},{"kind":"source","severity":"info","text":"Licence: Available under a Creative Commons Attribution-ShareAlike 4.0 International License"}],"derived_structure":{"narrative":119},"term_index":[],"citations":{},"segments":[{"i":1,"ref":"p1","source":"POSTERIORUM ANALYTICORUM ARISTOTELIS LIBRI DUO, AN. MANL. SEV. BOETIO INTERPRETE\n\nLIBER PRIMUS.\n\nCAPUT PRIMUM.\n\nDe præcognitis\n\nOmnis doctrinaet omnisdisciplina intellectiva ex præexistente fit cognitione.Manifestum autem hoc speculantibus in omnibus,mathematicae enim scientiae per hunc modum fiunt, et aliarum unaquaeque artium.Similiter autem et circa orationes,quæ per syllogismos et quæ perinductionem: utraque enim per prius nota faciunt doctrinam, hæ quidem accipientes tanquam a notis, illæ vero monstrantes universale, per id (quod manifestum est) singulare. Similiter autem et rhetoricae persuadent aut enim per exempla, quod est inductio, aut per enthymemata, quod quidem est syllogismus. Dupliciter autem est necessarium præcognoscere, alia namque quia sunt præopinari necesse est, alia vero quid est quod dicitur intelligere oportet, quaedam autem utraque.","english":"THE TWO BOOKS OF ARISTOTLE'S POSTERIOR ANALYTICS, TRANSLATED BY ANICIUS MANLIUS SEVERINUS BOETHIUS\n\nBOOK ONE.\n\nCHAPTER ONE.\n\nOn Things Known Beforehand\n\nAll doctrine and all intellectual discipline comes to be from pre-existing cognition. This is manifest to those who consider it in all cases; for the mathematical sciences come about in this way, and each one of the other arts as well. Likewise also concerning arguments, both those that proceed through syllogisms and those that proceed through induction: for both make doctrine through things previously known—the latter receiving, as it were, from things known, while the former demonstrate the universal through the particular, which is manifest. Likewise also rhetorical persuasions: for they persuade either through examples, which is induction, or through enthymemes, which is indeed a syllogism. But it is necessary to know beforehand in two ways: for some things it is necessary to assume beforehand that they are, while other things it is necessary to understand what the thing said is, and some things both.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":2,"ref":"p2","source":"Ut ql!loniam quidem omne aut affirmare,aut negare verum est, quia est, triangulum autem, quoniam hoc significat, sed unitatem utraque, et quid significat quidem,et quia est non enim similiter horum unumquodque manifestum est nobis.Estautem cognoscere aliaquidem prius cognoscentem,quorumdam autem simul accipere notitiarn,ut quæcunque contingunt esse sub universalibus quorum habent cogniLionem; quod enim omnis triangulus habeat tres angulos duobus rectis aequales, præscivit,quod vero hie qui est in semicirculo triangulus sit,sirnul inducens cognovit. Quorumdam enim hoc modo disciplina est, et non per medium ultimum cognoscitur, ut quæcunque jam singulariumcontingunt esse,et non de subjecto aliquo. Antequam autem sit inducere,aut accipere syllogismum, quodam quidem modo fortasse dicendum ett scire, modo autem alio, non quod enim nescivit si est simpliciter hoc quodam nodo scivit quod duos habet rectos simpIiciter,sed manifestumestquodsic quidem scitquoniarc.","english":"For just as it is true in every case either to affirm or to deny, because it is, and [to say] of a triangle that it signifies this, but both [are known] as a unity—both what it signifies and that it is; for not in the same way is each of these manifest to us. But it is possible to know some things by having known them beforehand, while of certain things we receive the knowledge at the same time—namely, whatever things happen to fall under the universals of which we have knowledge. For that every triangle has three angles equal to two right angles, one knew beforehand; but that this particular triangle in the semicircle is a triangle, one came to know at the same time by inducing it. For of certain things the discipline comes about in this way, and it is not known through the last middle term—namely, whatever things already happen to be among singulars and are not [said] of some subject. But before one induces or takes up the syllogism, in one way perhaps it must be said that one knows, but in another way not. For that which one did not know, whether it simply is this thing, in a certain way one knew that it simply has two right angles; but it is manifest that in this way one knows it as a universal.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":3,"ref":"p3","source":"universaliter scivit, simpliciter autem non scit; si vero non, Menonis ambiguitas continget,autenim nihil discet, aut ql1æ novit.Non enim,sicut quidam conantursotvere,dicendum est,nunquid scivisti omnem dualitatem quoniam par est,aut nonP dicente autem,attuIerat quamdam dualitatem, quam non opinatus est esse,quare neque parem.Solvunt enim dicentes non cognoscereomnem dualitatem parem esse,sed quam sciunt quod dualitas fit.Attamen sciunt quidem cujus vere demonstrationem habent,etcujus acceperunt: acceperunt autem non de omni cujus utique sciunt, quod triangulus aut quod numerus ait,sed simpliciter de omni numero et triangulo, neque enim una propositio accipitur hujus quod quem tu nosti numerurn,aut quod tu nosti rectilineulll,sed de omni. Sed nihil (utopinor) prohibet quod dicit quis,sit ut scire,sit etiam ut ignorare, inconveniens enim non est, si scit quodam modo quod discit,sed si hoc modo,ut in quantum discit, et scit.","english":"He knew it universally, but does not know it simply; if not, the ambiguity of Meno will follow—for either he will learn nothing, or [he will learn] what he already knows. For it must not be said, as some attempt to resolve it, \"Did you not know every duality, that it is even?\"—and when he says yes, [they reply] that he had brought forward some duality which he did not suppose to be, and therefore not [supposed to be] even. For they resolve it by saying that he does not know that every duality is even, but [only] the one which he knows to be a duality. Yet they do know that of which they truly have a demonstration, and of which they have received [it]; but they have not received [it] concerning every [thing] of which they know—as when he says \"triangle\" or \"number\"—but simply concerning every number and triangle. For no single proposition is taken of this [particular thing]—that \"the number which you know,\" or \"the rectilinear [figure] which you know\"—but of every [one]. But nothing (as I think) prevents what someone says from being both a way of knowing and a way of not knowing; for it is not incongruous if he knows in some way what he learns, but [only] if in such a way that, insofar as he learns, he also knows.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":4,"ref":"p4","source":"CAPUT II.\n\nDe modis sciendi, el demonstratione.\n\nScire autem opinamur unumquodque simpliciter, sed non sophistico n:odo,quiestsecundum accidens, cum causam arbitramur cognoacere,propter quam res est,quoniam illius causa est,et non est contingere hoc aliter se habere.Manifestum igitur est quoniam hujusmodi aliquid scire sit,et namque non scientes, et scientes quidem op:nantur ipsi sic se habere, scientes autem etiam,habent scientiam. Quare cujus simpliciter est scientia,hoc est impossibile aliterse habcre,Si quidem igitur et alius est sciendi modus, posterius dicemus. Dicimus autem scire, et per demonstrationem intelIigere. Demonstrationem autem dico syllogismum epistemon icon, id est facientem, scire, sed epistemonicoQ dico,secundumquem (in habendoipsum) scirnus.Si igitur est scire ut posuimus necesse demonstrativam scientiam ex veris esse et primis,et immedialis,et notioribus, et prioribus, causisque conclusionis.Sic enim principia erunt pro. pria ejus quod demonstraLur,nam syllogismus quidem erit, et sine his, demonstratio autem non erit, non enim faciet scientiam. Vera quidem igitur oportet esse, quoniam quod non est, non est scire, ut quod diameter sit symeter.Ex primis autem et indemonstrabiiibus est, quia non sciet, non babens de. monstrationem ipsorurn,scire enim quorum demonstrati est non secundum accidens, est habere demonstrationem.","english":"CHAPTER II.\n\nOn the modes of knowing, and on demonstration.\n\nWe think we know each thing simply—not in the sophistic way that is according to accident—when we believe we recognize the cause on account of which the thing is, that it is the cause of that thing, and that it cannot be otherwise. It is evident, therefore, that to know is something of this sort; for those who do not know, and those who do know, think they themselves are so disposed—but those who know also possess knowledge. Wherefore, whatever is the object of knowledge simply, this cannot be otherwise. If indeed there is also another mode of knowing, we shall speak of it later. But we say we know, and understand through demonstration. I call a demonstration a syllogism that is epistemonikos—that is, productive of knowing—but I call it epistemonikos in the sense according to which, in possessing it, we know. If, therefore, to know is as we have laid down, demonstrative knowledge must be from things true and primary, and immediate, and more known, and prior, and causes of the conclusion. For in this way the principles will be proper to what is demonstrated; for there will indeed be a syllogism even without these, but there will not be a demonstration—for it will not produce knowledge. It is necessary, then, that they be true, since what is not cannot be known—as that the diameter is commensurate. But it is from primary and indemonstrable things, because one will not know, not having a demonstration of them; for to know those things of which there is a demonstration—not according to accident—is to have a demonstration.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":5,"ref":"p5","source":"Causas quoque, et notiora oportet esse,et priora.Causasquidem,quoniam tunc scimus, cumcausam cognoscimus,et priora,siquidem causæ sunt, et notiora,non solum altero modo inteHigendo, sed in sciendo quoniam sunt. Priora autem et notiora dupliciter sunt, non enim idem est natura prius, et ad nos prius, neque notius natura,et nobis notius.\n\nDico autem ad nos priora,et notiora,propinquiora sensui. Simpliciter autem priora, et notiora, quæ longius sunt.Sunt autem longinquissima quidem, universalia maxime. Proxima autem, singularia, et opponuntur hæc ad se invicem. Ex primi autem est quod ex propriis principiis est, idem enim dico primum et principium.Est autem principium demonstrationis propositio immediata. Immediata autem est qua non est alia prior.Propositio autem est enuntiationis altera pars,unum de uno.Dialecticaquidern est similiter accipiens quamlibet.Demonstrativa autem determinatæ alterum quoniam verum esLEnuntiabio autem contradictionis quaelibet pars. Contradictio autem est oppositio cujus non est medium secundum se.Pars autem contradictionis, quae quidem aliquid de aliquo est, affirmatio est. Quae vero est aliquid ab aliquo,negatio est.lmmediati autem principii syIlogistici,positionem quidem dico,quam non est monstrare,nec necesse est habere docendum aliquid. Quam vero necesse est habere quemlibet doceudulll, dignitatem.","english":"It is also necessary that the causes be both better known and prior. Causes indeed, since we then know, when we recognize the cause; and prior, if indeed they are causes; and better known, not only by understanding in the other way, but by knowing that they are. But prior and better known are said in two ways, for the same thing is not prior by nature and prior to us, nor better known by nature and better known to us.\n\nI call prior and better known to us those things closer to sense. But simply prior and better known are those that are further away. And the furthest things are universals most of all. The nearest, however, are singulars, and these are opposed to one another. From the first is that which is from proper principles, for I call the same thing first and principle. But the principle of demonstration is an immediate proposition. An immediate proposition is one than which there is no other prior. A proposition is one part of an enunciation, one thing about one thing. Dialectic indeed similarly accepts any whatever. Demonstrative [proposition] determines one of the two, that it is true. I call an enunciation any part of a contradiction. A contradiction is an opposition of which there is no middle according to itself. But the part of a contradiction which is something about something is affirmation. That which is something from something is negation. Of an immediate syllogistic principle, I call position indeed that which it is not possible to demonstrate, nor is it necessary for one who is to be taught anything to have it. But that which it is necessary for anyone being taught to have, [I call] an axiom.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":6,"ref":"p6","source":"Sunt enim quædam hujusmodi, hoc enim maxime in hujuscemodi consuevimus nomen dicere. Positionis autem, uæquidem estquamlibetpartium enuntiationis accipiens, ut dico aliquid esse, aut non esse,suppositio est. Quæ vero sine hoc, definitio est, definitio enim positio quaedam est.Ponit enim arithmeticus unitatem,indivisibile esse secundum quantitatem, suppositio autem non est,id enim quod quid est unitas,et esse unitatem, non idem est. Quoniam autem oportet credere, et ecire rem, in hujusmodi habendo syIlogismum quemvocamus demonstrationem.Est autem hic eo quod ea sunt,ex quibus est syllogismus,necesse est non solum praecognoscere prima, aut omnia, aut quamdam, sed et magis. Semper enim propter quod unumquodque est)ilIud magis est, ut propter quod amamus, illud magis amicum est, quare siquidem scimus propter prima et credimus, et illa scimus et credimus magis,quoniam propter illa et posteriora.","english":"For there are certain things of this sort—for it is especially in cases of this kind that we are accustomed to use the name. Of a position, indeed, whatever takes any part of an enunciation, as when I say that something is or is not, is a supposition. But that which is without this is a definition; for a definition is a kind of position. For the arithmetician posits that the unit is indivisible according to quantity, but it is not a supposition; for what the unit is and that the unit is are not the same. But since one must believe and know a thing by having a syllogism of this sort, which we call a demonstration—and this is so because the things from which the syllogism is formed must be not only foreknown, either all or some of them, but also more so. For always that on account of which each thing is, is more so; as that on account of which we love is more dear; wherefore if we know and believe on account of the first things, we also know and believe those more, because on account of them the posterior things are known.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":7,"ref":"p7","source":"Non potest autem credere magis quae scit, quæ non conlingit neque sciens, neque melius dispositus quam si contigerit sciens,accidet autem hoc nisi aliquis præcognoverit propter demonstrationem credentium,magis enim necesse est credere princi piis, aut omnibus, aut quibusdam, quam conclusioni.Debenlem autem haberescientiam per demonstrationem, non solum oportet principia magis cognoscere et magis ipsis credere quam ei quod demonstratur,sed neque aliud ipsi credibilius esse, neque notius oppositis principiis, ex quibus erit syllogismus contrariae deceptionis, si quidem oportet simpliciter scientem, immutabilem esse.\n\nCAPUT III.\n\nQuod MUM omnium sit demonstrativa scientia.\n\nQuibusdam autem igitur propter id quod oportet prima scire, non videtur scientia esse. Quibusdam autem essequidern,omnium tamen demonstrationes esse, quorum neutrum neque verum neque necessarium.","english":"But one who knows cannot believe it more than he does the things he knows—not if he has not encountered it, nor as one knowing, nor as better disposed than if he had encountered it as knowing. But this will happen unless someone has foreknown the things that come to be believed on account of demonstration; for it is more necessary to believe the principles, either all of them or some, than the conclusion. But one who is to have knowledge through demonstration must not only know the principles more and believe them more than the thing demonstrated, but neither must anything else be more credible to him, nor more known than the opposite principles, from which the syllogism of the contrary deception will come—if indeed one who knows simply must be unchangeable.\n\nCHAPTER III.\n\nThat there is no demonstrative science of all things.\n\nTo some, therefore, because it is necessary to know the first principles, it seems that there is no science. To others, indeed, it seems that there is, but that there are demonstrations of all things—neither of which is true or necessary.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":8,"ref":"p8","source":"Ponentes autem non esse omnino scire,id ad infinitum voluntreduci,tanquam non sit utique scientes posteriora propter prjora,quorum non sint prima, recte dicentes.Impossibile enim est infinita pertransire, et si stent et sint principia haec, ignota esse, cum demonstratio non sit ipsorum, quod quidem dicum esse scire soIurn.Si vero noa eat prima scire, neque quae ex eis sunt, est scire, neque simpliciter neque proprie, sed ex conditione, si illa sint. Hi autem de eo quod quidem est scire,sic confitentur, per demonstrationem enim esse solurn,sed omnium esse demonstrationem nihil prohibet,contingit enim circulo fieri demonstrationem, et ex iis qum sunt ad invicem.Nos autemdicemusnequeomnem scientiam demonstrativam esse,3ed immediatorum esse nidemonstrabilem, et quod boc necessarium sit, manifestum est.","english":"But those who maintain that there is no knowledge at all wish this to be reduced to infinity, as if indeed there were no knowledge of posterior things through prior things, of which there are no first principles—and in saying this they speak correctly. For it is impossible to pass through infinite things; and even if they should stop and these should be principles, they are unknown, since there is no demonstration of them—which is precisely what they claim alone to be knowledge. But if there is no knowledge of first principles, neither is there knowledge of the things that follow from them, neither simply nor properly, but only conditionally, if those first principles exist. Yet these men agree about what knowledge is—for they confess that it exists only through demonstration—but nothing prevents there being a demonstration of all things; for it happens that demonstration comes about in a circle, and from things that are related to one another. But we shall say that not every knowledge is demonstrative, but that knowledge of immediate premises is indemonstrable, and that this is necessary is evident.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":9,"ref":"p9","source":"Si enim necesse est quidem scire priora, ex quibus est demonstratio, stant autem aIiquandoimmediata,hæc quidem indemonstrabilia necesse est esse, et hoc igitur sic dicimus, et non solum scientiam, sed et principium scientiae esse quoddam dicirnus,in quantum terminos cognoscimus.Circulo autem quod impossibile sit demonstrare simpliciter manifestum est, si quidem ex prioribus oportet demonstrationem esse,et notioribus,impossibile enim est eadem sibi invicem simul priora,et posteriora esse, nisi altero modo, ut haec quidem ad nos, illa vero simpliciter, quo certe modo inductio facit notum. Si autem sic est, non utique erit simpliciter scire beDe definitum, sed dupliciter. An non simpliciteralterademonstratio fig ex nobis nontioribus? Accidit vero dicentibus circulo demonstrationem esse, non solum quod nunc dictum est, sed nihil aliud dicere quam quoniam hoc est,si hoc est, sic autem facile est demonstrare omnia. Manifestum autem estquod hoc accidit tribus terminis positis,per multos enim, aut per paucos reflectere dicere nihil differt,per paucos autern,aut per duos. Cum enim siC a, siL ex necessitate b, hoc autem cum sit,et c, cum igitur a sit, erit et c; si igitur cum sit a, necesse est esse, hoc autem cum sii, a est. Hoc enim erit circulo:ponatur autem a in quo c,b igitur cum sit, a esse dicere, est et ipsum dicere esse.","english":"For if it is indeed necessary to know the prior things from which demonstration comes, and immediate propositions sometimes stand firm, these must be indemonstrable; and so we say this, and we say that not only knowledge but also a certain principle of knowledge exists, insofar as we cognize terms. But that it is impossible to demonstrate in a circle is plainly evident, since demonstration must proceed from prior and better-known things; for it is impossible for the same things to be simultaneously prior and posterior to themselves, unless in different ways—as some things are prior relative to us, others simply—in which way induction certainly makes something known. But if this is so, then to know a defined thing simply will not be possible, but only in two ways. Or is demonstration not simply from things better known to us? But those who say that demonstration is circular—it happens that they say not only what has just been stated, but nothing other than that this is so if this is so; and in this way it is easy to demonstrate everything. It is evident that this happens when three terms are posited; for to say that one reflects through many or through few makes no difference—through few, however, or through two. For when, if C is, A is by necessity, and this being so, B is, then when A is, C will also be; and so if, when A is, it is necessary that B be, and this being so, A is. This will be the circle: let A be posited as that in which C is; then to say that when B is, A is, is also to say that it itself is.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":10,"ref":"p10","source":"Hoc autem dicere est,quoniam cum sit a est c,c autem ipsi a idem est, quare accidit dicerc,circulo dicentes esse demonstrationem nihil aliud nisi cum sit a est ii, sic autem omnia demonstrare leve est. At vero neque hoc possibile,nisi in iis quae alternatim se consequuntur, sicut sunt propria. Uno quidem igitur posito ostensum est quod nequaquam ne. cesse aliquid esse alterum.Dico autem uno,quoniam nec termino uno, nec positione una posita,cx duabusautempositionibus primis et rninimis,siquidem contingit et syllogizare. Si igitur et a 6, et sequatur, et haec ad invicem, et ipsi a,si quidemigitur contingitexalternismonstrare omnia quæsita in prima figura,sicut ostensum estin iis qui de syIlogismo sunt.Ostensum est autem quod in aliis figuris aut non fit syIlogisrnus,aut non de acceptis qua? alltem non mutuo prædicantur,nequaquam est demonstrare circuIo,quare quoniam pauca quidem huju:modi in demonstrationibus sunt, manifestum est quod vanum quidem et impossibile sit dicere ex iis quæ sunt ad invicem esse demonstrationem,et propter hoc contingere omnium esse demonstrationem.","english":"To say this is to say that when A is, C is; and C is the same as A itself. Hence it happens that those who speak of circular demonstration say nothing other than that when A is, the conclusion follows; and in this way it is easy to demonstrate everything. But this is not possible except in things that follow one another alternately, as do proper attributes. So with one thing posited, it has been shown that it is by no means necessary that something else be. I mean \"one\" not as one term nor as one position posited, but from two primary and minimal positions, if indeed it is possible also to syllogize. If, then, both A and B follow, and these follow one another, and also A itself—if indeed it is possible to demonstrate from things that follow one another all the things sought in the first figure, as has been shown in the works on syllogism. But it has been shown that in the other figures either no syllogism occurs, or not concerning the things accepted; and concerning things that are not predicated of one another, it is by no means possible to demonstrate circularly. Therefore, since few things of this kind are found in demonstrations, it is manifest that it is both vain and impossible to say that demonstration comes from things that follow one another, and that on this account it happens that there is demonstration of all things.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":11,"ref":"p11","source":"CAPUT IV.\n\nQuid de omni, quid per se, et per universale..\n\nQuoniam autem impossibileest aliter se habere id cujus est scientia simpliciter, necessarium utique erit id esse scibile,quod est secundum demonstrativam scientiam. Demonstrativa autem est, quam habemus in habendo demonstrationem ex necessariis itaque syllogismis est dernonstratio.Accipiendum igi.","english":"CHAPTER IV.\n\nWhat \"of every,\" what \"in itself,\" and what \"universally\" mean.\n\nSince it is impossible for that of which there is unqualified knowledge to be otherwise, it will certainly be necessary that what is knowable according to demonstrative knowledge be of this sort. And demonstrative knowledge is that which we possess by having a demonstration; and demonstration is from necessary syllogisms. Therefore it must be grasped.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":12,"ref":"p12","source":"turestex quibus et qualibus demunstrationes sunt, primum quidem determinabimus quid dicimus de omni,et quid perse,etquid uoiversale.De omni quidem,hocdico,quod utique est non quodam quidem, in quodam autem non, neque quod aliquando quidem, aliquando vero non, ut si de omni homine animal, si verum est quidem dicere hominem, verum est et dicere animal, et si nunc alterum,et alterum et si in omni linea punctum, similiter est, signum autem est, namque instantias sic ferimus, ut de omni etiam iWerrogati, aut snquodam non, aut si aliquando non.Per seautem sunt quæcunque sunt in eo quod quid est,ut triangulo inest Iinea,et punctum Iineæ,substantia enim ipsorum ex his est, et in ratione dicenti quid est,insunt.EL qllibuscunque eorum quae insunt ipsis, ipsa in ratione insunt quid est monstrant!, ut rectum inest lineae, et circulare, et par, et impar numero, et primum, et compositum,et isopJeurum,et altera parte longius, et quæ omnibus his insunt, in ratione quid est dicente, illinc quidem linea, hinc vero numerus, similiter et in aliis hujusmodi, unicuique perse esse dico.Quæcunque vero neutraliter ineunl,accidentia sunt,ut musicum,aut album animal.","english":"Next, from what things and of what sort demonstrations are, we shall first determine what we mean by \"of every,\" what by \"in itself,\" and what by \"universally.\" By \"of every\" I mean that which is not in some cases so and in others not, nor at one time so and at another time not; for example, if animal is said of every man, then if it is true to say man, it is also true to say animal, and if the one now, then the other now; and similarly, if point is in every line. A sign of this is that we also bring objections in this way: if it is not so of every case, or if it is not so in some case, or if it is not so at some time. \"In itself,\" however, are all things that are present in the what-it-is; for example, line is present in triangle and point in line, for their substance is from these, and they are present in the account stating what it is. And also all things that are present in the things themselves are present in the account showing what it is; for example, straight is present in line, and circular, and even and odd in number, and first and composite, and equilateral and oblong, and all things that are present in all these—in the account stating what it is, from one side line, from the other number; and similarly in other such cases, I say that each is present in itself. But all things that are present in neither way are accidents; for example, musical or white in animal.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":13,"ref":"p13","source":"Amplius,quod non de subjecto alio quodam dicitur,ut ambulans, aut alburn,cum et alterum quiddam sit ambulans et album.Substantia autem et quæcunque boc aliquid significant, non alterum aliquid sunt quam quod quidem sunt; quæ quidem igitur non de subjecto alio sunt,per se dico, quae vero de subjecto, accidentia. Item alio modo quod quidem propter ipsum inest inicuique, per se dico, quod vero non propter ipsum, accidens est, ut si ambulans coruscavit, accidens est, non enim propter id quod ambulavit, coruscavit, sed accidens dicimus hoc. Si vero propter ipsum, per se, ut si aliquid interfectum interiit, secundum interfectionem, quoniam propter id quod interfectum est interiit, sed non quod accidat interfectum interire.Quæ ergo dicunturin simpliciter scibilibus perse sic sunt,sicut esse prædlCatis,aut inesse, propter ipsaque suni. et ex necessitate, non enim contingat non inesse, aut simpliciter, aut opposita, ut lineae aut rectum, aut obliquum, et numero aut par aut impar, est enim contrariorum, aut privatio, aut contradictio in eodem genere,ut par aut impar III numeris secundum quod consequitur; quare si necesse est affirmare, aut negare, necesse est et quæ sunt per se,inesse. De omni quidem, et per se, sed determinatum ait huc modo. U niversaIe autem dico,quod cum do omni sit,el per se est,et secundum quod ipsum est.","english":"Further, that which is not said of some other subject, as walking or white, since walking and white are also something else. But substance and whatever things signify this particular thing are not something else besides what they are; those things, therefore, which are not of another subject, I call per se, while those which are of a subject, accidents. Again, in another way, that which belongs to each thing on account of itself, I call per se, while that which is not on account of itself is an accident; for example, if someone walking flashed lightning, it is an accident, for it did not flash lightning on account of the fact that he walked, but we call this an accident. If, however, it is on account of itself, it is per se, as if something killed died by killing, according to the killing, because it died on account of the fact that it was killed, but not because it happened that the killed thing died. Therefore, the things that are said in the case of things knowable simply are per se in this way, as either to be predicates or to be present, and they are on account of themselves and from necessity; for it does not happen that they are not present, either simply or their opposites, as for a line either straight or oblique, and for a number either even or odd; for of contraries, either privation or contradiction is in the same genus, as even or odd in numbers according as it follows; wherefore if it is necessary to affirm or deny, it is necessary also that the things which are per se be present. Concerning \"of every,\" then, and \"per se,\" he has spoken thus in a determinate way. But I call \"universal\" that which, while it is of every and per se, is also according as it is itself.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":14,"ref":"p14","source":"Manifestum igitur est quod quæcunque su nt universalia ex necessitate insunt rebus.Per se autem et secundum quod ipsum est,ut per se lineæ inest punctum,et I rectitudo,et namque[inest enim] secundum quod linea est,et triangulo secundum quod triangulus est insunt duo recti, etenim per se triangulus duobus rectis aequalis est.UniversaIe autem est tunc,cum in quolibet, et primo monstretur, ut duos rectos habere, neque cuilibet figuræ inest universaliter, et tamen est monstrare de figura quod duos rectos habet,sed non de figura qualibet, nec utitur qualibet figura monstrans,quadrangulus enim figura quidem est, non habet autem duobus rectis æquales,sed isosceles habet quidem quodlibet duobus rectis æquales, sed non primurn,sed triangulus prius. Quodcunque igitur pnmum monstratur duos habere rectos,aut quodcunque aliud, huic primo inest universale, et demonstratio per se hujus universalis est, aliorum autem quodammodo, et uon per se,neque isoscelis est universaliter, sed in plus.","english":"It is manifest, therefore, that whatever things are universal belong to things of necessity. But [this is so] per se and according as it is itself, as a point belongs per se to a line, and straightness, for it belongs according as it is a line; and two right angles belong to a triangle according as it is a triangle, for per se a triangle is equal to two right angles. But it is universal then, when it is shown in every case and primarily, as to have two right angles; for it does not belong universally to any figure whatsoever, and yet it is possible to show of a figure that it has two right angles, but not of any figure whatsoever, nor does the one demonstrating use any figure whatsoever; for a quadrilateral is indeed a figure, but it does not have [angles] equal to two right angles; but an isosceles does indeed have [angles] equal to two right angles, but not primarily, but the triangle is prior. Whatever, therefore, is shown primarily to have two right angles, or whatever else, to this primarily the universal belongs, and the demonstration is per se of this universal; but of others in a certain way, and not per se, nor is it universal of the isosceles, but [extends] to more.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[{"kind":"lacuna","severity":"caution","text":"The source is fragmentary here: the edition marks a break or an editorial bracket, and the English carries across it. Treat the bridge as supplied, not translated."}]},{"i":15,"ref":"p15","source":"CAPUT V.\n\nQuo pacta contingat allucinotio circa universale primwn.\n\nOportet autem non latere quoniam multoties contingit peccare, et non esse quod demonstratur primum universale, secundum quod videtur demonstrari universale primum; oberramus autemhac; deceptione,cum aut aliud nihil sit accipere a superiori extra singulare, vel singularia. aut si sit quidem, sed innominatum sit in differentibus specie reo bus, aut contingat esse sicut in parte, totum in quo mons:ratar: iis enim quae sunt in parte,inest quidem demonstratio, et erit de omni, sed tamen non hujus erit primi universalis demonstratio,riico autem hujus primi secundum quod bujusdemonstrationem, cum sit primi universalis. Si ergo aliquis monstrabit quidem quod recte non intercidant,videbitur utique hujus esse demonstratio, propter id quod in omnibus est rectis.Non autem est, nisi quidem (quoniam sic aequales smt) fiat hoc, sed secundum quod quomodolibet æquales. Et sitriangulus non esset alius quam isosceles, secundum quod isosceles videretur utique inesse.","english":"CHAPTER V.\n\nHow error concerning the first universal comes about.\n\nIt must not escape notice that error often occurs, and that what is demonstrated is not the first universal, in the sense in which it seems to be demonstrated as the first universal. We go astray by this deception when either there is nothing else to take from a higher [principle] beyond the singular, or the singulars; or if there is indeed something, it is unnamed in things differing in species; or it happens to be as in a part, the whole in which it is demonstrated. For in things that are in a part, demonstration does belong, and it will be of every [instance], but nevertheless it will not be the demonstration of this first universal, but of this first [universal] according as [it is] of this [subject], since it is of the first universal. If, therefore, someone demonstrates that right [angles] do not intersect, it will seem, to be sure, that this is a demonstration of this [figure], on account of what is in all right [angles]. But it is not, unless it be shown (because they are equal in this way), but according as they are equal in any way whatever. And if the triangle were not other than the isosceles, according as it is isosceles, it would seem to belong.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":16,"ref":"p16","source":"Et proportionale quod cummunicabiIiter est, secundum quod numeri sunt, et secundum quod Jineæ, etsecundum quod solida, et secundum quod tempora sunt, quemadrnodum demonstratum est aliquando seorsum, contingens autem de omnibus una demonstratione monstrari aed propter id quod non est nominatum aliquid secundum quod hæc omnia unum sunt, numeri, longitudines, tempora, solida, et speciedifferentia, seorsum ab invicem accepta sunt, nunc autem universale monstratur. Non enim secundum quodlineæ sunt, aut secundum quod nurneri, inerat, sed secundum quod hoc est, quod universale supponunt esse. Propter bocnec si aliquis monstret unumquemque triangulum demonstratione aut una, aut altera, quod duos rectos babet unusquisque, isopleuron seorsum, et scalenon, et isosceles, nondum cognovit triangulum quod duos rectos habet, nisi sophistico modo, neque universalitertrianguIum, ne quidem si nullus est praeter haec triangulus alter, non enim secundum quod triangulus est, cognuvit, neque omnem triangulum, sed secundum numerum, secundum speciem autem non omnem, et si nullus est quem non novit. Quando ergo non novit universaliter, et quando novit simpliciter, manifestum est, quoniam si idem erit triangu esse, et isopleuro, aut unicuique, aut omnibus, si vero non idem, sed alterum, est autem secundum quod est triangulus, non novit.","english":"And the proportional, which is communicable, both insofar as they are numbers and insofar as they are lines and insofar as they are solids and insofar as they are times, as has been demonstrated at some time separately, it happens that it is shown of all by one demonstration, and for this reason, because something is not named insofar as all these are one: numbers, lengths, times, solids; and the specific difference is taken separately from one another, but now it is shown universally. For it was not present insofar as they are lines, nor insofar as they are numbers, but insofar as this is what they suppose to be universal. For this reason, even if someone demonstrates each triangle by one demonstration or another, that each has two right angles—the equilateral separately, and the scalene, and the isosceles—he does not yet know that the triangle has two right angles, except in a sophistical way, nor universally that it is a triangle, not even if there is no other triangle besides these; for he did not know it insofar as it is a triangle, nor every triangle, but according to number, not according to species every one, even if there is none that he does not know. When, therefore, he does not know universally, and when he knows simply, it is clear, since if being a triangle and being equilateral will be the same, either for each one or for all; but if not the same, but other, and it is insofar as it is a triangle, he does not know.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":17,"ref":"p17","source":"Utrum autem secundum quod est trianguIus, aut secundum quod est isosceles insit, et quando de hoc est primum et universale, cujus est demonstrat:o,manifestum est,quandoremotisinsit primum ut isosceli aeneo triangulo insunt duo recti, sed xneum esse remoto et isosceIe,sed non figura aut termino,sed non primis.Quo igitur primo? si itaque triangule est,et secundum hoc inest,et aliis,et hujus universalis est demonstratio.\n\nCAPUT VI.\n\nDemonstrationem ex necessariis et propositionibus per se esse.\n\nSi igitnr est demonstrativa scientia, et ex necessarus principiis,quod enim scitur non potest se aliter habere.Quæ autem per se sunt necessario insunt rehus,hæc enim insunt in eo quod quid est,quibus. dam autem bæc insunt in eo quod quid est,prædicantibus de ipsis,quorurn alterum oppositorum necesse est inesse.Manifestum est igitur quodexhu. jusmodi quibusdam utique fit demonstrativussylIogisrnus,omne enim aut sic inest,aut secundum accidens, accidentia autem necessaria non sunt. Aut, igitur sic dicendum,aut principium ponentibus quod demonstratio necessaria sit,et si demonstretur non aliter habere posse,ex necessariis igituroport.et esse syllogismum, ex veris quidem est, et non demonstrantem syIJogizare,ex necessariis autem non est, sed aut demonstrantem hoc enim propriumjamdeTQonstrationis est.","english":"But whether it belongs insofar as it is a triangle or insofar as it is isosceles, and when this is first and universal, of which it is the demonstration—this is clear. For when it belongs first with the subject removed, as two right angles belong to a bronze isosceles triangle, but bronze being removed and isosceles, but not figure or boundary, but not to the first things. In what, then, is it first? If therefore it is a triangle, and insofar as this it belongs, and to others, and of this there is demonstration of the universal.\n\nCHAPTER VI.\n\nThat demonstration is from necessary things and from propositions per se.\n\nIf, therefore, demonstrative knowledge exists, and from necessary principles—for what is known cannot be otherwise. But the things that are per se belong necessarily to things; for these belong in the what-it-is, to certain things, but these belong in the what-it-is, being predicated of them, of which one of two opposites must necessarily belong. It is clear, therefore, that from such things a demonstrative syllogism is made; for everything either belongs in this way or according to accident, but accidents are not necessary. Either, therefore, it must be said thus, or, for those who lay down as a principle that demonstration is necessary, and if it is demonstrated, that it cannot be otherwise, it must therefore be from necessary things. And from true things indeed it is possible to syllogize without demonstrating, but from necessary things it is not possible, except by demonstrating; for this is already proper to demonstration.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":18,"ref":"p18","source":"Signum autem est quod demonstratio ex necessariis sit,quoniam et instantias sic ferimus ad opinantes dea:onstrare.Quoniam non sitnecesse si opinamur,automnino contingere aliter,aut orationis causa.Manifestum autem exiis est,et quoniam stulti qui opinati sunt accipere bene principia,si probabilissit propositio,et vera,ut soph istae quoniam scire, scientiam est habere, non enim quod probabile est aut non, principium est,sed primum in genere circa quoemonstratur, et verum non omne, proprium. Quod autem ex necesssriis oportet esse sylIogismum,manifestum ex his est, si enim non est habens rationem propter quid existente demonstratione,non est sciens,sit autem utique ut quod a,de ex necessitate esse,b autem medium per quod demonstratum est non ex necessitate, non scivit propter quod,non enim est hoc propter medium.boc quidem contingit non inesse,concIusio autem necessaria. Amplius si aliquis nescit,nunc babens rationem,etsaIvatus est, et salva re,nec oblitus est neque prius scivit, corrumpetur autem utiquo medium nisi sit necessarium. Quare habebit quidem rationem saIvus,salva re,nescit autem,nec ergo prius scivit,si vero non corruptum est,contingit autem corrumpi quod accidit,uti' que erit possibile,et contingens,sed est impossibile.","english":"A sign that demonstration proceeds from necessary things is that we also press objections in this way against those who think they have demonstrated. For we say that it is not necessary if we merely opine, nor does it altogether happen that it could be otherwise, nor is it for the sake of argument. It is also clear from these things that those who have supposed they take up principles well are foolish, if the proposition is merely plausible and true—as the sophists claim that to know is to have knowledge; for the principle is not what is plausible or not, but the first in the genus about which the demonstration is made, and not every truth is proper. That the syllogism must be from necessary things is clear from these considerations: for if one does not have the reason why, when the demonstration exists, he does not know; but let it be supposed that A belongs of necessity to that which is demonstrated, while B, the middle term through which it was demonstrated, is not necessary—then he has not known why, for this is not the case because of the middle term. For it is possible for the middle term not to belong, while the conclusion is necessary. Further, if someone does not know, though he now has the reason, and if he is preserved and the matter is preserved, and he has not forgotten, nor did he know before, then the middle term will be corrupted unless it is necessary. Therefore he will indeed have the reason while preserved and the matter preserved, yet he does not know; nor, then, did he know before. But if the middle term is not corrupted, yet it is possible for it to be corrupted, then what has happened will be possible and contingent—but this is impossible.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":19,"ref":"p19","source":"sic se habentem scire.Cum igitur conclusio quidem ex necessitate est, nihil prohibet medium non esse necessarium,per quod monstrata est,est enim necessariumet ex non necessariis syIlogizare,sit et veru ex non veris.Cum autem medium ex necessitate est, et conclusio est ex necessitate,sicut ex veris veru'1l est sem;:er.Sit enim a de ex necessitate,et boc de c,necesse est ergo et a inesse,sed cum non ex necessitate sit conclusio, neque medium necessarium esse possibile est,sil enim a in non ex necessitate inesse,in autem a,et hoc in ex necessitate erit, sed non esse supponebatur. Quoniam igitnr si scit demonstrative,oportet ex necessitate in esse, manifestum quoniam et per medium necessarium oportet babere demonstrationem,aut non sciet,neque enim propter quid, neque quia, quare necesse est illud esse,sed aut opinabitur,nesciens, si opinabitur non necessariam tanquam necessarium, aut neque opinabitur similiter, sive quoniam sciat per media, sive propter quid, et per immediaLa. Acci.","english":"Things that are so disposed, to know. Since, then, the conclusion indeed is from necessity, nothing prevents the middle term, through which it has been shown, from not being necessary; for it is possible to syllogize what is necessary even from non-necessary things, and what is true from non-true things. But when the middle term is from necessity, the conclusion also is from necessity, just as from true things a true conclusion always follows. For let A be present from necessity, and this be present in C; therefore it is necessary that A also be present. But when the conclusion is not from necessity, neither is it possible for the middle term to be necessary. For if A is present in B not from necessity, but B is present in C, and this from necessity, then A will also be present from necessity; but it was supposed not to be. Since, therefore, if one knows demonstratively, it is necessary that the thing be present from necessity, it is clear that one must also have the demonstration through a necessary middle term, or else one will not know—for neither the reason why nor the fact that will be [known], whereby it is necessary that that be. But either one will opine, not knowing—if one opines the non-necessary as necessary—or one will not even opine similarly, whether because one knows through middle terms, or the reason why, and through immediate [premises]. Take.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":20,"ref":"p20","source":"dentium autem non per se quo modo definitum est, per se quidem non est scientia demonstrativa, non enim est ex necessitate monstrare concIusionem,accidens enim contingit non esse,de tali autem dico accidente.Et tamen ambiget fortasse aIiquis,cujus causa haec oportet interrogare de his,si non necesse est conclusionem esse, nihil enim differt si aliquis interrogatus contingentia, postea dicat conclusionem oportet autem interrogare non tanquam necessarium esse propter interrogata,sed quod dicere necesse est illa dicenti,et vere dicere si verae sunt qum insunt.\n\nCAPUT VII.\n\nDemonstrationes ex iis quæ per se sunt et ex perpetuis esse.\n\nQuoniam autem ex necessitate sunt circa unumquodque genus quaecunque per se sunt,et secundum quod unum quodque estmanifestum estquoniamde iis quEe sunt per se,scientificæ demonstrationes,et ex talibus sunt.Accidentiaenimnon necessaria sunt.Quare non necessarium conclusionem scire propter quid sit, nequesi sempersint,non per se autem,utsunt per signa syllogismi,boc enim per se,oon per se sciet, neque propter quod.Propter quid autem scire et per causam scire.Propter hoc ipsum ergo oportet et tertio rnedium,et primum medio inesse. Non ergo est ex alio genere descendentem demonstrare, ut geometricum in arithmeticam.","english":"Of things that do not exist per se in the way defined, there is no demonstrative knowledge; for it is not possible to show the conclusion from necessity, since an accident can fail to be—and I mean such an accident. And yet someone might perhaps ask why, in the case of these things, one must put questions about them, if the conclusion is not necessary; for it makes no difference whether someone, when asked about contingent matters, afterwards states the conclusion. But one must ask questions not as though the conclusion were necessary because of the things asked, but because it is necessary for the one who says those things to say this too, and to speak truly if the things that are present are true.\n\nCHAPTER VII\n\nThat demonstrations are from things that are per se and from eternal things.\n\nSince, then, whatever things are per se are necessary in each genus, and it is evident inasmuch as each thing is, it is clear that demonstrations of knowledge concern things that are per se, and are from such things. For accidents are not necessary. Wherefore it is not necessary to know the conclusion and why it is, nor, even if they are always, if they are not per se—as are the conclusions of syllogisms through signs; for one will know this per se, not per se, nor the reason why. But to know the reason why is to know through the cause. For this very reason, then, the middle term must also be of this sort, and the first term must be present in the middle. Therefore it is not possible to demonstrate by descending from another genus, as a geometer does into arithmetic.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":21,"ref":"p21","source":"Tria euim sunt in demonstrationibus: unum quidem quæ demonstratur concIusio,hoc autem est quod inest alicui generi per se; unum autem dignitates; dignitates autem sunt ex quibus est demonstratio; tertium autem genus subjectum,cujus passiones,et per se accidentiaostendit demonstratio.Ex quibus igitur demonstratio fit,contingileadem esse. Quorum autem genus alterum est, sicut arithmeticæ et geomelriæ, non est aritbmeticam demonstrationem convenire in magnitudinibus accidentia,nisi magnitudinesnumeri sint(hoc autem quo modo contingitinquibusdam posterius dicetur), sed arithmetica demonstratio sem per habet genus circa quod fit demonstratio,et aliae sirniliter.Quare aut simpliciter necesse est idem esse genus,aut aliquo mouo,si debet demonstratio descendere, aliter autem quoniam impossibile,manifestum est,ex eodem enim genere necesse est ultima, et media esse, si namque non sunt per se,accidentia erunt.","english":"For there are three things in demonstrations: one is the conclusion that is demonstrated, and this is what belongs per se to some genus; another is the dignities, and the dignities are those from which the demonstration is made; and the third is the subject genus, whose passions and per se accidents the demonstration shows. Therefore, the things from which the demonstration is made can be the same. But of those whose genus is different, as of arithmetic and geometry, it is not possible for an arithmetical demonstration to apply to the accidents of magnitudes, unless magnitudes are numbers (and in what way this happens in certain cases will be said later), but an arithmetical demonstration always has a genus about which the demonstration is made, and likewise the others. Wherefore either it is simply necessary that the genus be the same, or in some way, if the demonstration is to descend; but otherwise, since it is impossible, it is evident; for the last and the middle terms must be from the same genus, for if they are not per se, they will be accidents.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":22,"ref":"p22","source":"Propter hoc geometriae non est demonstrare quod contrariorum una sit scientia, sed neque quod duo cubi sit unus cubus, neque alterius scientiæ, quod alterius est, sed aut quaecunque sic se habent ad invicem, ut quod alterum sit sub altero,llt perspectivo ad geometriam,et consonantia ad aritmethicam, neque si aliquid inest lineis non secundum quod lineae sunt, et non in quantum ex propriis principiis,ut si puIcherrima linearum recta est,aut si contrario modo se habeat circuIaris,non enim secundum quod proprium ipsarum genusest,sed in quantum commune quoddam.Manifestum autem est,et si sint proposi-. tiones universales ex quibus est syllogismus,quod necesse est etconclusionem perpetuam esse hujusmodi demonstrationis, et simpliciter (ut est dicere demonstrationis. Non est ergo demonstratio corruptibilium,neque scientia simpliciter, sed sic est sicut secundum accidens,et non universalis ipsius est, sed aliquando et sic; cum autem ita sit, necesse est alteram non universalem esse propositio. nem et corruptibilem; corruptibilem quidem,quoniam et conclusio est; non universalem autem, quod hoc quidem erit, hoc autem non erit ex quibus est, quare non est syllogizare universaliter, sed quoniam nunc est. Similiter se habet de definitione, quoniam quidem est definitio aut principium demonstrationis, aut demonstratio positione differens, aut conclusio quaedam demonstrationis.","english":"For this reason it is not for geometry to demonstrate that there is one science of contraries, nor that two cubes are one cube, nor is it for one science to demonstrate what belongs to another science, but only whatever things are related to each other in such a way that one falls under the other—as perspective falls under geometry, and harmony under arithmetic—nor if something belongs to lines not insofar as they are lines, and not insofar as it follows from their proper principles, as for instance that the straight line is the most beautiful of lines, or that the circular line is disposed in the contrary way; for this is not insofar as it is their proper genus, but insofar as it is something common. It is also evident, even if the propositions from which the syllogism proceeds are universal, that the conclusion of such a demonstration must also be perpetual, and, simply speaking, of a demonstration. Therefore there is no demonstration of corruptible things, nor science simply speaking, but it is so only in the manner of what is per accidens, and it is not universal of it, but sometimes even so; but when this is the case, one of the propositions must be non-universal and corruptible—corruptible indeed, since the conclusion also is; non-universal, because one part of it will be and another will not be, from which it proceeds; wherefore it is not possible to syllogize universally, but only that it is now. The same holds concerning definition, since a definition is either a principle of demonstration, or a demonstration differing in position, or a certain conclusion of a demonstration.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":23,"ref":"p23","source":"Eorum autem quae saepe fiunt, sunt demonstrationes et scientiae (ut luna? defeotus), manifestum est quoniam secundum quod hujusmodi sunt, semper sunt, in quantum autem non semper secundum partem sunt. Sicut autem defectus est, similiter et in aliis.\n\nQuuniam autem manifestum est quod demonstrare unumquodque non est, sed aut ex unoquoque principiorum si i'i quod demonstratursitsecundum quod estiIlud, non autern est scire hoc quidem, si ex veris et indernonstralibus monstretur, et immed iatis. Est enim sic monstraresicutBryson tetragonismon: secundum commune enim monstrant rationes hujusmodi quod etalteri inest, unde et in aliis co-iveniunt hæ rationes non congeneis. Non itaque secundum il!-ud scit, sed secundum accidens, non enim convenit demonstratio et in aliud genus. Unumquodque autem scimus non secundum accidens, cum secundum illud cognoscimus, secundum quod est ex principiis illius in quantum illud est, utduobusrectisæquales habere, cui inest per se quod dictum est, ex principiis illius. Quare si per se et illud inest cui inest, necesse est medium in eadem proximitate esse; si vero non sit, sed sicutharmonica perarithmeticam hujusmodi autem dernonstraturquidem similiter, se ditTerunt. Nam ipsum quidem quia alterius quidem I scientiæ est, subjectum enim genusalterum est, sed propter quid, est superioris, cujus per se passiones sunt.","english":"Of things that happen often, there are demonstrations and sciences (for example, the eclipse of the moon); it is clear that insofar as they are of this sort they are always so, but insofar as they are not always so, they are so in part. And as the eclipse is, so also in other cases.\n\nSince it is clear that to demonstrate each thing is not [to demonstrate it] from just any principles, but from those proper to it, if what is demonstrated is [demonstrated] insofar as it is that thing—for it is not to know this, if it is demonstrated from true and immediate principles. For to demonstrate in this way is like Bryson's squaring of the circle: such arguments demonstrate by a common principle what belongs also to another thing, and hence these arguments apply also to other things not of the same kind. Therefore one does not know it according to that, but according to accident; for demonstration does not apply to another genus. But we know each thing not according to accident when we know it according to that by which it is from the principles of that thing insofar as it is that thing—as, for example, to have angles equal to two right angles, that to which this belongs per se, [is known] from the principles of that thing. Therefore if it belongs per se and to that to which it belongs, the middle term must be in the same proximity; but if it is not so, but as harmonic [proofs are] through arithmetic, such a thing is indeed demonstrated similarly, but they differ. For the fact itself, that it belongs to another science, [is clear] because the subject is another genus; but the reason why belongs to the superior science, whose per se properties they are.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":24,"ref":"p24","source":"Quare ex his manif'estum est quod non sit demonstrare unumquodque simpliciter, alilerquarn ex propriis uniuscujusque principiis, sed horum principia habent commune. Si autem manifestum hoc, manifestum et quoniam non est uniuscujusque propria principiademonstrare. Eruntenim ilia omnium principia, et scientia eorum domina omnium, et namque scit magis ex sperioribus causis sciens, ex prioribus enimscit, cum non excausatis sciat causis quare si magis scit, et maxime et scientia illa erit et magis, et maxime. Sed demonstratio non covenit in aliud genus aliter quam, ut dictum est, geornetricæ in machinativas,aut perspectivas,et arithmeticae in harmonicas. Difficile autem est nosse si ex uniuscujusque principiis scimus, aut non, quod quidem est scire, opinamur autem hoc, si babemus ex veris aliquibus syllogismum et primis scire; sed hoc non est, sed congenea oportet esse primis.","english":"Therefore from these things it is manifest that it is not possible to demonstrate each thing simply, otherwise than from the principles proper to each thing, but the principles of these have something in common. But if this is manifest, it is also manifest that it is not possible to demonstrate the proper principles of each thing. For those will be the principles of all things, and the science of them will be mistress of all things; for the one who knows knows more from higher causes, for he knows from prior causes, since he knows the causes of the things caused. Wherefore if he knows more, that science will also be the highest and most of all. But demonstration does not apply to another genus otherwise than, as has been said, geometrical demonstrations apply to mechanical arts, or optical ones, and arithmetical ones to harmonics. But it is difficult to know whether we know from the principles proper to each thing or not—which indeed is to know—but we opine this, if we have a syllogism from certain true and primary things, we think we know; but this is not so, but the principles must be of the same genus.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":25,"ref":"p25","source":"CAPUT VIII.\n\nDe principiis tum vagis ac addictis.communibusque,tum propriis\n\nDico autem principia in unoquoque genere, illa quae quoniam sint non contingit demonstrare.Quid quidem igitur significent et prima et quæ sunt ex primis, accipiendum; quod [F. quoa.d] autem principia, quidem [an. quædam?] necesse est accipere, alia vero demonstrare: ut qu unitas, aut quid rectum, et quid triangulus, esse tem unitatem accipere, et magnitudinem, altera vero monstrare. Sunt autem quibus utunturin demonstrativis scientiis, alia quidem propria uniuscujusque scientiæ, alia vero communis. Communia vero secundum analogiam, quoniam utile est quantumcunque est in eo (quod est sub scientia) genere. Propria principia quidem, ut lineam esse ejusmodi, et rectum. Communia autem, ut, æqualia ab æqualibussi auferas, quod aequalia reliqua sunt. Sufficientes autem unumquodque horum, quantumcunque in genere est. Idem enim faciet, etsi non de omnibus acciiat, sed in magnitudinibus solum, aritmeLicæ autem in numeris. Sunt autem propria quidem, et quae accipiuntur esse, circa.quæ scientia speculatur, quae sunt per se,utarithmetica unitates, geometria autem signaetlineaa, hæc enim recipiunt, esse ethoc esse, horum autem passiones per se.","english":"CHAPTER VIII.\n\nOn principles both indeterminate and determinate, and common and proper.\n\nI call principles in each genus those things which, since they are, it is not possible to demonstrate. What indeed they signify, both the primary things and those which are from the primary things, must be assumed; but that some are principles, it is necessary to assume, while others are to be demonstrated: for example, what unity is, or what a straight line is, and what a triangle is—that unity exists must be assumed, and magnitude, but the others must be shown. Now of the things which they use in demonstrative sciences, some are proper to each science, others are common. But common things are so according to analogy, since it is useful as much as is in that genus which falls under the science. Proper principles are, for example, that a line is of such a sort, and a straight line. Common ones are, for example, that if you take equals from equals, the remainders are equal. And each of these is sufficient, as much as is in the genus. For it will do the same, even if one does not apply it to all things, but only in magnitudes, and in arithmetic in numbers. But proper principles are also those which are assumed to be, about which the science speculates, which are per se, as arithmetic [assumes] units, but geometry [assumes] points and lines; for these receive that they are and that this is so, but their passions are per se.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[{"kind":"lacuna","severity":"caution","text":"The source is fragmentary here: the edition marks a break or an editorial bracket, and the English carries across it. Treat the bridge as supplied, not translated."}]},{"i":26,"ref":"p26","source":"Quid quidem unaquæquesignificet,accipiunt, utarithmetica quidem, quid par, aut impar, aut quadratus, aut cubus,geometria vero quid irrationale, aut inflecti, aut concurrere, quod autem sint, demonstrant per cornmunia, et ex iisque demonstrantur. etastrologia similiter. Omnis enim demonstrativa scientia circa tria est, quaecunque esse ponuntur. Hæc autem sunt genus, cujus per se passionum speculativa est, et quae communesdicuntur dignitates, ex quibus primis demonstrant, et tertium passiones, quarum quid sign ificet unaquaque accipit. Quasdam tamen scientias nihil prohibet quædam eorum despicere: ut genus non supponere esse, si sit manifestum quoniam est, non enim similiter manifestum est quoniam numerus sit, et quod calidum; et frigidum, et passiones non est recipere quid significent, si sint manifestæ, sicut neque communia non recipit qui significent quod est æqualia ab a'qualibus demere quoniam notum est. Sed nihil minus natura tria haec sint, circa quod demonstrat, et quæ demonstrat, et ex quibus Non est suppositio, neque petitio, quod necesse et propter seipsum esse, et videri necesse est: non enim ad exterius orationem demonstratio, sed ad eam quae est in anima, quoniam neque syllogismus. Semper enim est instare ad exterius orationem, sed ad interius orationem non smper.","english":"What each term signifies, they take as given—as arithmetic takes what is even, odd, square, or cube, and geometry what is irrational, or inflected, or converging—but that they exist, they demonstrate through common principles, and from these they are demonstrated. And astrology likewise. For every demonstrative science is concerned with three things, whatever are posited to exist. These are: the genus, whose per se affections it contemplates; the common principles, so called, from which it demonstrates as from primary truths; and third, the affections, of which it takes what each one signifies. Nevertheless, nothing prevents some sciences from overlooking some of these: for instance, not to suppose the genus to exist, if it is manifest that it exists—for it is not equally manifest that number exists and that the hot and the cold exist—and not to receive what the affections signify, if they are manifest, just as one does not receive what the common principles signify, since it is known that equals subtracted from equals leave equals. But none the less, by nature these three are what it demonstrates about, what it demonstrates, and from what. It is not a supposition, nor a petition, that which is necessary both to be and to be seen for its own sake; for demonstration is not directed to external speech, but to that which is in the soul, since neither is syllogism. For one can always object to external speech, but not always to internal speech.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":27,"ref":"p27","source":"Quæcunque ergo quidem demonstrabilia esseaccipit ipse non demonstrans, æcsquem quæ videntur accipiat, dicenti suppositio, et non est simpliciter suppositio, sed illum solum, si vero neque unius opinionis, aut contraria est, accipiat, idem petit. Et in hoc differt suppositio, et petitio, est enim petitio in contrarium discentis opinioni, aut quodcunque aliquisdemonstrabilecum sit,accipiat,et utatur non demonstrans.Terminiigitur non sunt suppositiones, nibil enim esse aut nos esse dicunt, sed in propositionibus sunt suppositiones. Terminos solumintelligere oportet, hoc autem non est suppositio, nisi et audire aliquis suppositionem esse dicat, sed quibuscunque existentibus in eo quod illa sunt, fit conclusio. Neque autern geometra falsa supponit, sicut quidam affirmant dicentes quod oportet non falso ut geometram, mentiri autem dicentem lineam esse unius pedis, quas non est unius pedis aut rectam lineam, nou rectam existentem, sed geometia nihil secundum hanc lineam concludit, quam ipse posuit, sed qua? per hanc ostenduntur. Amplius. Petitio et suppositio omnis, aut sicut torum est, aut in parte, termini autem neutrum horum. Species quidem igttur esse, aut unum aliquid extra multa non necesse est esse, si demonstratio erit, esse tamen urum de multis verum dicere, necesse est. Non enim erit universale nisi hoc sit.","english":"Whatever things, then, he accepts as demonstrable while not himself demonstrating them—just as he accepts things that appear to be the case—the one who says this calls it a supposition, and it is not a supposition in the unqualified sense, but only in that particular respect; but if he accepts something that is not of one opinion, or is contrary, he begs the same thing. And in this a supposition differs from a begging of the question, for a begging of the question is against the opinion of the learner, or whatever is demonstrable, when someone accepts it and uses it without demonstrating it. Terms, then, are not suppositions, for they do not say that anything is or that we are, but suppositions are in propositions. It is necessary only to understand the terms, and this is not a supposition—unless someone says that even to hear a supposition is a supposition—but when those things exist which are in the terms, the conclusion follows. Nor does the geometer suppose false things, as some affirm, saying that one must not use falsehood as a geometer, but lie when saying that a line is one foot which is not one foot, or that a line is straight which is not straight; for the geometer concludes nothing according to this line which he himself has posited, but according to those things which are shown through it. Furthermore, every begging of the question and supposition is either as a whole or in part, but terms are neither of these. That the species exist, or that there is some one thing besides many, it is not necessary that it be, if there is to be demonstration; but that one thing be truly said of many, it is necessary. For there will not be a universal unless this is so.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":28,"ref":"p28","source":"Si vero universale non sit, medium non erit, quare neque demonstratio, oportet itaque aliquid unum, et idem de pluribus esse non æquivocum. Non contingere autem idem simul affirmare, et negare, neque una recipit dernonstratio, sed aut si indigeat monstrare condusionem sic, ostenditur autem accipientibus primum de medio quod verum, negare autem non verum, medium autem nihil differt esse, et non est accipere, similiter autem et tertium, si enim assignetur de aliquo hominem, verum est dicere, et si non hominem, verum, sed si solum bominem animal esse, omne, non animal autem non. Erit enim verum dicere Calliam, sive non Calliam esse animal, non animal autem, non. Causa autem est quod primum non solum de medio dicitur,sed de alio, propter id quod de pluribus, quare neque si medium et idem est, et non idem, ad conclusionem nihil differt. Commune autem affirmare, aut negare, quæ est ad impossibile demonstratio, accipit, et boc nequesemper,universaliter,sed quantum sufficiens est sufficiensautemest ingenere:dicoautemin genrre, ut circa quod genus demonstrationes fert, sicut dictum est prius. Communicantautem omnes scien. tis secundum communia. Communia autem dico, quibus utuntur tanquam ex eis demonstrantes, sed non ex quibus demonstrant, neque quod demonstraut. Et dialectica.","english":"If, however, it is not universal, there will be no middle term, and therefore no demonstration either. Hence there must be something one and the same predicated of many things, and not equivocally. But that the same thing cannot be affirmed and denied at the same time, no single demonstration undertakes this, unless it needs to show the conclusion in this way; and it is shown to those who first accept something true of the middle term, but deny what is not true. For it makes no difference whether the middle term is something or is not, and similarly with the third term. For if it is assigned of something that it is a man, it is true to say so; and if it is not a man, it is true; but if it is assigned that man alone is animal, then every man is animal, but not every non-animal is not animal. For it will be true to say of Callias, whether he is or is not a man, that he is an animal, but not that he is a non-animal. The reason is that the first term is predicated not only of the middle term but also of another, because it is predicated of many things; and therefore, even if the middle term is the same and not the same, it makes no difference to the conclusion. But that it is common to affirm or deny, the demonstration that leads to the impossible accepts, and this not always universally, but as much as is sufficient; and it is sufficient in the genus. I mean in the genus, as it were, that about which the demonstrations are concerned, as was said earlier. But all the sciences share in common principles. By common I mean those which they use as demonstrating from them, but not those from which they demonstrate, nor what they demonstrate. And dialectic too.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":29,"ref":"p29","source":"quidem de omnibus, et si aliqua universaliter tentet monstrare communia, ut quod est affirmare omne aut negare, aut quod est æqualia ab æqualibus demere, aut talium quælibet sed dialectiea non est definitorum sic quorumdam neque generis alicujus unius, non enim interrogaret demonstrantem autem non est interrogare, propter id quod oppositorum esse non monstrat idem. Ostensum autem est hoc in iis quæ de syllogismo.\n\nCAPUT IX.\n\nCujusque disciplinæ proprias, accommodatasque esse interrogationes.\n\nSi autem idem est interrogatio syllogistica, et propositio contradictionis. propositiones autem suntsecundum unamquamque scientiam,exquibus est sytIogismus, secundum unaquamque erunt utique aliquae interrogationes scientiales, ex quibus qui est secundum unamquamque proprius fit syllogismus. Manifestum itaque quod nonomnisinterrogatio geometrica erit, neque medicinalis, similiter autem et aliis, sed ex quibus aut monstratur aliquid de quibus geometrica est, aut quod ex eisdem monstratur geometriae, ut visibilia, similiterautem et in aliis. Et de iis qu!dem et rationem ponendam esse ex geometricis principiis et conclusionibus, sed principiorum rationem non ponendam esse geometrae secundum quod est geometria, similiter autem et in aliis scientiis.","english":"For it is not the case that [it is predicated] of all things, even if it attempts to show certain common [principles] universally, such as that every [thing] is affirmation or denial, or that equals may be taken away from equals, or any such things—but dialectic is not [concerned with] things thus defined, nor with any one genus; for it would not ask [such questions]. But it is not for the one who demonstrates to ask questions, because of the fact that it does not show the same thing to belong to opposites. But this has been shown in the [books] concerning the syllogism.\n\nCHAPTER IX.\n\nThat the questions proper to each discipline are suited to it.\n\nIf, however, a syllogistic question is the same as a proposition of contradiction—and propositions are according to each science, from which the syllogism [is formed]—then according to each [science] there will certainly be certain scientific questions, from which the syllogism proper to each is produced. It is manifest therefore that not every question will be geometrical, nor medical, and similarly also in other [sciences], but [only those] from which either something is demonstrated concerning the things of which geometry treats, or that which is demonstrated from the same [principles] as geometry, such as visible things, and similarly also in other [sciences]. And concerning these things, indeed, one must give an account from geometrical principles and conclusions, but the geometer, insofar as he is a geometer, must not give an account of the principles, and similarly also in other sciences.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":30,"ref":"p30","source":"Neque omne est utique unumquemque scientem interrogandu:ll, neque secundum omne interrogatum esse respondendum de unoquoque, sed quæ sunt secundum scientiam de-' terminata. Si autem disputet cum gecrnelra, secundum quod est geometra, sic manifestum est quod et bene, si ex iis aliquid demonstret, si vere non, non bene, manifestum autem est quod non arguit geornetram, sed aut secundum accidens. Quare non utique erit non geometricis de geometria disputandum latebit enim prave disputans, similiter autem et in aliis se se babet scientiis. Quoniam sunt geometn\" cae interrogationes, nonne sunt et non geometricæ? Et quae sunt secundum unamquamque scientiam, et quae secundum ignorantiam qualis geometrica est? Et utrum qui secundum ignorantiam syllogismus, qui est ex oppositis syllogismus, an paraIogismus? Secundum geometriam autem, aut ex alia arte ut musica, est interrogatio non geometrica, de geometrica autem, ut ad invicem parallelas concurrere opinari, geometrica quodammodo est, et non geometrica alio mcdo, dupliciter enim hoc est sicut aritbmon, alterum quidem non geometri. cum est in non habendo, alterum vero in prave babendo, et ignorantia hæc quæ est ex ejus principiis, contraria est. In doctrinis autem non est similiter paralogismus, quia medium semper est dupliciter, etenim de hoc omni, et boc iterum de alio dicitur, omni, quod autem prædicatur, non dicitur omne.","english":"Nor is it in every case necessary to interrogate everyone who has knowledge, nor must one answer every question about each thing, but only those questions that are determined according to the science. But if someone disputes with a geometer insofar as he is a geometer, it is evident that he will do so well if he demonstrates something from these principles, and if not, not well; and it is evident that he does not refute the geometer, except incidentally. Therefore one must not dispute about geometry with those who are not geometers, for the one who disputes badly will go unnoticed; and the same holds in the other sciences. Since there are geometrical questions, are there not also non-geometrical ones? And those that are according to each science, and those that are according to ignorance—what sort of thing is a geometrical one? And whether the syllogism according to ignorance, which is the syllogism from opposites, is a paralogism? But a question according to geometry, or from another art such as music, is non-geometrical; but about a geometrical matter, such as opining that parallel lines converge, is in a way geometrical and in another way non-geometrical—for this is twofold, just as with the arithmetician: one is non-geometrical in not having [the science], the other in having it badly, and this ignorance, which comes from its principles, is contrary. But in the sciences there is no paralogism in the same way, because the middle term is always twofold; for it is said of this whole, and this again of another whole, but what is predicated is not said of every whole.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":31,"ref":"p31","source":"Haec autem sunt ut est videre in intellectu; sed in orationibus Iatet, utrum omnis circulus I]gura sit, si scribatur autem, manifestum est. Quid autem, sintne carmina circulus? manifestum quoniam non sunt. Non oportet autem instantiam in ipsum ferre si sit propositio inductiva, sicut enim neque propo. sitio est, quae non est in pluribus, non enim erit in omnibus, ex universalibus autem syllogismus manifestum est quod neque instantia est, easdem enim sunt propositiones et instan tiæ, quam enim fert instantiam, haec fiet utique propositio demonstrativa, aut dialectica. Contingit autem quosdam non syilogistice dicere propter id quod accipiunt utriusque consequentia, ut et Cæneus facitquod ignis in multipticata analogia fit, et namque ignis cito generatur, sicut dicit, et bæc est analogia. Sic autem non est syIlogismus,sed si veIocissima analogia sequiturmul tiplicata,et ignem velocissima in mutatione analogia. Aliquando quidem igitur syllogizare non contingit ex acceptis, aIiqllando vero contingit, sed non videtur. Siautemesset. impossibile ex falsisvero monstrare, facile utique esset resolvere, converterentur enim ex necessitate. Sit enim a ens, hoc autem cum sit, ea utique suntquæ novi quoniam sunt ut b, ex his igitur monstrabo quoniam illud est.","english":"These things are, as one may see, in the intellect; but in words it is hidden whether every circle is a figure—yet if it is drawn, it is manifest. But what of poems—are they a circle? It is manifest that they are not. One ought not, however, to bring an objection against the proposition itself if it is inductive; for just as there is no proposition that is not in many things—for it will not be in all things—and from universals a syllogism is manifest, so it is clear that there is no objection either; for propositions and objections are the same things. For that which one brings as an objection will certainly become a demonstrative or dialectical proposition. It happens, however, that some speak non-syllogistically because they take the consequence of both, as Ceneus does—that fire comes to be in multiplied proportion; for fire is quickly generated, as he says, and this is proportion. But thus it is not a syllogism, but rather if the swiftest proportion follows what is multiplied, and fire follows the swiftest proportion in change. Sometimes, then, it is not possible to syllogize from what has been accepted, but sometimes it is possible, though it does not appear so. But if it were possible to demonstrate from false premises, it would surely be easy to resolve; for they would be converted by necessity. For let A be a being; and this being so, those things which I know to be, such as B, are; from these, therefore, I shall show that that is.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":32,"ref":"p32","source":"Convertuntur autem magis quae sunt in mathematicis, quoniam nullum recipiunt accidens (et in hoc differuntab iis quae sunt in dia]ogis), sed definitiones. Augentur autem non per media, sed in assumendo, ut a de b, hoc autem de c. Item hoc dfJ d, et boc in infinitum, et in latus, ut a de c, et de e, ut est numerus quantus, vel infinitus. Hoc autem in quo sit a nu.nerusimpar quantus in quo b, numerus impar in quo c, est et itaque a de c, et est par quantus numerus in quo sit d, par numerus in quo es e, est ergo a de e.\n\nCAPUT X.\n\nDe demonstratione propter quid, et quod est.\n\nSed quia differt, et propter quid scire, primum in eadem scientia, et in hac dupliciter. Uno quidem modo si non per immediata fiat syllogismus, non enim accipitur prima causa, sed quæ propter quid scientia, est secundum primam causam. Alio modo si per immediata quidem, sed non per causam, sed per convertentia, et per notius, prohibet enim nihil æque prædicantium, notius aliquando esse non causa, quare per hanc erit demonstratio. Ut quod prope sint planetæ, per illud quod non scintillare, sit in quo planetæ, in quo non scintillare, in quo a prope esse, verum igitur est de dicere, planetæ enim non scintillant, sed et a de b, non scintillans enim prope est. Hoc autem accipitur per inductionem, aut per sensum, necesse ergo a ipsi inesse, quare demonstratum est quod planetae prope sunt.","english":"But those things which are in mathematics are converted more readily, since they receive no accident (and in this they differ from those which are in dialogues), but definitions. They are increased, however, not through middle terms, but in assuming, as a of b, and this of c. Likewise this of d, and this to infinity, and laterally, as a of c and of e, as a number, how great or infinite. But that in which a is, an odd number, how great, in which b, an odd number, in which c, it is, and so a is of c; and a number, how great, even, in which d is, an even number, in which e, therefore a is of e.\n\nCHAPTER X.\n\nOn demonstration of the reason why, and of the fact.\n\nBut because to know the reason why differs, and first in the same science, and in this in two ways. In one way, indeed, if the syllogism is not made through immediates, for the first cause is not taken, but the science of the reason why is according to the first cause. In another way, if indeed through immediates, but not through the cause, but through convertibles, and through what is better known; for nothing prevents one of those things predicated equally from sometimes being better known and not the cause, wherefore the demonstration will be through this. As that the planets are near, through that which is not to twinkle; let there be that in which the planets are, that in which not to twinkle, that in which a is to be near. It is true, therefore, to say this, for the planets do not twinkle, but also a is of b, for what does not twinkle is near. But this is taken through induction, or through sense; it is necessary, therefore, that a be present in it, wherefore it has been demonstrated that the planets are near.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":33,"ref":"p33","source":"Hic ergo siUogismus non est propter quid, sed quia, non enim ex eo quod non scintillant prope sunt, sed propter illud quod prope sunt, non scintillant. Possibile est autem et per alterum,I alterum monstrare,eterit propter quid demonstratio, ut sit planetæ, it; quo prope esse, a non scintillare est igitur in c, quod est non scintillare, quare et in c, et erit propter quid syllogismus, accepta enim est prima eausa. Iterum siclunam demonstrant quod quidem circularis sit per incrementa, si enim quod augetur sic circulare quidem sit augetur autem sic luna manifestum quoniam circuIaris sicigituripsius, quia factus est sillogisrnus, e converso autem posito medioipsius propter quod syllogismus fit. Non enim propter augmenta ipsius circularis est, sed quia circularis est, accipit augmenta hujusmodi. Luna sit in quo c, in quo 5;t augmentum, sit in quo a circulare Inquibusautem media non convertuntur, et est notius quod non est causa, quia monstratur, sed et propter quid, non amplius in quibus medius J extra ponitur, etenim in his non propter quid, sed ipsius quia demontratio, non enim dicitur causa. Ut propter quid non respirat paries, quia non est animal, si enim non respirandi causa est hoc, oportet esse animal causa respirandi.","english":"This syllogism, then, is not a demonstration of the reason why but of the fact; for it is not because they do not twinkle that they are near, but because they are near that they do not twinkle. But it is possible to demonstrate the one through the other, and there will be a demonstration of the reason why: let the planets be that in which C, nearness that in which A, not twinkling that in which B. Therefore not twinkling is in C, and so also in B; and there will be a syllogism of the reason why, for the first cause has been taken. Again, they demonstrate that the moon is circular by its waxing; for if what waxes in this way is circular, and the moon waxes in this way, it is manifest that it is circular. So the syllogism of the fact has been made in this way; but when the middle term is converted, the syllogism of the reason why is made. For it is not because it waxes that the moon is circular, but because it is circular that it receives waxing of this kind. Let the moon be that in which C, waxing that in which B, circular that in which A. But in those cases in which the middle terms are not converted, and that which is not the cause is better known, the fact is demonstrated, but no longer the reason why. In those cases in which the middle term is placed outside, there is in these too not a demonstration of the reason why but of the fact; for the cause is not stated. For example, why does a wall not breathe? Because it is not an animal. For if this is the cause of not breathing, it is necessary that an animal be the cause of breathing.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":34,"ref":"p34","source":"Ut si negatio causa est ipsius non esse, affirmatio causa est ipsius esse, sicut si sine mensura esse calida et frigida, causa est non sanandi, et mensura hujus causa erit sanandi. Similiterautem etsi aFfirmatio est causa ipsius esse, et negatio ipsius non esse. In his autem sic demonstratis non contingit quod dictum est, non enim omne animal respirat. Sillogismus autem hujus causæ est in media figura, ut sit a animal, in quo respirare, in quo paries, in quo quidem igitur omni est a omne enim respirans est animal, in autem nullo, quare neque in nullo est, non igitur respirat paries. Comparantur autem hujusmodi causæ secundum excellentiam dictis, hoc autem est plurimum distans medium dicere, sicut enim illud est quod Anarcharsir:lis, quod in Scytbis non sunt sibilatores, neque enim vites. Secundum igitur eamdem scientiam, et secundum mediorum positionem, hae differentiae sunt ipsius, quia ad eum qui propter quid est syllogismum. Alio autem modo differt propter quid ab ipso quia, quod est per aliam scientiam utrumque speculari. Hujusmodi autem sunt, quaecunque sic se habentad invicem, quod alterum sub altero est, ut perspectiva ad geometriam, et machinativa ad stereometriam, et harmonica ad arithmeticam, et apparentia ad astrologiam.","english":"For if the negation is the cause of its not being, the affirmation is the cause of its being; as, if being without measure is the cause of not being healthy in respect of hot and cold, then measure will be the cause of being healthy. And similarly, if the affirmation is the cause of being, the negation is also the cause of not being. But in things demonstrated in this way, what was said does not hold; for not every animal breathes. Now the syllogism of this cause is in the middle figure, so that A is animal, that in which is breathing, and that in which is wall: for in every one, indeed, A is present—for everything that breathes is an animal—but in none of the walls, so that it is in no wall; therefore a wall does not breathe. Causes of this kind, however, are compared according to excellence with what has been said; and this is to state a middle term that is very far removed, as, for instance, that of Anacharsis, that among the Scythians there are no flute-players, for neither are there vines. According, then, to the same science, and according to the position of the middle terms, these differences belong to the fact as compared with the syllogism that gives the reason why. But in another way the reason why differs from the fact, because it is through another science that each is contemplated. Of this kind are all those that are so related to one another that the one is under the other, as perspective to geometry, and mechanics to stereometry, and harmonics to arithmetic, and the appearances to astronomy.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":35,"ref":"p35","source":"Fere quidem univocæ sunt harum quædam scientiarum, ut astrologia mathematica, et quae navalis est, et harmonica mathematica, quæ est et secundum auditum. Hic enim ipsum, quia sensibilium est scire, sed propter quid, mathematicorum. Hi enim habent causarum demonstrationes, et frequenter nesciunt ipsum, quia sicut illi universale considerantes, sæpe quædam singularium nesciunt propter id quod non intendunt. Suntautem haec quæcumque alterurn quiddam sunt secundum substantiam et utunturspeciebus.Mathematicæ enim circa species sunt, non enim de subjecto aliquo, si enim de aliquo subjecto geometrica sunt, sed non suntsecundum quod geometrica sunt. Habet autem se ad perspectivam sicut haec ad geometriam, et alia ad istam, ut id quod est de iride ipsum quidem quia est scire physici, sed propter quid perspectivi, aut simpliciter, aut secundum disciplinam.. Multae autem, et non sub se invicem scientiarum, habent sic, ut. medicina ad geometriam. quod enim vulnera cicularia tardius sanantur. medici est scire quia, propter quid autem geometrae.","english":"Some of these sciences are generally univocal, such as mathematical astronomy, and the science of navigation, and mathematical harmonics, which is also according to hearing. For here it is the fact that belongs to the senses to know, but the reason why belongs to the mathematicians. For these have the demonstrations of causes, and frequently they do not know the fact, because just as those who consider the universal often do not know some of the particulars, for the reason that they do not attend to them. And these are whatever things are something else according to substance and use the species. For the mathematical sciences are concerned with species, for they are not about some subject; for if geometry is about some subject, it is not [considered] according as it is geometry. It is related to perspective as this is to geometry, and another to this, as the fact concerning the rainbow is for the natural philosopher to know, but the reason why belongs to the perspectivist, either simply or according to the discipline. And many sciences, not subordinate to one another, are related in this way, as medicine to geometry: for that circular wounds heal more slowly is for the physician to know as a fact, but the reason why is for the geometer.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":36,"ref":"p36","source":"CAPUT XI.\n\nPrimam figuram maxime scientiæ esse accomodatam.\n\nFigurarum autem faciens scire maxime,prima est. Mathematicæenim scientiarumper hanc demonstrationes ferunt, ut arithmetica, et geometria, et perspectiva, et fere esl dicere quæcunque propter quid speculari t'aciuntconsiderationem, aut enim omnino, aut sicut frequentius,etin pIurimis,per hanc figuram (qui est propter quid) fit syllogismus, quare et propter hoc erit maxime faciens scire, propnissimum enim scire, propter quid speculari. Postea ipsius quod quid est scientiam, per banc solam venari possibile est. In media enim figura non fit praedicativus syllogismus, sed ipsius quod quid est scientia, af[jrmationis est, in ultima autem fit quidem, sed non universaliter, sed quod quid est, universalium est. non enim quodammodo est animal bipes homo. Amplius haec quidem illis nihil indiget, illae autem per hanc densantur, etaugmentantur quousque utique ad immediata veniant, manifestum igitur e.st quod maxime propria scientiæ est prima figura, Sicut autem a esse in contingit indivisibiliter, sic et non esse possibile est; dico autem indivisibiliter esse, vel non esse eo quod non est aliquid eorum medium, sic enim non erit secundumaliud esse. Cum igitur aut a aut in toto aliquo sit, aut etiam ambo, non contingit a in primo non esse.","english":"CHAPTER XI.\n\nThat the first figure is most suited to science.\n\nOf the figures, the one that most produces knowledge is the first. For the mathematical sciences carry their demonstrations through this figure, such as arithmetic, geometry, and perspective, and one may almost say whatever sciences investigate the reason why. For either altogether, or as is more usual and in most cases, it is through this figure that the syllogism of the reason why comes about; wherefore for this reason too it will be most productive of knowledge, for to investigate the reason why is most properly knowing. Afterwards, it is through this figure alone that knowledge of the what-it-is can be sought. For in the middle figure there is no affirmative syllogism, but knowledge of the what-it-is is of an affirmation; in the last figure it does come about, but not universally, whereas the what-it-is belongs to universals. For man is not in some way a two-footed animal. Moreover, this figure needs nothing from those, but those are made dense and increased by this one until they arrive at the immediates. It is evident, therefore, that the first figure is most proper to science. But just as it happens that a is present indivisibly, so also it is possible that it is not present; and I say \"to be or not to be indivisibly\" in that there is no middle term of these, for thus it will not be according to another. When, therefore, either a or [the subject] is in some whole, or even both, it is not possible that a is not in the first.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[{"kind":"lacuna","severity":"caution","text":"The source is fragmentary here: the edition marks a break or an editorial bracket, and the English carries across it. Treat the bridge as supplied, not translated."}]},{"i":37,"ref":"p37","source":"Sit enim a in toto c, igitur si non est in toto (potest enim a quidem esse in quodam toto, sed non esse in hoc), syllogismus erit quod non sit a in; si enim in a quidem omni est c, in autem nullo est,;in nullo est a. Similiter autem et si in aliquo toto est, ut in b, enim in omni est, in a autem nullo, d, quare ain nullo erit per syllogismum. Eodem autem modo monstrabitur et si utraque in toto aliquo sit, Quod autem contingit non esse in quo toto est a, aut iterum a in quo est b, manifestum est ex coordinationibus, quaecunque non commutantur ad invicem, si enim nihil eorum quæ sint in a coordinatlone, de nullo prædicatureorum quæ sunt in ef, a autem in toto g, sic coordinatione existente, manifestum est quod non erit in g, commutarentur enim coordinationes similiterautem estetsi in toto aHquoest. Si vero neutrum sit in toto aliquo nullo, non sit autem a in b, necesse est indivisibiliter non esse; si enim erit aliquod medium, necesse est alterum horum in quodam toto esse, autenimin prima figura, aut in media erit syllogismus, si quidem igitur in primafigura b, erit in toto aliquo, affirmativam enim ad hoc oportet fieri propositionem. Si vero in media, utrumcontingitadutrumqueenim posito privativo erit syllogismus, cum autem utraque privativa sit, non erit, manifestum igitur est quod contingit et aliud in alio non esse iDdivibijiter, et quando contingit, et quo modo diximus.","english":"For let A be in the whole of C; therefore if it is not in the whole (for A can indeed be in some whole, but not be in this one), there will be a syllogism that A is not in it. For if C is in every A, and is in no B, then A is in no B. Similarly also if it is in some whole, as in B: for if C is in every B, and in no A, then D, wherefore A will be in no B through a syllogism. In the same way it will be shown also if both are in some whole. But that it happens that A is not in the whole in which it is, or again that B is in the whole in which A is, is manifest from the coordinations, whichever are not interchanged with one another. For if none of the things that are in the coordination of A is predicated of any of the things that are in E F, while A is in the whole of G, with the coordination being thus, it is manifest that it will not be in G; for the coordinations would be interchanged. In the same way it is also if A is in some whole. But if neither is in any whole, and A is not in B, it is necessary that it is not in it indivisibly. For if there will be some middle term, it is necessary that one of these be in some whole; for either the syllogism will be in the first figure, or in the middle. If indeed in the first figure, B will be in some whole; for the proposition must be made affirmative with respect to this. But if in the middle figure, it happens with respect to either; for with a privative proposition posited, there will be a syllogism, but when both are privative, there will not be. It is manifest, therefore, that it happens also that one thing is not in another indivisibly, and when it happens, and in what way we have stated.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":38,"ref":"p38","source":"CAPUT XII.\n\nDe ignorantia et syllogismo primo immediateque imperitiæ eorum inJunt.quæ\n\nIgnorantia autem non secundum negationem, sed secundum dispositionem dicta, est quidem persyllogismum facta deceptio. Hæc autem in iis, que insunt primo, aut non insunt, contingitdupIiciter, aut enim est cum simpliciter accipiat esse, vel non esse, aut cum per syllogismum accipiat opinionem, simplicis quidem ergo opinionis simplexdeceptio, sed qua? est persyllogismurn plures sunt. Non sit enim a in nullo indivisibiliter, ergo si syllogizet a esse in me. dium accipiens c, deceptus erit per syllogismum, contingit igitur utrasque propositiones esse falsas, contingit autem alteram solum esse falsam, si enim neque a in nullo erit, neque cin nullo erit, accepla autem utraque e contrario, utraque enim erunt falsae. Potes autem sic se habere ad a, et ad b, quod neque sub a sit, neque in universaliter; quidem impossibile est esse in aliquo toto, primum enim dictum est in ipso a non esse, a autem non necesse, est omnibus inesse, quæ suntc universaliter, quare utraeque falsae sunt. Sed alteram contingit veram accipere, non tamen quamlibet Contingit, sed quas est a c, nam propositio semper falsa crit, propter id quod in nullo est, sed qua; est a potest, ut si a et in c, et in indivisibiliter est, cum enim primum prædicetur idem de pluribus, neutrum in neutro erit.","english":"CHAPTER XII.\n\nOn ignorance, and the first immediate syllogism, and the inexperience of those in matters that are\n\nBut ignorance, spoken of not according to negation but according to disposition, is deception brought about through syllogism. This happens in two ways in things that are present primarily or are not present: for either it is when one accepts simply that it is or is not, or when one accepts an opinion through syllogism. Of simple opinion, then, the deception is simple, but those that are through syllogism are more numerous. For let A be in no indivisible; therefore if one syllogizes that A is in the middle, taking C, he will have been deceived through syllogism. It is possible, then, that both propositions are false, but it is also possible that only one is false. For if neither A is in anything nor C is in anything, but both were accepted contrariwise, then both will be false. But it is possible to be so disposed toward A and toward B that it is neither under A nor in a universal; indeed it is impossible for it to be in some whole—for it was first said that it is not in A itself—but A does not necessarily belong to all the things that are universally; wherefore both are false. But it is possible to accept one as true, yet not any one at random, but the one that is A C; for that proposition will always be false, because of the fact that it is in nothing, but the one that is A can be true, as if A is both in C and in an indivisible; for when the same thing is predicated primarily of several things, neither will be in either.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":39,"ref":"p39","source":"Differt autem nihil, neque si non indivisibiliter insit, ipsius quidem esse, igitur deceptio per ista, et sic fit solum, non enim erat in alia figura ipsius esse syllogismus, qui vero ipsius non esse, in prima figura, et in media est, primum igitur dicamus quot modis in prima fit, et quomodo se habentibus propositionibus. Contingit igiturutrisque falsis, ut si a et in et in si indivisibiliter, sit, si enim accipiatur a in nullo esse, autem in omni b, falsae sunt propositiones. Contingit autem et altera Falsa, et hac quacunque contingente, potest enim quae est a vera esse, que vero falsa, sed que esta vera, quoniam non in omnibus quæ sunt, inest a, sed quae est falsa esse, quoniam sibile imposest esse in c, in quo nullo est a non enim etiam veraent, quae est a propositio. simul autem et si sint utræque veræ, et conclusio vera erit, sed etiam quae est /) b. Contingit veram esse cum altera sit falsa, ut si in sit, et in a, necesse est enim alterum sub altero esse, quare si accipiatur a in nullo esse, faIsa erit propositio, palam igitur quoniam et cum altera si falsa, et in utrisque, falsus syllogismus erit.","english":"It makes no difference even if it does not inhere indivisibly; so much for the deception arising through these, and thus it comes about only in this way, for there was no syllogism of its being in another figure, whereas the syllogism of its not being is in the first figure and in the middle. Let us first state in how many ways this comes about in the first figure, and how the propositions must be related. It happens, then, with both propositions false, as if A is in no C and in every B indivisibly; for if it is assumed that A is in no C, but in every B, the propositions are false. It also happens that one is false, whichever one it may be; for the proposition about A can be true, while the other is false—but the one about A is true because A is not in all things that are, while the other is false because it is impossible for it to be in C, in which A is in nothing; for the proposition about A would not even be true. At the same time, if both are true, the conclusion will also be true, but also the one about B. It happens that it is true when the other is false, as if it is in C and in A; for one must be under the other, so that if it is assumed that A is in nothing, the proposition will be false. It is clear, then, that even when one is false, and when both are false, the syllogism will be false.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":40,"ref":"p40","source":"Sed in media quidem figura totas propositiones esse utrasque falsas non contingit, eum enim in omni a sit, nihil eritacciperequod in altero erit omni, in altero vero nullo erit, oportet autem sic in media figura accipere propositiones, et quod in hoc quidemsit,et quod in hoc non sit, siquidem erit syllogismus, si igitur accipiantur sic falsae, palarn quod contrariae e converso se habebunt, hoc autem impossibile est. In aliquo autem utramque tionem proposinihil prohibet falsam esse, ut si ina, et in aliquo est; si enim a in omni accipiatur esse, autemin nullo, falsæ quidem utræque propositiones, non tamen totæ, sedin aliquo, e converso autem posito privativo similiter. Alteram autem falsam, et qualibet contingit, quod enim est in a omni, et in est, si igitur acciapiatur in a quidem toto esse c, in autem toto non esse, guæ quidem est a erit vera, sed quae estc falsa. Iterum quod in nullo est, neque in a omni erit, si enim in a est, et in b, sed non inerat, siigituraccipatur cintoto quidema esse in autem nullo quidem, quæ est propositio vera est, altera vero falsa. Similiter autem fit transposito privativo, quod enim in nullo est a, neque in nullo erit ei igitur accipiatur cin toto quidem a non esse, in autem esse toto, quæ quidem est a propof'itio vera est, altera autem falsa.","english":"But in the middle figure it is not possible for both entire propositions to be false. For when A is in every B, there will be nothing to take that will be in every one of the other and in none of the other; but in the middle figure the propositions must be taken thus: that which is in this one, and that which is not in this one, if indeed there is to be a syllogism. If, then, they are taken thus as false, it is clear that the contraries will stand in reverse relation to one another; but this is impossible. In the case of particular propositions, however, nothing prevents both from being false, as if A is in some B and in some C; for if A is taken to be in every B and in no C, both propositions are indeed false, yet not wholly, but in some part; and similarly when the privative is posited in reverse. But it is possible for one of them to be false, whichever one you like. For that which is in every A is also in B; if, then, C is taken to be in the whole of A and not in the whole of B, the proposition concerning A will be true, but that concerning C false. Again, that which is in none is neither in every A; for if it is in A, it is also in B, but it was not; if, then, C is taken to be in the whole of A and in none of B, the one proposition is true, but the other false. The same happens likewise when the privative is transposed. For that which is in none of A will be in none of B; if, then, C is taken to be in the whole of A and to be in the whole of B, the proposition concerning A is true, but the other false.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":41,"ref":"p41","source":"Et iterum quod in omni est, in nullo accipere a esse, falsum est, necesse enim est si in omni b, et in quodam a esse, si igitur accipiatur in omni quidem esse c, ina autem nullo, quæ quidem est b, vera erit, quæ autem est a c, falsa. Manifestum igitur quod utrisque falsis, et altera solum, erit syllogismus deceptivus indivisionibus.\n\nCAPUT XIII.\n\nDe syllogismo imperillæ eorum quæ insunt mediate.\n\nIn iis autell1 quae non indivibiliter insunt, aut non insunt,cum quidem per proprium medium falsitatis fiat sylLogismus, non possibile est falsas utrasque esse propositiones,sed solum quæ ante majus extremum. Dico autem proprium medium, per quod fit contradictionis syllogismus: sit enim a. in per medium c, quoniam igitur necesse est quae est affirmativam accipi syllogismo facto, manifestum quod semper hæc est vera, non enim convertitur,sed quae est a falsa, hac enim con versa, e contrario fiet sylIogismus. Similiter autem est, et si ex alia coordina. tione accipiatur medium, ut d, si et in toto a, et de prædicatur omni, necesse est enim (quæ quidem est b) propositionem manere, alteram autem converti. Quare hæc quidem semper vera, illa vero semper falsa, et fere hujusmodi deceptio, eadem est ei quae fit per proprium medium.","english":"And again, that what is in every one is received as in none, is false; for it is necessary that if it is in every B, it is also in some A. If, then, it is taken that it is in every C, but in no A, the proposition concerning B will be true, but that concerning A and C false. It is clear, therefore, that with both false, and with only one, there will be a deceptive syllogism in indivisibles.\n\nCHAPTER XIII.\n\nOn the syllogism that deceives in those things which inhere mediately.\n\nBut in those things which do not inhere indivisibly, or do not inhere, when a syllogism of falsity is produced through a proper middle term, it is not possible for both propositions to be false, but only the one before the major extreme. Now I call that a proper middle term through which the syllogism of contradiction is produced; for let A be in [something] through the middle term C. Since, therefore, it is necessary that the affirmative proposition be taken when the syllogism has been made, it is clear that this is always true, for it does not convert; but the proposition concerning A is false, for when this is converted, the syllogism will be produced in the opposite way. It is the same, moreover, if the middle term is taken from another coordinate order, as D, if it is predicated both of the whole of A and of every [instance of] the subject; for it is necessary that the proposition concerning B remain, but that the other be converted. Wherefore this one is always true, but that one always false; and the deception of this kind is for the most part the same as that which occurs through a proper middle term.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":42,"ref":"p42","source":"Si vero non per proprium medium fiat syJIogism uS,curn quidem sub a sit medium, in autem nullo est,necesseestutrasque falsas esse,sumendæ enim e contrario sunt quam ut se habeant propositiones, si debeat syllogismus esse:sic autem acceptis, utræque fiunt falsæ, ut si a quidem in toto est, autem in nullo b, conversis enim iis, syllogismus erit, et propositiones utraeque falsæ. Cum vero non sit sub a medium ut d, quae quidem est a vera erit, quæ vero est falsa, quae enim est a vera est, quia non erit in a, d, quae vero est falsa, quia si esset vera, et conclusio esset vera, sed falsa era!. Sed per mediam figuram facta deceptione, utrasque quidem non contingit falsas esse propositiones totas, cum enim sit quidem sub a, nibil contingit in hoc quidem omni, in illo autem nullo esse, sicut dictum est et prius. Altera vero potest esse falsa, et quæcunque contingit. Si enim et in b, et in a est, si accipiatur in a quidem esse, in vero non esse, quae quidem a vera erit, altera autem falsa. Item si in accipiatur esse, in cc autem nullo est, qua quidem est vera erit, altt'Jra autem falsa, siquidem igitur privativus sit deceptionis syIlogismus, dictum est quando et per quae erit deceptio.","english":"But if the syllogism does not come about through a proper middle term, when the middle is indeed under A, but is in no B, both premises must be false; for they must be assumed contrary to the way the propositions are related, if there is to be a syllogism; but when they are accepted in this way, both become false, as if A is in the whole and is in no B; for when these are converted, there will be a syllogism, and both propositions will be false. But when the middle, such as D, is not under A, the premise concerning A will be true, but the other false; for the premise concerning A is true because D will not be in A, but the other is false because if it were true, the conclusion would also be true, but it was false. But when the deception is produced through the middle figure, it is not possible for both propositions to be wholly false; for when the middle is indeed under A, it is possible for it to be in this one wholly and in that one in no way, as was also said before. But the other can be false, and whichever way it happens. For if it is both in B and in A, if it is taken to be in A indeed but not to be in B, the premise concerning A will be true, but the other false. Again, if it is taken to be in B but is in no C, the one will be true, but the other false. If, then, the syllogism of deception is privative, it has been stated when and through what the deception will occur.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":43,"ref":"p43","source":"Si vero sit affirmativus, tunc cum perproprium medium, impossibile est utrasque esse falsas, necesse est enim quæ est manere, siquidem erit syllogismus sicut dictum estet prius, quare a semper erit falsa, hæc enim est con versa. Similiter autem est et si ex alia ordinatione accipiatur medium, sicut dictum est et in privativa deceptione, necesse enim est qua; quidem est manere, quae vero est a converti, et haec deceptio eadem est priori. Cum vero sic non per proprium, si quidem sit sub a, haec quidem erit vera, alteravero falsa, potest enim a in pluribus esse, quae non sunt sub se invicem. Si vero non sit sub a, hæc quidem semper rnanifestum est quoniam est falsa, affirmativa enim accipiatur. Quae vero est a b, contingit et veram esse, et falsam, nihil enim prohibet a quidem in nullo esse, autem in omnib, ut animal in scientia, scientia autem ut in musica, neque utique a in nullo d, neque in nullo esse. Manifestum igitur est quon iam cum non sit medium proprium, et utra? possunt simul esse faIsæ, et quaecunque contingit. Quot quidem igitur modis, et perquae possuntfieri secundum syllogismum deceptiones, et in aliis quae sunt sine medio, et in iis quae sunt per demonstrationem manifestum est.","english":"But if it is affirmative, then when the middle term is proper, it is impossible for both premises to be false; for the one must remain, since there will be a syllogism, as was said also earlier. Therefore the premise concerning A will always be false, for this is the converse. The same holds also if the middle term is taken from another arrangement, as was said also in the case of privative deception; for one premise must remain, while the one converted from A—and this deception is the same as the former. But when it is not through a proper middle term, if the middle is under A, this premise will be true, but the other false; for A can be in many things that are not subordinate to one another. But if it is not under A, this premise is always manifestly false, for it is taken as affirmative. But the premise A B can be both true and false; for nothing prevents A from being in nothing, while B is in all things—as animal in knowledge, and knowledge as in music—so that neither is A in any D, nor is it in nothing. It is clear, therefore, that when the middle term is not proper, both premises can be false at the same time, and whichever ones can be so. In how many ways, then, and through what, deceptions according to syllogism can occur, both in those cases that are without a middle term and in those that are through demonstration, is clear.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":44,"ref":"p44","source":"CAPUT XIV.\n\nSi sensus a natura deficit, sensibilium propriorumsensibilium illius deficere.\n\nManifestum est autem, et si aliquis sensus defecerit, necesse est aliquam scientiam deficere, quam impossible est accipere, si quidem discimus, aut per inductionem, aut per demonstrationem. Est autem demonstratio ex univerpalibus, inductio autem ex iis quae sunt particularia. Impossibile autem est universalia speculari, nisi per inductionem, quoniam et quæ ex abstractione dicuntur, est per inductionem nota facere, si quis vult nota facere, quia sunt in unoquoque genere quædam, et si non separabilia sint secundum quod hujusmodi unumquodqueest. Inducereautem non habentes sensum, impossibile est, singularium enim sensus est, non enim contingit accipere ipsorum scientiam, neque enim est ex universalibus sine inductione, neque per inductionem sine sensu.","english":"CHAPTER XIV.\n\nIf a sense is lacking by nature, the knowledge of that sense's proper sensibles is also lacking.\n\nIt is evident, moreover, that if any sense has failed, some knowledge must necessarily fail—knowledge which it is impossible to acquire, since we learn either by induction or by demonstration. Demonstration, however, is from universals, while induction is from particulars. But it is impossible to contemplate universals except through induction, since even the things said by abstraction must be made known through induction, if one wishes to make them known, because there are certain things in each genus, even if they are not separable insofar as each thing is of this sort. But to induce without having sense perception is impossible; for sense perception is of singulars, and it is not possible to acquire knowledge of them, since neither is there [knowledge] from universals without induction, nor through induction without sense perception.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":45,"ref":"p45","source":"CAPUT XV.\n\nEx quat et qualibus constat syllogismns, et an sursum deorsumve fiat in infinitum abitio\n\nEst autem omnis syllogismus per tres terminos, et quidem monstrare possibilis est quoniam a est in c, propter id quod est in b, et hoc nc. eprivativus est quidem alteram propositionem habens quoniam est aliquid aliud in alio, alteram autem quoniam non est. Manifestum igitur est quod principia, et suppositiones dicta haec sunt, accipientem enim hæc sic, necesse est monstrare ut quod a sit in per 6, iterum autem quod a sit in per aliud medium, et quod sit in similiter, Secundum igttur opinionem syllogizantibus, et solum dialectice, manifestum est quod hoc solum intendendum, si ex quibus contingit maxime probabilibus fiat syIIogismus. Quare et si est aliquid in veritate eorum quae sunt a medium, videtur autem non esse per hoc syllogizans, syllogizat dialectice. Ad veritatem autem, ex iis quae sunt oportet intendere, habet autem se sic. Quoniam aute-!] est quod ipsum quidem dealia praedicatur, non secundum accidens.Dico autem secundum accidens, ul album aliquando dicimus illud esse bominem, non similiter dicentes et hominem album, cum enim non sit alterum, aliquod album est, album autem est homo, quoniam accidit homini esse album, sunt igitur quædam hujusmodi, quaecunque secundum se prædicantur.","english":"CHAPTER XV.\n\nFrom what and of what sort a syllogism consists, and whether the process goes upward or downward to infinity\n\nEvery syllogism is through three terms, and it is possible to show that A is in C because of B, and this in turn because of something else. A privative syllogism has one proposition stating that something is in something else, and the other stating that it is not. It is evident, therefore, that the principles and suppositions are what have been stated; for one who accepts these must show that A is in B through C, and again that A is in C through another middle term, and likewise that it is in that term. Accordingly, for those who syllogize according to opinion and in a purely dialectical manner, it is evident that this alone must be their aim: that the syllogism be formed from the most probable premises possible. Hence, even if there is some middle term in the truth of things, though it seems to the dialectical reasoner that there is none, he still syllogizes dialectically. But for truth, one must aim at things as they are, and the matter stands thus. Since there is that which is predicated of something else itself, not according to accident—I mean \"according to accident\" in the sense that we sometimes say the white is a man, not meaning the same as when we say the man is white; for when the one is not the other, white is a certain thing, but white is a man because it happens to the man to be white—there are, then, certain things of this sort, whatever are predicated in themselves.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":46,"ref":"p46","source":"Si igitur hujusmodi quod ipsum quidem non in alio sit, in hoc autem sit primo, et non per aliud medium, iterum e de dsit, et similiter et hoc in G, nunquid igitur hoc necesse est stare, au contingit in infinitum ire? Et iterum si de a quidem nihil prædicatur per se, a autem in y est primo, medium autem in nullo priori, et I in a, et hoc in b, nunquid et hoc stare necesse est? an et hic contingit in infinitum abire? Differt autem hoc a priori intantum, quoniam hoc quidem est nunquid, contingitincepturum ad hujusmodiquod in nullo est altero, sed aliud in illo, in sursum in infinitum abire, alterum autem inccepturum ab bujusmodiquod ipsum quidem de alio, de illo autem nihil prædicatur, in deorsum intendentem, si contingit in infinitum ire. Amplius media nunquid contingit infinita esse determinatis terminis? Dico autem ut si a in sit, medium ipsorum sit b, ab ipso autem b, et ab a altera, sed horum alia, nunquid et bæc in infinitum contingit abire? an impossible est? est autem hoc quidem intendere idem et si demonstrationes in infinitum veniunt, et si est demonstratio omnis rei, an ad invicem concludantur.","english":"If, then, a thing of this sort—which itself is not in another, but is in this first, and not through another middle—should again be in D, and similarly this in G, must this then necessarily come to a stop, or can it proceed to infinity? And again, if nothing is predicated of A in itself, but A is first in Y, and the middle is in no prior term, and I is in A, and this in B, must this too necessarily stop? Or can it here also proceed to infinity? This differs from the former case to this extent, that the one is the question whether it is possible to proceed upward to infinity beginning from that which is in no other, but another is in it; while the other is to begin from that which itself is predicated of another, but nothing is predicated of it, tending downward, whether it is possible to proceed to infinity. Further, can the middles be infinite when the terms are determinate? I mean, for example, if A is in C, and the middle of them is B, and another middle of B and A, and another of these, can these too proceed to infinity? Or is it impossible? This is the same as to ask whether demonstrations come to infinity, and whether there is demonstration of everything, or whether they are concluded reciprocally.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":47,"ref":"p47","source":"Similiter autem dico et in privativis syllogismis et propositionibus, ut si a non inest Ii nulli aut primo, aut est aliquid medium, cui priori non inest a, ut si sit quod omni in est, et iterum hoc non etiam alii priori, ut si est quod sit in omni 6, et namque in his aut infinita sunt, iti quibus non est in priori bus, aut statur. Sed inconvertibilibus non similiter se habet,non enim est in seque prædicabilibus de quo primo prædicatur, aut ultimo, omnia enim ad omma similiter se habent, sive sunt infinita de ipso prædicata, sive utraque sunt dubitata infinita, nisi similiter converti contingat, sed hoc quidem sicut accidens, illud vero sicut prædicatum.\n\nCAPUT XVI.\n\nDeterminatis extremis, summo imoque, media non esse in fillita.\n\nQuoniam igitur media non contingit infinita esse, si in sursum etdeorsum stent prædicata, manifestum est. Dico autem sursum quidem, quod universale magis est, deorsum autem, quod particulare est. Si enima prædicante de c, infinita sunt media, in quibus est b, manifestum est quod continget utrique, ut ab a in deorsum alterum de altero contingit praedicari in infinitum, antequam enim in veniat, infinita sunt media. et ab in sursum infinita, antequam in a veniat. Quare si hæc impossibilia sunt, et ipsius a et impossibile esse media.","english":"Similarly I speak also in privative syllogisms and propositions, as if A is in no I, either primarily or there is some middle to which A does not belong prior, as if there is that which is in every one, and again this is not also in another prior, as if there is that which is in every 6; for in these too either they are infinite, in those in which it is not in prior things, or one comes to a stop. But in inconvertibles it does not hold similarly, for there is not among those predicable of one another that of which it is predicated first, or last; for all things are related to all similarly, whether the predicates of it are infinite, or both are doubted infinite, unless it happens to be converted similarly, but this indeed as an accident, that however as a predicate.\n\nCHAPTER XVI.\n\nWith the extremes determined, the highest and the lowest, the middles are not infinite.\n\nSince, therefore, it is not possible for the middles to be infinite, if the predicates come to a stop both upward and downward, it is manifest. I say \"upward\" indeed, what is more universal, but \"downward,\" what is particular. For if, with A predicated of C, the middles in which B is are infinite, it is manifest that it will happen to both, that from A downward one can be predicated of another to infinity; for before it arrives, the middles are infinite; and from B upward, infinite, before it arrives at A. Wherefore if these things are impossible, it is also impossible for the middles of A itself to be infinite.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":48,"ref":"p48","source":"Neque enim si aliquis dicat quod hæc quidem quae a contingentia sunt ad invicem, ut et non sint media, illa vero non esse accipe, nihil differt. Quodcunque enim accipio eorum quæ sunt b, erunt ab a, aut infinita media. An non a quo jam prima sint infinita sive statim, sive non statim, nihil differt? quæ enim sunt post hæc, infinita sunt.\n\nCAPUT X VII.\n\nPropositionis negativæ mediate media, quibus revocetur ad immediatam,non esseinfinita,\n\n1llanifestum autem et in privata demonstratione quoniam statur, si quidem in prædicativa statur in utrisque. Sit enim non contingens neque in sursum ab ultimo in infinitum ire (dico autem in quo statur, quod ipsum quidem in alio nullo est, sed in illo aliud ut c) neque a primo in ultimum. Dico autem primum quod ipsum quidem de alio, sed de illo nullum aliud dicitur: si igitur hæc erunt, manifestum quod et in negatione stabitur. Tripliciter au-tem monstratur non esse, aut enim in quo quidem estc, inest omni, sed in quo est nulIi, inest a, ipsum igitur c, et semper alterum spatium necesse est ire in immediata, praedicativum enim est hoc spatium. Sed alterum manifestum est, quod si in alio non est priori, ut in d, hoc indigebit in omni II esse, et si iterum a in alio priore quam non fuerit, illud indigebit in omni esse: quare quoniam in deorsum stat, via, et quae in sursum stabit, et erit aliquid in quo primo non erit a.","english":"For even if someone says that these things which are from contingency in relation to one another, as also that they are not middle terms, but accept that those are not, it makes no difference. For whatever I take of the things that are b, they will be from a, or there will be infinite middle terms. Or does it make no difference whether the things from which the firsts already are are infinite, whether immediately or not immediately? For the things that are after these are infinite.\n\nCHAPTER XVII.\n\nThat the mediate middle terms of a negative proposition, by which it is reduced to an immediate one, are not infinite.\n\nIt is evident also in privative demonstration that a stop is made, if indeed in predicative demonstration a stop is made in both directions. For let it be supposed that it is not possible to go upward from the last term to infinity (I mean that at which a stop is made, which itself is in no other, but another is in it, as c), nor from the first to the last. I mean the first, which itself is said of another, but of which no other is said. If, then, these things are so, it is evident that a stop will also be made in negation. But it is shown in three ways that it is not infinite. For either, that in which c is, is present in every one, but a is present in that in which it is in no one; therefore c itself, and always the other interval, must go to immediates, for this interval is predicative. But the other is evident, that if it is not in some prior, as in d, this will need to be in every one; and if again a is in some prior than that in which it was not, that will need to be in every one. Wherefore, since a stop is made in the downward way, the upward way will also stop, and there will be something in which a first is not.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":49,"ref":"p49","source":"Item si quidem in omni a, in autem nullo, a in nullo erit. Iterum hoc si oportet monstrare, maniFestum est, quod aut per superiorem modum sursum monstrabitur, aut per hunc, aut tertium. Primus quidem igitur dictus est, secundus autem demonstrabitur. Sic autem utique monstrabitur, ut quod in omni est, in autem nullo, si necesse est aliquid esse in b, et iterum si hoc in non erit, aliud vero in est quod in non est, igitur quoniam esse semper superiori stat, stabit et non esse. Tertius autem modus est, si a omni insit,c vero in nullo sit, non in omni c, in quo est a. Iterum autem hoc persuperius dicta aut similiter demonstrabitur. Illis igitur modis statur. Si vero sic est, iterum accipietur in e esse, in quo non in omni e, et hoc iterum similiter. Quoniam autem suppositum est stare et in deorsum, manifestum est quod stabit et quod in non est. Manifestum autem est quoniarn et si nun una via monstretur,sed omnibus,aIiquando quidem ex prima figura, aliquando vero ex secunda, aut ex tertia, quoniam et sic stahitur, finitae enim sunt vix.. Fimta autem finite sumpta pluries, necesse est finiri omnia. Quod quidem igitur in privatione si quidem et inesse statim, manifestum est.","english":"Likewise, if it is in every a, but in no b, then a will be in no b. Again, if this must be demonstrated, it is clear that it will be demonstrated either by the higher method upwards, or by this one, or by a third. The first has indeed been stated, but the second will be demonstrated. It will, however, be demonstrated thus: that which is in every b, but in no c—if something must be in b, and again if this is not in c, but something else is in c which is not in b—therefore, since being always stands to the superior term, non-being will also stand. The third method is: if a is in every b, but c is in no b, then a is not in every c in which b is. Again, this will be demonstrated by the methods stated above or in a similar way. By these methods, then, one comes to a stand. But if it is so, it will again be taken that e is in something in which b is not in every e, and this again in a similar way. Since, however, it has been supposed that there is a stand also in the downward direction, it is clear that there will also be a stand regarding what is not. It is clear, moreover, that even if it is not demonstrated by one way only, but by all—sometimes from the first figure, sometimes from the second, or from the third—there will also in this way be a stand; for the finite things are limited. But when finite things have been taken many times, all things must be limited. That, therefore, in privation, if indeed it immediately stands also in being, is clear.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":50,"ref":"p50","source":"CAPUT XVIII.\n\nPropositionis afffirmativæ infinita. mediatæ, media non esse\n\nSed quid in illis qui quidem logice speculantur, sic manifestum fit. In iis quidem igitur qua: quidem in eo quod quid est prædicantur,manifestum est;si est enim definire, aut si notum est quod qui erat esse, infinita autem non est transire, necesse est finiri in eo quod quid est prædicata.","english":"CHAPTER XVIII.\n\nOn the infinite intermediates of an affirmative proposition, that there is no middle term\n\nBut how this is so in those who speculate logically will become clear as follows. In those things, then, which are predicated in respect of what a thing is, it is manifest; for if definition exists, or if the essence is known, and it is impossible to pass through infinite things, the predicates must be terminated in what a thing is.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":51,"ref":"p51","source":"Universaliter autem sic dicimus, est enim vere dicere album ambulare, et magnum illud lignum esse,etiterum lignum magnum esse, et hominem ambulare, sed alteram est sic dicere, aut illo modo, cum enim album quidem esse dico quod cui accidit album esse, lignum est, sed non quod subjectum signo, album sit, et namque neque quod album est, neque quod quidem album aliquod est, factum lignum est, quare non est aliter quam secundum accidens.Cum aulem lignum album esse dico, non quod aliquod alterum sit album, illi autem accidit lignum esse, ut cum musicum album esse dico, tunc enim quoniam homo est albus, cui acciditesse musicum,dico,sed lignum est subjectum quodquidemet factum est, non cumalterum aliquid sit quam quod quidem lignum est, aut lignum aliquod.Si igitur oportet nomina ponere, sit sic dicere prædicari,sed illo modo,aut nullo modo praedic tri, aut praedicari quidem non simpliciter,sedsecundum accidens prædicatur,est autem tanquam album quidem quod prædicatur,sed sicut lignum est de quo prædicatur.Supponatur ergo prædicatum prædicari gem per de quo prædicatur,simpliciter,sed non secundum accidens. Sic enim demonstrationes demonstrant.","english":"But we speak universally as follows: for it is truly said that the white thing walks, and that that great thing is a log, and again that the log is great, and that a man walks; but the other way of saying it is different from this. For when I say that the white thing is a log, I say that that to which whiteness happens is a log, but not that whiteness is the subject of the predicate; for neither what is white nor some particular white thing has become a log, so it is not otherwise than according to accident. But when I say that the log is white, I do not say that some other thing is white to which it happens to be a log—as when I say that the musical thing is white, for then I say it because the man is white to whom it happens to be musical—but the log is the subject which has itself become such, not when something other than the log itself, or some particular log, is [white]. If, then, one must set down names, let it be said in this way that [the predicate] is predicated, but in that other way either not to be predicated at all, or to be predicated not simply but according to accident. And it is as though the predicate is indeed white, but as the log is that of which it is predicated. Let it be supposed, therefore, that the predicate is predicated of that of which it is predicated simply, and not according to accident. For thus demonstrations demonstrate.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":52,"ref":"p52","source":"Quare in eo quod quid est, aut quoniam quale,aut quantum,aut ad aliquid,aut faciens, aut paticns, aut ubi, aut quando, cum unum de uno prædicabitur.Amplius,substantiam quidern significantia,quod quidem illud est,aut aliquod illu,t quidem significantdequo prædicantur.Quæcunque vero non substantiam significant,sed de aliquo subjecto dicuntur, quod non est,ne'lue quod illud est, neque quod quidem illud aliquid est,accidentia sunt,ut de homine album.Neque enim est homo, neque quod quidem album est, neque quod quidem album est aliquid, sed animal forsan,quod quidem enim animal est, homo est. Quaecunque vero non substantiam sigoificant, oportet de aliquo subjecto prædicari,et non esse quid album,quod non cumaJtefum aliquod sit, album est. Species enim valeant, et genera,monstra enim sunt,et si sint,nibil ad rationem sunt,demonstrationesenim dehujusmodi sunt.Amplius,si non est hoc hujus qualitas,et illud hujus, neque;qualitatis quaJitas,impossibile est aeque praedicari ad invicem sic,eed verum quidem contingit dicere sic, æque autem vere prædicari non contingil.An enim sicut substantia prædicabitur, aut ut genus, aut ut differentia præd;cari? haec autem ostensa sunt,quoniam non erunt infinita, neque in sursum, neque in deorsum,ul homo bipes,hoc animal.","english":"Therefore in what something is, or of what quality, or how great, or in relation to something, or acting, or undergoing, or where, or when, when one thing is predicated of one thing. Moreover, those things that signify substance signify what that thing is, or some particular this; and they signify that of which they are predicated. But whatever things do not signify substance, but are said of some subject, which is not, neither what that thing is, nor what some particular this is, are accidents, as white of a man. For neither is man, nor is white, nor is white some particular thing, but perhaps animal; for what animal is, is man. But whatever things do not signify substance must be predicated of some subject, and it is not the case that white is something which is not white when it is some particular thing. For let species and genera have force—for they are monstrosities, and even if they exist, they contribute nothing to the account; for demonstrations are about such things. Moreover, if this is not the quality of this, and that of that, nor is there a quality of a quality, it is impossible for them to be predicated equally of one another in this way, but it is possible to say something true in this way, yet it is not possible for them to be predicated equally truly. For shall it be predicated as substance, or as genus, or as differentia? But these things have been shown, that they will not be infinite, neither upward nor downward, as man is biped, this is animal.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":53,"ref":"p53","source":"hoc autem alterum est, neque animal de homine,boc autem de Callia, boc autem de alio in eo quod quid est,substantiam enim omnem est definire hujusmodi,infinitaautemnon est transire intelligen. tem,quare neque in sursum,neque in deorsum infinita sunt,illam enim non est definire, de qua inHnita prædicantur.Sic igitur genera ad invicem,non æqualiter prædicantur,erit enim ipsum, quod quidem ipsum aliquid est, neque tamen de qualitate, aut aliorum nullo, nisi secundum accidens prædicabitur, omnia enim baec accidunt, et de substantiis prædicantur,sed quoniam neque in sursurn,infinita sunt. De unoquoque enim praedicatur quod significat aut quantum aliquid,aut quale aliquid,aut hujusmodi quae Bunt in substantia, hæc autem finita sunt, et genera prædicamentorum finita, aut enim quale,aut quantum,aut ad aliquid, aut facere, aut pati, aut ubi, aut quando. Suppositum autem est unum de uno prædicari, ipsa autem de ipsis quæcunque noa ad aliquid sunt,prædicari,non dicimus, accidentia enim sunt omnia,sed haec quidem secun. dum seipsa, alia vero secundum alterum modum.","english":"But this is another point: neither is animal predicated of man, nor this of Callias, nor this of another, in respect of what something is; for every substance is defined by such means, but it is not possible for the intellect to pass through things that are infinite. Therefore neither upward nor downward are they infinite, for that of which infinite things are predicated cannot be defined. Thus, then, genera are not predicated of one another equally; for that which is itself something, yet not in respect of quality or any of the others, will be predicated of nothing except according to accident. For all these things are accidents and are predicated of substances, but since neither upward are they infinite. For of each thing is predicated either what signifies a quantity, or a quality, or such things as are in substance; and these are finite, and the genera of the categories are finite: for it is either quality, or quantity, or relation, or acting, or undergoing, or where, or when. But it has been assumed that one thing is predicated of one thing; however, we do not say that those things which are not in relation are predicated of themselves, for all are accidents, but some according to themselves, others in another way.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":54,"ref":"p54","source":"Hæc autem omnia de subjecto quodam prædicari dicimus,accidens alltem nonesse subjectum aliquod, nihil enim talinm ponimus esse,non quod alterum aliquod esse dicitur,sed ipsum de aliis.et alia quidem de alio, neque in sursum, ergo unum de uno, neque in deorsum esse dicetur,de quibus enim dicuntur accidentia,quæcunque in substantia uniuscujusque sunt, hæc autem non sunt infinita,sed sursum ip8a quoque et accidentia utraque non infinita sunt.Necesse est ergo esse aliquid, de quo primum prædicetur, et de hoc aliud,et hoc stare, et esse aliquid quod non amplius,neque de alio priori, neque de illo aliud prius prædicetur. Unus quidem igitur modus demonstrationis, dicitur hic. Adhuc autem alius,si de quibus priora quaedam prædicantur,est horum demonstratio,quorurn autem est demonstratio,neque potius habere possibile est ad ipsa,quam scire,neque scire est sine demonstratione, si autem boc,per bæc sit notum. Haec autem nescimus, neque melius habemus ad ipsa quam scire,neque per bæc notum sciemus. 5i igitur est aliquid scire per demonstrationem simpliciter.","english":"We say that all these things are predicated of some subject, but that an accident is not some subject; for we posit that no such thing exists—not that which is said to be some other thing, but the thing itself predicated of others. And some things are said of another, and not upward, therefore one of one, nor downward; for the things of which accidents are said, whatever are in the substance of each, these are not infinite, but upward these themselves and both accidents are not infinite. It is necessary, therefore, that there be something of which it is first predicated, and another of this, and that this come to a stop, and that there be something which is no longer predicated either of another prior thing or of which another prior thing is predicated. One mode of demonstration, then, is said to be this. But there is yet another: if there is demonstration of those things of which certain prior things are predicated, but of those things of which there is demonstration, it is not possible to be disposed toward them better than to know, nor is knowledge without demonstration; but if this is so, let it be known through these. But these we do not know, nor are we disposed toward them better than to know, nor shall we know what is known through these. If, then, there is anything to know simply through demonstration.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":55,"ref":"p55","source":"et non ex aliquibus, neque ex suppositione,necessarium est stare prædicationes mediorum, si enim non steterint, sed est semper acceptio in superius, omnium erit demonstralio,quare si infinita non possibile est pertraasire,quorum est demonstratio,hæc non sciemus per demonstrationem.Si ibitur neque melius habemus ad ipsa quam scire, non erit scire per demonstrationem simpliciter, sed ex suppositione. Logice quidem igitur ex his utique aliquis credat, de eo quod dictum est. Analytice autem manifestum est per bæc velocius, neque in sursum, neque in deorsum infinita prædicata contingit esse in demonstrativi scientiis, de quibus intentio est; demonstratio enim est ex his quaecunque ipsa quidem insunt secundum seipsa rebus, secundum seipsa vero dupliciter i quæcunque enim in illis insunt in eo quod quid est,ct in quibus ipsa in eo quod quid est insunt ipsis,ut in numero impar, quod inest quidem numero,, est autem ipse numerus in ratione ipsius, et iterum multitudo, aut divisihiJe,in ratione numeri, horum autem neutr:t contingit infinita esse, neque ut impar numeri.Iterum enim si impar illud insit, cui ineratexistenti hoc, si est primum numerus,erit iis uxinsunt ipsi.Si igitur non contingit infinita hujusmodi esse in uno,neque in sursum erunt intinita,at vero necesse est omnia inesse primo, ut nurnero,et inillis numerum,quare convertibilia erunt, sed non excedentia.","english":"And not from certain things, nor from a supposition, it is necessary that the predications of the middle terms come to a stop. For if they did not stop, but there is always an taking of something higher, there would be demonstration of all things; wherefore, if it is not possible to pass through infinite things, we shall not know by demonstration those things of which there is demonstration. If, then, we are no better disposed toward them than toward knowing, there will be no knowing simply by demonstration, but only from a supposition. Logically, then, from these considerations anyone might believe what has been said. But analytically it is manifest through these more quickly, that neither upward nor downward is it possible for the predicates to be infinite in the demonstrative sciences, about which our intention is. For demonstration is from those things which are present in the things themselves according to themselves, and according to themselves in two ways: for whatever things are present in them in that which is what it is, and those things in which the things themselves are present in that which is what it is—as in number, the odd, which is present in number, and number itself is in the account of it; and again, multitude, or the divisible, is in the account of number. But neither of these can be infinite, nor can the odd be infinite of number. For again, if the odd were present in that to which it is present as existing in it, if number is first, it will be present in those things in which it is present. If, therefore, it is not possible for such things to be infinite in one thing, neither will they be infinite upward; but it is necessary that all be present in the first, as in number, and number in those things; wherefore they will be convertible, but not exceeding.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":56,"ref":"p56","source":"Neque tamen quæcunque sunt in eo quod quid est,neque haec infinita sunt,neque esset definire: quare si pradicataper se quidem omnia dicuntur, haec autem non infinita sunt,stabunt utique in sursum, quare et in deorsum, si autem sic est,et quae sunt in medio duorum terminorum semper sunt finita. Si vero hoc est, manifestum jam est,et demonstratio non quod necesse est principia esse, et non omnium esse demonstrationem, quod quidem diximus quosdam dicere,jugta principium, si enim principia sunt. Non omnia sunt demonstrubilia,neque in infinitum possibile ire, esse enim horum quodlibet, nibil est aliud quam esse nullum spatium sine medio,et indivisibile,sed omnia divisibiJia.lntus enim immittendoterminum,sed non assumendo demonstratur quod demonstratur, quare sihoc in infinitum contingit ire,contingit utique duorum terminorum infinita esse interius media,sed hoc impossibile est, si praedicationes steterint in superius, et in inferius: quod autem stent, monstratum est logice prius, analytice vero nunc.","english":"Yet neither are all the things that are in the what-it-is infinite, nor would there be definition; wherefore if all predicates are said per se, and these are not infinite, they will certainly come to a stop in the upward direction, and hence also in the downward direction; and if this is so, the terms that lie between two extremes are always finite. But if this is the case, it is already manifest both that demonstration requires principles to exist and that not everything is demonstrable—which, as we said, some people assert—in accordance with the principle, if indeed there are principles. Not all things are demonstrable, nor is it possible to proceed to infinity; for the existence of any of these is nothing other than there being no interval without a middle and indivisible, but all things are divisible. For what is demonstrated is demonstrated by inserting a term within, not by assuming it; wherefore if it is possible to proceed to infinity in this, it follows that the intermediate terms between two extremes are infinite, but this is impossible if predications come to a stop both upward and downward; and that they do stop was shown logically earlier, but analytically now.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":57,"ref":"p57","source":"CAPUT XIX.\n\nElementa monstrandarum mediatarum non infinita esse.\n\nMonstratis autem his, manifestum est si aliquid idem insit duobus, uta et in c, et in d, non prædicante altero de altero, aut nullo modo, aut non de om ni,quod non semper secundum commune aliquid inerit,ut isosceIis,et scaleno, æquales duobus rectis habere, secundum commune aliquid in est, secundum enim quod figura quædam sunt, etnon secundum alterum. Hoc autem non semper sic se habet. Sit enim secundum quod a,in et d, erit manifestum igiturquod in cd secundum aliud commune est et illud secundum alterum, quare duorum terminorum medii infiniti utique inciderunt termini, sed hoc est impossibile, secundum igitur aliquid commune inesse,non necesse est semper idem pIuribus,quoniam quidem erunt immediata spatia. In eodem tamen genere, et ex eisdem atomis necesse est terminos esse, siquidem iis quæ per sunt,erit commune, non enim erat ex alio genere in aliud genus descendere quae demonstrantur.Manifestum est autem quoniam et cum a in sit, siquidem est aliquid medium, est demonstrare quod a in sit, et elementa hujus sunt bæc et tot quot media sunt,irnmediatae enim propositiones suntelementa,aut omnes, aut universales,. si vero non est medium, non amplius erit demonstratio, sed in principia via est hæc. Similiter autem erit et si a in non sit,siquidem enim aut medium est, aut prius cui non inest, ent demonstratio.","english":"CHAPTER XIX.\n\nThat the elements of demonstrated middle terms are not infinite.\n\nHaving established these points, it is clear that if the same thing belongs to two subjects, as A to both C and D, with neither predicated of the other, either in no way or not universally, it will not always belong in virtue of something common—as for isosceles and scalene triangles, to have angles equal to two right angles belongs to them in virtue of something common, namely in that they are a certain figure, and not in virtue of one or the other. But this does not always hold so. For let it be in virtue of A that it belongs to both C and D; it will be clear, then, that it belongs to C and D in virtue of some other common term, and that in turn in virtue of another, so that the middle terms of two terms would turn out to be infinite—but this is impossible. Therefore it is not necessary that it always belong in virtue of something common to several things, since there will be immediate intervals. Nevertheless, the terms must be in the same genus and from the same indivisibles, since whatever is predicated per se will have something common; for it was not the case that things demonstrated descend from one genus into another genus. It is clear, moreover, that when A belongs, if there is some middle term, it is possible to demonstrate that A belongs, and the elements of this are these, as many as the middle terms are; for the immediate propositions are the elements, either all or the universal ones. But if there is no middle term, there will no longer be demonstration, but this is the way to the principles. It will be the same also if A does not belong; for if either there is a middle term, or a prior term to which it does not belong, there will be demonstration.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":58,"ref":"p58","source":"Si vero non sit medium,non est demonstratio, sed principia, et elementa sunt tot quotsunt lermini,borum enim propositiones principia demonstrationis sunt,et sicut quædam principia suntindemonstrabilia quod sit hoc iIlud,et quod sit hoe in illo, sic quod non erit boc illud, neque quod sit hoc in illo.Quare haec quidem esse aliquid, alio non esse aliqllid,erunt principia,Cum ergo indigat monstrare aliquid, accipiendum qU'ld de primum prædicetur. Sit c, et de boc similiter a, et sic semper eunti nunquam extra, erit propositio, deque si esse ipsius a accipiatur ut demonstretur, sed semper medium densetur quousqueindivisibilia fiant, et unum,est autem unum, cum immediatum fiat, et una propositio simplex est immediata, et quemadmodum in aliis est principium simplex. Hoc autem non idem ubique est,sed ingravi quidem uncia in melodia autem diesis,aliud autem in alio,sic est in syllogismo Ullum, propositio immediata, in demonstratione autem, et scientia, intellectus. In ostensivis igitur syllogismis ejus quod est,nibil cadit extra,Sed in privativis,ubi quidem quod oportet esse, nihil cadit extra hoc, ut si a in per non inest, si enim in quidem omni f., est autem a in nullo c. Iterum si indigeat quod in c, a nullo sit, medium accipiendum est ipsius a etc, et sic semper procedet.","english":"If, however, there is no middle term, there is no demonstration, but the principles and elements are as many as the terms; for the propositions of these are the principles of demonstration. And just as certain principles are indemonstrable—namely, that this is that, and that this is in that—so too [are the principles] that this will not be that, nor that this is in that. Wherefore these—that something is, and that something is not—will be principles. Since, therefore, one needs to show something, one must take what is predicated primarily of something. Let it be C, and of this similarly A, and so proceeding always one will never go outside; there will be a proposition, and if the being of A itself is taken as to be demonstrated, but the middle term is always condensed until things become indivisible and one. And it is one when it becomes immediate, and one simple proposition is immediate, and just as in other things there is a simple principle. But this is not the same everywhere: in a heavy body, indeed, an ounce; in melody, a diesis; another in another; so in syllogism there is a certain immediate proposition, but in demonstration and knowledge, intellect. In ostensive syllogisms, therefore, of that which is, nothing falls outside. But in privative ones, where indeed that which ought to be is [concerned], nothing falls outside this: as if A is not present in [something] through [a middle term]; for if it is in every F, but A is in no C. Again, if one needs [to show] that A is in no C, the middle term of A itself must be taken, and so on, and thus it will always proceed.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":59,"ref":"p59","source":"Si vero indigeat monstrare quod in e non sit,eo quod est in quidem omni, in e autem nulIo,aut non in omni,enunqullm extra cadit, hoc autem est,cui non oportet inesse.ln tertio autem rnodo,neque a quo oportet,neque quod oportet privari,nequaquam extra ibit.\n\nCAPUT XX.\n\nQuod demonstratio universalis præstantior sit particulari..\n\nCum autem sit omnis demonstratio,alia quidem universalis, alia vero particularis, et haec quidem catbegorica, illa vero privativa, dubitabitur qualis potior sit,simiIiter autem et de ea,quæ demonstrare dicitur,et deducenti ad impossibile demonstratione. Primum quidem igitur intendamus de universaliet particulari. Ostendentes autem hoc, et de ea quae demonstrare dicitur,et quae est ad impossibile, dicemus.Videbiturigitur fortassis utique quibusdam sic intendentibus, quod particularis est potior, si enim secundum quam magis scimusdemonstrationem, potior demonstratio est,hæc enim virtus demonstrationis. Magis autem scimus unumquodque cum ipsum cognoscimus secundum ipsum,quam se. cundum aliud,ut musicum Coriscum,quando cognoscemus quod Coriscus musicusest,quamquod homo musicus sit.","english":"If, however, one needs to show that it is not in E—because it is in all of that which is in the whole, but in no E, or not in every E—then something falls outside, and this is that to which it ought not to belong. But in the third mode, neither that from which it ought nor that which ought to be deprived will in any way fall outside.\n\nCHAPTER XX\n\nThat universal demonstration is more excellent than particular.\n\nSince every demonstration is either universal or particular, and the one is categorical while the other is privative, it will be asked which is the stronger; and likewise concerning that which is called demonstration by reductio ad impossibile. First, then, let us consider the universal and the particular. Having shown this, we shall also speak of that which is called demonstration and of that which leads to the impossible. It will perhaps seem to some who consider the matter thus that the particular is stronger; for if a demonstration is stronger by which we know more, then this is the virtue of demonstration. But we know each thing more when we know it according to itself than according to another—as the musical Coriscus, when we know that Coriscus is musical, than that a human being is musical.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":60,"ref":"p60","source":"Similiter autem et in aliis-Sed universalis quoniam aliud,non quoniam ipsum fortassedsmonstrat, ut quoniam isosceles habet tres angulos æquales duobus rectis,non quoniam isosceles, sed quoniam triangulus,sed particularis quoniam ipsum est; si igitur potior est quae est secundum ipsum, hujusmodi autem est particularis,et universali magis et potior utique secundum partem demonstratio erit.","english":"Similarly also in other cases—but the universal demonstration shows that something belongs for another reason, not because of the subject itself, perhaps; for example, that the isosceles has three angles equal to two right angles, not because it is isosceles, but because it is a triangle. But the particular demonstration shows it because of the subject itself. If, then, the demonstration that proceeds from the subject itself is more valuable, and the particular demonstration is of this sort, then the demonstration according to the part will be both more universal and more valuable.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":61,"ref":"p61","source":"Amplius,siuniversaIe quidemnon eataliquidpraeter singularia,demonstratio autem opinionem conficit esse aliquid hoc de quo demonstrat,et quamdam naturam esse hanc in iis quae sunt(ut trianguli praeter quosdarn,et figura praeter quasdam, et numeri praeter quosdam numeros), potior autem est quae est de esse quam de non esse, et propter quam non errabitur, quam propter quam errabitur; est autem universalis hujusmodi (procedentes enim demonstrant universale quemadmodum de eo quod est proportionale ut quod sit tale, erit proportionale quod neque linea, neque numerus, neque solidum, neque planum est, aed praeter hæc aliquid),si igitur universalis magis haec est,et de eo quidem quod est minus,universalis quam particuIaris,et fecitopinionem faIsam,indignior utique erit universalis particuIari.Et primum quidem nihilrnagis in universali quam in particulari altera ratio est, si enim quod duobus rectis inest,,non est secundum quod est isosceles, sed secundum quod triangulus est, cognoscens quoniam isosceles habet tres inquantum ipsum est, minus cognovit quam cognoscensa, quoniam triangulus est, et omnimo si non quidem secundum quod sit triangulus, et postea monstrat, non erit utique demonstratio; si vero sit cognoscens unumquodque secundum quod unumquodque est, magis cognovit.","english":"Further, if the universal is not something apart from singulars, but demonstration produces the opinion that there is something of this sort about which it demonstrates, and that there is a certain nature of this in the things that exist (as of triangle apart from certain triangles, and figure apart from certain figures, and number apart from certain numbers), and the demonstration that concerns being is more powerful than that which concerns non-being, and that by which one will not err is more powerful than that by which one will err; but the universal is of this sort (for those who proceed demonstrate the universal in the way that, concerning what is proportional, they show that such a thing exists—that there will be something proportional which is neither line nor number nor solid nor plane, but something besides these)—if, therefore, the universal is more of this sort, and the universal is concerned with what is less, and it has produced a false opinion, then the universal will be less worthy than the particular. And first, there is no more reason in the universal than in the particular; for if having angles equal to two right angles belongs not insofar as it is isosceles but insofar as it is triangle, one who knows that the isosceles has three angles insofar as it is itself has known less than one who knows that the triangle does, and in general, if one does not demonstrate it insofar as it is triangle, there will be no demonstration; but if one knows each thing insofar as each thing is, one has known more.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":62,"ref":"p62","source":"si igitur triangulus in plus est, et eadem ratio, et non secundum aequivocationem triangulus est, et inest omni triangulo quod est duobus rectis aequales habens, non utique edt lriangulusinquantum isosceles, sed isosceles secundum quod triangulus hujusmodihabet tres angulos. Quare uni. versaliter sciens magis cognovit secundum quod est, quam particuIariter,potiorestergo universalis qnam particularis. Amplius, siquidem sit quaedam ratio una, et non aequivocatio, universale erit utique nil minus secundum partem quibusdam, sed magis est quanto incorruptibiliora suntillis,quæ vero secundum partem sunt corruptibilia magis. Amplius, nec una necessitas est opinari abquid esse hoc præter hæc, quoniam ostendunt unum nihil magis quam in aliis quaecunque non aliquid significant, sed aut quale, aut ad aliquid, aut augere; si ergo, non demonstratio causa est, sed audiens. Amplius, si demonstratio est syllogismus demonstrativus qui fit causae et propter quod, universale magis causa; cui enim per se inest aliquid, hoc idem ipsi causa est:universale autem primum, causa ergo universale est, quare et demonstratio dignior est, magis enim causæ est universale, et ejus quod propter quid est. Amplius, usque ad hocquærimus propter quid, etenim tunc opinamur scire, cum non sit aliquid aliud quam hoc aut quod fiat, aut quod sit, finis enim et terminus ultimus jam sic est, ut cujus causa venit?","english":"If, then, triangle is predicated of more things, and the definition is the same, and it is not called triangle by equivocation, and there belongs to every triangle to have angles equal to two right angles, then it is not insofar as it is isosceles, but the isosceles, insofar as it is a triangle, has three angles of this sort. Therefore one who knows universally has known more insofar as it is, than one who knows particularly; therefore the universal is more powerful than the particular. Further, if indeed there is some one definition, and not equivocation, the universal will nonetheless be no less in respect of the parts in certain cases, but is more insofar as they are more incorruptible than those things which are in respect of the parts and are more corruptible. Further, there is not one necessity of opining that something is apart from these things, since they show one thing no more than in other cases, whatever do not signify something, but either a quality, or a relation, or increase; if, then, it is not the demonstration that is the cause, but the hearer. Further, if demonstration is a demonstrative syllogism that is concerned with the cause and the because, the universal is more the cause; for that to which something belongs per se, this same thing is the cause to it; but the universal is first, therefore the universal is the cause, wherefore the demonstration is also more worthy, for the universal is more of the cause, and of that which is the because. Further, it is up to this point that we seek the because, for indeed then we think we know, when there is nothing else than this either that it comes to be, or that it is, for the end and the last terminus is already thus, as for the sake of what has it come?","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":63,"ref":"p63","source":"ut accipiat argentum. Hoc autem est quatenus reddat cui debuit. Hoc autem utfioo injuste agat,etsic procedentescum non sit amplius propterquid,nec alteriuscausa,propter hoc sicut propter finem dicimus venire, et esse, et fieri, et tunc est scire maxime propter quid venit; si igitur se habetsimiIiter, etin omnibus causis, et quae sunt propter quid, in iis autem quæcunque sic sunt causæ,sicut quae est cujuscausasic scimus rnaxime,et in aliis igitur tunc maxime scimus,cum non amplius sit hoc quoniam aliud est:cum igitur cognoscimus quidem quod quatuor qui extra sunt æquales sunt, quoniam isosceles, adhuc deest propter quid isosceles? quia triangulus,et hoc, quia est figura rectis lineiscontenta.Si autem hoc non amplius propter quod aliud,tunc maxime scimus,universale est autem tunc,universalis igitur potior.Amplius quantocunque utique magis secundum partes est,in innnita cadit,universale autem in sirnpIex,et in finem, sunt autem secundum quod infinita non scibilia,sed secundum quod finitascibilia sunt,secundum utique quod universalia, magis scibilia sunt, quam quae sunt secundum partem demonstrabilia,ergo magis un iversalia.De magis demonstrabiltbus autem magis est demonstratio.sirnul enim magis ad aliquid sunt, dignior igitur universalis est,quoniam quidem et magis demonstratio est.","english":"so as to receive silver. But this is insofar as he should give it back to the one to whom he owed it. But this is so that he not act unjustly, and thus proceeding, when there is no longer a \"for the sake of what,\" nor a cause of another thing, for the sake of this, as for the sake of an end, we say he comes, and is, and is made, and then one knows most of all for the sake of what he came; if, then, it holds similarly also in all causes, and those which are for the sake of what, and in those things, however many are causes in this way, as which is the cause of which, we know most of all, and in other things, therefore, then we know most of all, when there is no longer this because another is: when, therefore, we know indeed that the four exterior [angles] are equal, because it is isosceles, there still remains the question why [it is so] for the isosceles? because it is a triangle, and this, because it is a figure contained by straight lines. But if this is no longer because of another, then we know most of all; but it is then universal, therefore the universal is more powerful. Moreover, by however much it is more according to parts, it falls into the infinite, but the universal into the simple, and into the end; but things according to the infinite are not knowable, but according to the finite they are knowable; according to that, therefore, which is universal, they are more knowable than those which are demonstrable according to part, therefore the more universal [are more knowable]. But of the more demonstrable things the demonstration is more; for at the same time they are more in relation to something, therefore the universal is more worthy, since indeed it is also more a demonstration.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":64,"ref":"p64","source":"AmpIius,si magis eligenda est secundum quam hoc et aliud, quam secundum quam hoc solum eognovit, universale autem babens, cognovit particulare, hoc autem, universale non scivit,quare et sic utique magis eligenda erit universalis.Amplius autem et sic.UniversaIe enim magis scire est eo quod est per medium demonstrare,cum propius sit principio, proxime autem immediatum est, hoc autem est principium.Si igitur quae ex principio est ea qua: non ex principio, quae magis ex principio ea quae minus est,certior est demonstratio,estautem huju8modi universalis magis,dignior utique erit universalis, ut si oportet monstrare a de d, media aulem siol in quibus est bc,magis autem sursum sit G quam c, quare sper magis est universalis, sed eorum quae dicta sunt quaedam logica sunt.Maxime autem manifestum est quod universalia magis praecipua sit, quoniam propositionum quidem hanc priorem habentes, scimus quodammodo, et pOEleriorem et habemus potentia, ut si aliquis cognoverit quod omnis triangulus habeat tres duobus rectis æquaIcs, scivit quodam modo et quod isosceles duobus rectis potentia sit,et si non cognovit isosceles quod triangulus sit,hanc autem babens propositionem, nullo modo universale cognovit, neque potentia, neque actu. Et universalis quidem intelligibilis est, sed particularis in sensu perficitur.Quod igitur universalis dignior sit particulari, tot nobis dicta sint.","english":"Further, if that which is more to be chosen is that according to which this and another thing is known, than that according to which this alone is known, and one who has the universal knows the particular, but this one did not know the universal, then even so the universal will in any case be more to be chosen. Further, also in this way. For to know the universal is more than to demonstrate that which is through the middle term, since it is nearer to the principle, and the immediate is nearest, and this is the principle. If, therefore, the demonstration that is from the principle is more certain than that which is not from the principle, and that which is more from the principle is more certain than that which is less so, and the universal is of this sort more, then the universal will be more worthy, as if one must show a from d, and the middle terms are those in which are b and c, and g is higher than c; therefore that which is through g is more universal. But some of the things said are logical. But it is most manifest that universals are more principal, since when we have the prior of the propositions, we know in a certain way also the later one and have it in potentiality, as if someone has known that every triangle has three angles equal to two right angles, he has known in a certain way also that the isosceles triangle has [angles equal to] two right [angles] in potentiality; and if he did not know that the isosceles is a triangle, but has this proposition, he has in no way known the universal, neither in potentiality nor in act. And the universal is indeed intelligible, but the particular is perfected in sense. That therefore the universal is more worthy than the particular, let so much have been said by us.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":65,"ref":"p65","source":"CAPUT XXI.\n\nQuod demonstratio affirmativa præstantior evadat negativa.\n\nQuod autem monstrativa sit dignior privativa,hinc manifestum est,sit enim haec demonstratio dignior (aI]is eisdem existentibus)aut ex minoribus quæstionibns,aut suppositionibus, aut propositionibus. Si enim notae sunt similiter velocius cognoscere per hoec erit, hoc autem appetibilius est, Ratio autem proposttionis quod melior sit ex minoribus, universaliter estsic,si enim contingitsimiliter cognitaesse mediæ, priora autem notiora suet. Si autem per media demonstratio eorum,quæ sunt cd quod a in sit,allera autem demonstratio quod a in sit per similiter igitur se babet hoc quod a in sit.et quod a in e sit,sed quod a in sit prius est, et co. gnoscibilius quam quod a in e, per hoc enim illud demonstratur: credibilius autem est per quod. Et quæ per pauciora demonstratio, potior aliis eisdem existentibus. Utraeque quidem per terminos tres et propositiones duas monstrant,sed hæc quidem esse aliquid accipit,illa vero et esse,et non esse aliquid. Per plura itaque, quare dignior est.Amplius, quoniam ostensum est impossibile per utramque privativarum propositionum fieri syIlogisrnum,sed oportere quidem hujusmodi esse unam,aliam vero quoniam est.","english":"CHAPTER XXI.\n\nThat affirmative demonstration is more excellent than negative.\n\nThat demonstrative [demonstration] is more worthy than privative [demonstration] is clear from this: let this demonstration be more worthy (with the same things existing) either from fewer questions, or suppositions, or propositions. For if they are known similarly, it will be possible to know more quickly through these; and this is more desirable. The reason of the proposition that it is better from fewer is universally as follows: for if it happens that the middle terms are known similarly, yet the prior ones are more known. But if demonstration of the things that are is through middle terms, to the effect that A is in C, and another demonstration that A is in C through similar [terms], then this, that A is in C, and that A is in E, stand similarly; but that A is in C is prior and more knowable than that A is in E, for through this the latter is demonstrated; and that through which [something is demonstrated] is more credible. And the demonstration through fewer [terms] is more powerful than others, with the same things existing. Both indeed show through three terms and two propositions, but the one assumes that something is, while the other [assumes] both that it is and that it is not something. Therefore [it proceeds] through more [assumptions], wherefore it is more worthy. Further, since it has been shown to be impossible for a syllogism to be made through both privative propositions, but it is necessary that one be of this sort, and the other that [something] is.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":66,"ref":"p66","source":"Amplius,præter hoc oportet et hoc accipere,prædicativas enim augmentata demonstratione necesse est fieri plures,privativasautem impossibile, plures una in omni syllogismo esse.Sit enim in nullo esse a in quibus est b, in autem omni sit b, si igitur opus est rursus augere utrasque propositiones, medium injiciendum est, hujus quidem a sit d, sed sit e,e igitur manifestum est praedicativum esse,sed de quidem prædicativum, a autem de tanquam privativum ponitur: enim de omni b, sed a oportet in nullo esse,fit ergo una privativa propositio.Idem autem modus est et in aliis syllo gismis. Semper enim medium prædicativorum terminorum,prædicativum in utraque est,sed privativi in altera privativum necesse est esse,quare hæc una hujusmodi fit propositio,aliæ vero prædicativæ. Si igitur notius est per quod demonstratur, et credibilius, demonstratur autem privativa quidem per prærdicativam,hæc autem per illam non demonstratur, prior ergo, et notiorn etcredibilior cum sit, melior itaque erit.Amplius,si principium syllogismi propositio universalis sit immediata, est autem ut in monstrativa prædicativa,in privativa autem,negativa prior, et notior (per affirmativam enim negativa nota) et prior affirmativa est, sicut esse prius est non esse. Quare potius est principium monstrativæ quam privativæ, dignioribus autem principiis utitur dignior.","english":"Further, besides this, one must also accept this: with an augmented demonstration, affirmative propositions must become more numerous, but it is impossible for privative ones to be more than one in every syllogism. For let A be in none of the things in which B is, but let B be in every [thing]. If, then, there is need again to augment both propositions, a middle term must be inserted: of this [B], let D be [the middle], but let it be E. E, therefore, is manifestly affirmative; but D is predicated affirmatively of B, while A is posited as privative of D: for D must be in every B, but A must be in no D. There results, therefore, one privative proposition. The same mode applies also in other syllogisms. For always the middle term of affirmative terms is affirmative in both [premises], but of a privative [term] it must be privative in one [premise]. Wherefore this one proposition becomes of this sort, but the others are affirmative. If, therefore, that through which something is demonstrated is more known and more credible, and a privative [conclusion] is demonstrated through an affirmative [premise], but this [affirmative] is not demonstrated through that [privative], then the former is prior, and since it is more known and more credible, it will accordingly be better. Further, if the principle of a syllogism is a universal immediate proposition, and as in demonstrative [syllogisms] the affirmative [is prior], so in privative [syllogisms] the negative is prior and more known (for the negative is known through the affirmative), and the affirmative is prior, just as to be is prior to not to be. Wherefore it is more [a principle] of demonstrative than of privative [demonstration]; and [demonstration] that uses more worthy principles is more worthy.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":67,"ref":"p67","source":"Adhuc principalior est, sine enim monstrativa non est privativa,Quod quidem prædicativa, privativa dignior sit, manifestum est.\n\nCAPUT XXII.\n\nDemonstrationem ostensivam incommodum.potiorem esse ea quæ i ducit ad\n\nEt ad impossibile ducente, oportet autem scire quæ differentia sit ipsarum.Si igitur a in nullo b, in autem omni b, necesse est in nullo esse a; sic igitur acceptis, ostensiva privativa erit demonstratio, quoniam a in non erit. Quæ vero est ad impossibila sic se habet,si opus est demonstrare quod a in non sit,accipiendum est a esse in b, et in c, quare accidit a in esse. Hoc autem si notum, et concessum quod ipsum est impossibile esse, non igitur possibile est a in esse.Si ergo in concessum est inesse, a in impossibile est esse, termini igitur similiter ordinantur.Differl autem quo, qualis sit notior privativa propositio, utrum igitur quia a non inest,an quia a c,cum igitur est conclusio notior quoniam non est,quod est impossibile, fit dernonstratio,cum autem in syIlogismo sit,demonstrativa est.Natura autem prior est,quæ est quod a in non sit, quam a in e non sit, priora enim conclusione sunt,ex quibus est conclusio,est autem quæ est a in non esse,conclusio,a autem in ex quibus est conclusio. Non enim si contingit removeri aliquid, hoc concI usio est, illa autem ex quibus sunt, sed boc quidem ex quo syllogismus est,utiqlle sic se ha.","english":"Further, it is more principal; for without the ostensive demonstration there is no privative demonstration. That the predicative demonstration is indeed more worthy than the privative is manifest.\n\nCHAPTER XXII.\n\nThat the ostensive demonstration is more powerful than the one that leads to the impossible.\n\nAnd concerning the one that leads to the impossible, one must know what difference there is between them. If, then, A is in no B, but is in every C, it is necessary that A be in no C; with terms thus taken, the ostensive privative demonstration will be that A is not in C. But the demonstration that leads to the impossible is as follows: if it is needful to demonstrate that A is not in B, one must assume that A is in B, and in C, whence it happens that A is in C. But if this is known and conceded, namely that it is impossible for it to be, then it is not possible for A to be in B. If, therefore, it is conceded that A is in B, it is impossible for A to be in C; the terms, then, are ordered similarly. But they differ in this: which of the two is the more known privative proposition—whether it is that A is not in B, or that A is not in C. For when the conclusion is more known, namely that it is not, which is the impossible, the demonstration comes about; but when it is in the syllogism, it is demonstrative. By nature, however, that which is [the proposition] that A is not in B is prior to that which is that A is not in C; for the things from which the conclusion comes are prior to the conclusion. And that which is that A is not in B is the conclusion, while that A is not in C is among the things from which the conclusion comes. For it is not the case that, if it happens that something be removed, this is the conclusion, and those are the things from which it comes; but this is that from which the syllogism is, and that is as follows.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":68,"ref":"p68","source":"bet, ut aut sicut totum ad partern,aut ut pars ad totum se habet, sed quae sunt a c, et a propositiones,non sic se habent ad invicem. Si igitur ex 3ignioribus et credibilioribus digniur est,sunt autem utraeque ex non esse aliquid, credibiles, sed hæc quidem ex priori,ilia vero ex posteriori,potior utique simpliciter erit ea quæ est ad impossibile,privativa demonstratio,quare et hac dignior prædicattva. Manifestum est ergo quod ea quae est ad impossibile, potior est.\n\nCAPUT XXIII.\n\nQuæ scientia certior, quæ una, demonstrationes. quæ aUem, et ejusdem plures esse posse","english":"but they do not relate to one another as whole to part or part to whole; whereas the propositions derived from c do not so relate to one another. If, then, the more worthy is that which proceeds from things more known and more credible, and both are credible from something's not being so, but the one from what is prior and the other from what is posterior, then the demonstration to the impossible—the privative demonstration—will be more worthy without qualification; wherefore the predicative demonstration is also more worthy than it. It is manifest, therefore, that the demonstration to the impossible is more worthy.\n\nCHAPTER XXIII.\n\nWhich science is more certain, which is one, demonstrations. And that there can be several of the same","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":69,"ref":"p69","source":"Certior autem est scientia,scientia et prior, quae ipsius quia et propter quid eadem est quam non, extra eam quas est propterquid.El quæ non est de subjecto, ea quae est de subjecto, ut arithmetica, harmonica.Et quæ est ex minoribus,ea quæ ex appositione,ut arithmetica, geometria:dico autem ex additione, ut unitas substantia est sine positione, punctum autem substantia posita,hoc autem exappositione.Una autem scientia est,quæ est unius generis,quæcunque ex primis componitur,et partes sunt aut passiones horum,quæ sunt per se.AItera autem scientiaestab altel'a,quarumcunque principianeque ex eiadem,neque ex alteris sunt.Hujus autem est signum,cum in demonstrabilia veniant, oportet enim in eodem gecere esse cum iis quæ demonstrantur, signum autem est et hujus,cum demonstrabilia, per ipsa in eodem generesunt,et proxima.Plures autem demonstrationes ejusdem possibile est esse,non solum ex eodem ordine accipiendi non continuum medium (ut eorum quas sunt a b,t' et et e),sed et ex altero,ut sit a transmutari,in quo autem moveri, sed lætari sit in quo 6, et iterum e quiescere,ve.rum igitur est et de b,et de prædicari, lætans enim movetur,et quod movetur transmutatur,iterum a de e, et e de b, verum prædicari,omnis enim lætans quiescit,et quiescens transmutatur,q uare per altera media, et non ex eodem ordine syllogismus est, non tamen est neutrum de neutro dici mediorum.","english":"But the science that is of the fact and of the reason why is the same, and it is more certain than the science that is not of the reason why, and it is prior. And the science that is not of the subject is more certain than the science that is of the subject, as arithmetic is more certain than harmonics. And the science that is from fewer principles is more certain than the science that is from addition, as arithmetic is more certain than geometry; for I call it \"from addition\" because the unit is a substance without position, while the point is a substance with position, and this is from addition. And one science is that which is of one genus, whatever is composed from the first principles, and the parts or passions of these things that are per se. But another science is from another, whatever principles are neither from the same nor from one another. And the sign of this is that when they come to things demonstrable, they must be in the same genus as the things that are demonstrated; and the sign of this too is that the things demonstrable through them are in the same genus and are proximate. But it is possible for there to be several demonstrations of the same thing, not only by taking a non-continuous middle term from the same order (as of those that are from a, b, and c and d and e), but also from another, as let a be \"to be changed,\" that in which it is moved, but let \"to rejoice\" be that in which b is, and again e \"to be at rest\"; then it is true to predicate both of b and of a: for the one rejoicing is moved, and what is moved is changed; again, a of e and e of b are true to predicate: for everyone rejoicing is at rest, and the one at rest is changed. Therefore the syllogism is through other middle terms and not from the same order, yet it is not that neither is said of neither of the middle terms.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":70,"ref":"p70","source":"Necesse estenim idem e alicui utraque inesse, intendere autem est per alias figuras, quot modis contingit ejusdem fieri syllogismum._\n\nCAPUT XXIV.\n\nNon esse scientiam fortuitorum, neque in sensuum functione.\n\nSed ejus quod est a fortuna non est scientia per demonstrationem. Neque enim sicut necessarium, neque sicut frequenter quod est a fortuna,sed extra hoc fit, sed demonstratio alterius horum.Omnis enim syllogismus aut per necessarias, aut per eas quæ sunt tanquam frequenter propositiones,et siquidem propositiones necessariae sunt,et conclusio erit necessaria, si vero sint sicut frequenter, et conclusio hujusmodi.Quare si id quod est a fortuna neque est sicut frequenter,neque necessarium, neque utique erit ipsius demonstratio.Neque persensum est scire, si enim est sensus talis hujus,et non hujus alicujus, sed sentire hoc aliquid est necesse et ubi et nunc. Universale autem quod est in omnibus,irnpossibile est sentire,neque enim hoc aliquid est,neqlle nunc, neque ubi, neque enim utique esset universale, quod enim semperest,et ubique,universales dicimus esse; quoniam igitur demonstrationes universales sunt, hæc autem non est sentire, maniFestum est quod neque scire per sensum est.","english":"For it is necessary that the same thing be present in both from something, but to intend [to show] through other figures in how many ways it happens that a syllogism of the same thing comes about.\n\nCHAPTER XXIV.\n\nThat there is no science of things that happen by chance, nor in the operation of the senses.\n\nBut of that which is from fortune there is no science through demonstration. For neither as necessary, nor as happening for the most part, is that which is from fortune, but it happens beyond this, whereas demonstration is of one of these. For every syllogism is either through necessary propositions or through those that are as it were for the most part, and if the propositions are necessary, the conclusion will also be necessary; but if they are as for the most part, the conclusion will be of this sort. Wherefore if that which is from fortune is neither as for the most part nor necessary, there will surely be no demonstration of it. Nor is it possible to know through sense perception; for if sense is of such a kind as to be of this, and not of some particular thing, yet it is necessary to perceive this particular thing, and where and now. But it is impossible to perceive the universal that is in all things; for it is not a particular thing, nor now, nor where; for then it would not be universal either, for we call universal those things that are always and everywhere. Since, therefore, demonstrations are universal, but these things are not to be perceived by sense, it is manifest that neither is it possible to know through sense.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":71,"ref":"p71","source":"Sed manifestum quoniam si esset sentire triangulum, quod duobus rectis haberet a'quales angulos, quæreremus utique demonstrationem, et nOn,sicut quidam fatentur,scirernus.Sentire enim necesse est singulariter, scientia autem est in cognoscendo universale. Unde et si su per lunam essemus,et videremus objectam terral), non utique sciremus causam defectus, sentiremus enim quoniam deficeret,sed non propter quid omnino,non enim universalis,sensus.Sed ex considerare hoc multoties accidere universale venantes,demonstrationem habemus, ex singularibus enim pluribus universale manifestum est. Uuniversale autem honorabile,quoniam ostendit causam: quare de hujusmodi universalis honorabilior est sensibus et cognitione quorumcunque altera causa est, sed de primis alia ratio est. Manifestum igitur est quod im possibile sit sentiendo scire aliud demonstratorum,nisi aliquis dicat sentire,scienliam habere per demonstrationem.Sunt tamen quaedam reducta ad sensus defectum in propositis, quaedam enim si videremus, non utique quæreremus. Sed nontanquam scientesin videndo, sed tanquam habentes universale ex eo quod videmus, ut si vitrum foratum videremus, et lumen pertransiens, manifestum utique erit et propter quid illurninat,propter id quod videremus quidem seorsum in unoquoque,intelligere autem simul est, quoniam in omnibus sic est.","english":"But it is clear that if we were to perceive a triangle, that it has angles equal to two right angles, we would certainly seek a demonstration, and we would not, as some admit, know it. For perception must be of something singular, but knowledge consists in cognizing the universal. Hence even if we were on the moon and saw the earth placed before us, we would certainly not know the cause of the eclipse; for we would perceive that it is eclipsed, but not at all why, since perception is not of the universal. But from considering that this happens many times, hunting the universal, we have a demonstration; for from many singulars the universal is made manifest. But the universal is honorable, since it shows the cause; wherefore concerning such things the universal is more honorable than the senses and than the cognition of whatever other things have another cause, but concerning first principles the account is different. It is therefore manifest that it is impossible by perceiving to know anything of the things demonstrated, unless someone says that to perceive is to have knowledge through demonstration. Yet there are certain things reduced to a defect of sense in the matters proposed; for some things, if we saw them, we would certainly not seek. But not as knowing in seeing, but as having the universal from what we see—as, if we saw glass pierced and light passing through, it would certainly be manifest, and why it illuminates, because we would see indeed separately in each one, but to understand at the same time is that it is so in all.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":72,"ref":"p72","source":"CAPUT XXV.\n\nNon omnium syllogismorum eadem principit! esse Jlosse\n\nEadem autem esse principia omnium syllogismorum impossibile est, primum quidem logice specuIantibus, hi enim veri sunt syllogismi, alii autem falsi. Et si enim sit verum ex falsis syllogizare, sed semel hoc nt,ut si a de verum sit, medium autem falsum, neque enim a in 6, neque in; sed si harum media accipiantur proposition um, falsæ erunt, ex eo quod omnis conclusio falsa ex falsis est, vera autem ex veris, altera autem sunt vera et falsa. Postea neque falsa ex eidem sunt, est enim falsa ad invicem, et contraria, et impossibilia simul esse, ut justitiam esse injustitiam, aut timorem audaciam, aut bominem equum aut bovem, aut æquale,majus et minus. Ex oppositis autem sic est, neque enim verorum eadem principia omnium sunt,aItera. enim multorum genere principia sunt, et neque conveniunt, ut unitates punctis non conveniunt, hæ enim non habent positionem. Illa autem habent. Necesse autem est aut in mediaconvenirR, autin sursurn,aut deorsum, aut hos interius habere, illos autem exterius terminorum.Sed neque communium principiorum possunt ex aliqua ex quibus omnia demonstrabuntur,dico autem communia,ut omneaffirmare aut negare, genera enim eorum quæ sunt, altera sunt, etalia quidem in quantitatibus, alia vero in qualitatibus suntsolum cum quibus demonstrantur per communia..","english":"CHAPTER XXV.\n\nThat the principles of all syllogisms cannot be the same\n\nIt is impossible that the principles of all syllogisms be the same—first, indeed, for those who consider the matter logically; for some syllogisms are true, others false. For even if it is possible to syllogize something true from false premises, this happens only once, as, for instance, if A is true of something while the middle term is false—for neither is A in B nor in C; but if the middle terms of these propositions are taken, they will be false, since every false conclusion follows from false premises, while a true conclusion follows from true premises, and the premises are in one case true and in another false. Moreover, false conclusions do not arise from the same premises, for some are false in relation to one another, and contraries, and things that cannot exist together, such as that justice is injustice, or that fear is boldness, or that a man is a horse or an ox, or that the equal is greater and less. From opposites, then, the case stands thus; nor are the same principles of all true things—for the principles of many things differ in kind, and do not agree, just as units do not agree with points; for the latter have no position, while the former have position. But it is necessary either that they coincide in the middle, or above, or below, or that some have their terms within and others without. But neither can the common principles be derived from any of those from which all things are demonstrated—I mean the common principles, such as to affirm or deny everything; for the genera of beings are different, and some are in quantities, others in qualities alone, with which they are demonstrated through the common principles.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":73,"ref":"p73","source":"Amplius, principia non:nulLo mlnora suntconclusionibus,principia enim propositicnes Eunt, propositiones autem assum pti termini,aut immissi termini sunt. Adhuc conclusiones suntinfinitæ, termini autem finiti. Amplius,principia haec quidem ex necessitate, illa contingentia. Sic igitur considerantibus impossibile est eadem principia esse, aut finita, cum infinitae sunt conclusiones. Si vero aliter quodammodo dicat quis, quod bæc quidem geometriæ, illa vero numerorum,illa autem medicinæ,quid utique erit aliud quod dicitur, nisi quod sunt principiascientiarum d:versa?sed eadem dicere derisio est, quoniam eadem eisdem eadem erunt, omni namque sic fiunt eadem. At vero neque quod est ex omnibus demonstrare quod1ibet,est quaerere omnium esse eadem principia, multum enim insipiens est.Neque enim in manifestis doctrinis boc Hit, neque in resolutione boc est possibile, immediatae enim propositiones sunt principia,altere autem conclusio fit accepta propositione imrnediata.Si autem dicat aliquis primas immediatas propositioneseadem esse principia, una in unoquoque genere est.Si vero neque ex omnibus ut opus estdemonstrari contingit quodlibet, neque sic ex alLero tanquam erunt uniuscujusque scientiæ altera, relinq uitur quod proxima sint principia omnium, et ex his quidem hæc, ex illis autem ilia.","english":"Further, the principles are not fewer than the conclusions; for the principles are propositions, and propositions are assumed terms, or terms let in. Moreover, the conclusions are infinite, but the terms are finite. Further, of these principles some are necessary, others contingent. So then, for those who consider the matter thus, it is impossible that the same principles be, or be finite, when the conclusions are infinite. But if someone says in some other way that these are the principles of geometry, those of numbers, and those of medicine, what else will be said than that the principles of the sciences are diverse? But to say they are the same is ridiculous, since the same things will be the same for the same things; for in every way they become the same. But neither is it to seek that the principles of all things be the same, that one should demonstrate anything whatever from all of them; for that is very foolish. For this does not happen in manifest doctrines, nor is it possible in resolution; for immediate propositions are principles, and another becomes a conclusion when an immediate proposition is accepted. But if someone says that the first immediate propositions are the same principles, there is one in each genus. But if neither is it possible to demonstrate anything whatever from all of them as needed, nor thus from one another as though there were different principles of each science, it remains that the principles of all things are proximate, and from these indeed these, from those however those.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":74,"ref":"p74","source":"Manifestum autem et hoc est, quoniam non contingit,monstratumest enim quod altera principia genere sunt differentium genere. Principia enim duplicia sunt, ex quibus et circa quod,ex quibus quidem igitur,communia sunt quæautem sunt circa quod, propria sunt, ut numerus, magnitudo.\n\nCAPUT XXVI.\n\nQnod scientia et scibile ab opinatione et opinabili discrepent.\n\nScibile autem et scientia differunt ab opinabili et opinione, quoniam scientiauniversalis et pernecessaria est, necessarium autem non contingit aliter se babere. Sunt autem quaedam vera, quæ contingit aliter se babere, maniFestum est igitur quod circa hæc scientia non est, essent enim utique impossibilia aliter se habere. At vero neque intellectus, dico enim intellectum principium esse scientiæ, neque scientia indemonstrabilis, hæc autem est acceptio immediata? propositionis,verus enim est, intelIectus.et scientia,et opinio,et quid per hæc dicitur. Quare relinquitur opinionem esse circa. uerum quidem, aut falsum, contingens autem est et aliter se habere. Hoc autem est acceptio immediatæ propositionis, et non necessariæ. Certum autem est sic apparentibus, opinio ei incertum est,et natura hujusmodi est.","english":"It is also clear that this is so, since it is not possible; for it has been shown that the principles of the other kind are different in kind. For the principles are twofold: those from which and those about which. Those from which, then, are common, but those about which are proper, as number and magnitude.\n\nCHAPTER XXVI.\n\nThat knowledge and the knowable differ from opinion and the opinable.\n\nThe knowable and knowledge differ from the opinable and opinion, since knowledge is universal and through necessity, and what is necessary cannot be otherwise. But there are certain true things that can be otherwise; it is clear, therefore, that there is no knowledge concerning these, for they would then be impossible to be otherwise. Nor, indeed, is there understanding—for I call understanding the principle of knowledge—nor indemonstrable knowledge; but this is the immediate apprehension of a proposition, for understanding is true. And knowledge, and opinion, and what is meant by these. Wherefore it remains that opinion is about what is true or false, but contingent and able to be otherwise. This, however, is the apprehension of an immediate proposition, and not a necessary one. And it is certain that for things that appear thus, opinion is concerned with what is uncertain, and its nature is of this kind.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":75,"ref":"p75","source":"Adhuc autem nullus arbitratur opinari, cum opinetur impossibile aliterse habere,sed scire, sed quando esse quidem sic, sed tamen aliter, nihil prohibet et tunc opinari, tanquam hujusmodi quidemopinionem esse, necessariam autem scientiam. Quomodo estigiturnon idem opinari, et scire? et quare non erit opinio scientia, si quis posueritomne quod scit contingere opinari? consequitur enim hic quidem sciens, ille vero opinans per media, quo-, usque ad immediata veniat, quare si ille quidem scivit, et opinans scivit, sicut enim et quia opinari, et propter quid,boc autem medium est. An si quis sic arbitrabitur non contigentia aliter se babere, sicut se habent definitiones per quas sunt demonstrationes,non opinabitursed sciet?Si autem vera quidem esse, non tamen bæc ipsis inesse secundum substantiam, et secundum speciem opinabitur, et non sciet vere, et quia et propter quid, si quidem per immediata opinabitur, si vero non per immediata opinabitur, solum ipsum quia opinabitur. Ejusdem autem opinio, et scientia non penitus est,sed sicut vera,et falsa ejusdem quodam modo est,sic et scien. tia et opinio ejusdem, et opinionem ei veram, et falsam (aicut dicunt quidam) ejusdem esse, inconvenientia accidunt appetere aliaque, et non opinari qux opinantur fabæ.","english":"Furthermore, no one supposes that he opines when he opines that a thing cannot be otherwise, but that he knows; yet when it is so, but nevertheless could be otherwise, nothing prevents him from opining then too, taking opinion to be of this sort of thing, but knowledge of what is necessary. How then is it not the same to opine and to know? And why will opinion not be knowledge, if someone supposes that whatever he knows he may also opine? For it follows that the one who knows and the other who opines proceed through middle terms until they come to immediates; so if the one knew, the one who opines also knew—for just as there is opining that and opining why, and this is the middle term. Or if someone judges that things which cannot be otherwise stand as the definitions stand, through which demonstrations are made, will he not opine but know? But if he judges that they are true, yet that these do not belong to the things themselves according to substance and according to species, he will opine and not know truly both that and why—if indeed he opines through immediates; but if he does not opine through immediates, he will opine only the fact itself. But opinion and knowledge of the same thing are not altogether the same; rather, just as the true and the false are in a certain way of the same thing, so too are knowledge and opinion of the same thing, and true and false opinion of the same thing (as some say); otherwise inconvenient consequences follow—to desire other things, and not to opine the things they opine to be fables.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":76,"ref":"p76","source":"Quoniam autem idem multiplicit.cr dicitur, estautem sicut contingit, estautem ut non,eommensuratam enim diametrum essevere, opinari inconveniens est, sed quod diameter (circa quam sunt opiniones)idem sic ejusdem est,sed quod quid erat esse, unicuique secundum rationem non est idem. Similiter autem et scienda, et opinio ejusdem est, hæc enim si animalis est quod non est contingere non esse anirnal, sed illa quidem quae est contingere, ut si hæc quidem quod hominis quidem est, iIla vero hominis quidem, non autem quod quidem hominis est, idem enim est, quia homo, hoc autem sicut non idem. Manifestum autem ex his est quod neque opinai'i simu! idem, et scire contingit, simul enim haberet utique opinionem aliter habendi, et non aliter idem, quod quidem non contingit, in alio enim unumquodque esse contingit ejusdem, sicut dictum est, sed in eodem nihil sic potest esse, haberet enim opinionern simul. Ut quod homo essetsecundum quod est animai, hoc enim fuerit non contingere esse non animal, et non secundum quod animal, hoc enim sicut contingere. Reliqua autem quomodo oportet distribuere in rationem, et intellectum, et scientiam, et artem,et prudentiam, et sapientiam, hæc quidem physicæ est, ilia vero elhicæ speculationis magis.","english":"But since the same thing is spoken of in many ways, and one sense is as it happens, another as it does not—for to opine that the diagonal is commensurate is unfitting, but that the diagonal (about which opinions are held) is the same in this way belongs to the same thing, yet what it was to be is not the same for each according to the account. And similarly both things knowable and opinion are of the same thing; for these, if it is of an animal, that it cannot not be an animal—but the one is what belongs as a matter of contingency, as if this indeed is of man, while that is of man but not what man is; for it is the same because it is man, but this is as not the same. From these it is clear that it is not possible at the same time to opine the same thing and to know it; for he would at the same time have an opinion that it is otherwise and that it is not otherwise, which indeed does not happen; for each thing can be in another, as has been said, but in the same thing nothing of the sort can be, for he would have the opinion at the same time. As that man is according to what is animal—for this would be that it cannot not be an animal—and not according to what is animal, for this is as a matter of contingency. But how the remaining things ought to be distributed into account, and understanding, and knowledge, and art, and prudence, and wisdom—this belongs to physics, but that to ethical speculation more.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":77,"ref":"p77","source":"CAPUT XXVII.\n\nDe solertia.\n\nSolertia autem est subtilitas quaedam in non perspecto tempore medii. Ut si aliquis videns quod lunasplendorem semper habet ad solem,statim intellexerit propter quid huc sit, quia propter id quod illustratur a sole, aut disputantem cum divite, cognovit quoniam commodatum est, aut propter id quod amici sunt, quia inimici ejusdem sunt.Omnes enim causas medias videns, cognovit et ultima. Splendidum esse ad solem sit, in quo a lucere a sole, b: luna, c, inest igitur lunæ quidem ipsic b, quod quidem est lucere a sole, ipsi autem a, quod estad hoc esse splendidum, a quo splendet, quare et ipsi c, inest a per b.\n\nLIBER SECUNDUS.\n\nCAPUT PRIMUM.\n\nQuot quæri solent disciplinis.\n\nQuæstiones aequales sunt numero iis quaecunque vere scimus. Quaerimus autem quaWor, quia propter quid, si est, et quid est. Cum enim utrum hoc insit, aut hoc quærimus, in numerum ponentes ut utrum sol deficiat aut non, ipsum quia quærimus. Signum autem hujus, invenientes enim quia deficit, pausamus,et si in principio scirem us quia deMceret, non quæreremus utrum.Cum autem sciamus ipsum, quia ipsum propter quid quærimus,ut scientes quia deficit sol, et quia movetur terra.","english":"CHAPTER XXVII.\n\nOn Sagacity.\n\nSagacity is a certain subtlety in grasping the middle term without the passage of time. As if someone, seeing that the moon always has its brightness from the sun, should immediately understand why this is so—because it is illuminated by the sun; or, seeing someone conversing with a rich man, should recognize that it is because a loan is owed; or, because they are friends, that they are enemies of the same person. For seeing all the middle causes, one also knows the ultimate ones. Let \"to be bright toward the sun\" be that in which \"to shine from the sun\" is present; let b be the moon, c the sun. Therefore, \"to shine from the sun\" is present in the moon, that is, in b; and in a, that is, in \"to be bright from this,\" from which it shines; therefore a is present in c through b.\n\nBOOK TWO.\n\nCHAPTER ONE.\n\nHow Many Things Are Customarily Asked in the Disciplines.\n\nThe questions are equal in number to the things we truly know. But we ask four things: that it is, why it is, whether it is, and what it is. For when we ask whether this is present or that, placing it among the number—as whether the sun is eclipsed or not—we are asking the fact itself. A sign of this: for when we find that it is eclipsed, we stop; and if we knew at the outset that it was eclipsed, we would not ask whether it is. But when we know the fact itself, we ask why it is—as, knowing that the sun is eclipsed, and that the earth moves.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":78,"ref":"p78","source":"et propter quid deficit, et propter quid terra movetur,quærimus hæc quidem sic.Quædam autem alio modo quærimus,ut si est, aut non est centaurus, aut Deus,hoc autem si est aut non, simpIicite, dico, sed non si albus est, aut non. Cognoscentes autem quoniam est, quid est quærimus,ut quid igiturestDeus,aut quid est homo. Quæ quidem igitur quærimus, et quae invenientes scimus, haec et tot sunt.\n\nCAPUT II.\n\nOmnem quæstionem medii esse.\n\nQuaerimus autem, cum quærimus quia est, aut si est simpliciter, utrum sit medium ipsius, aut non; cum autem cognoscentes aut quia est,autsi est, aut in parte,aut simpliciter,iterum propter quid quærimus, aut quid est, et tunc quærimus quid sit medum. Dico autem quia est,aut sest, aut nparte, aut simpliciter. In parte quidem, ut utrum deficit luna, aut augetur, si enim est aliquid, aut non est aliquid,in hujusmodi quaerimus; simpliciter autem si est, aut non est luna, aut nox. Contingit itaque in omnibus quæstionibus quærere, aut si est medium, aut quid est medium. Causa enim est medium, in omnibus autem hæc quæritur, ut utrum deficit luna, utrum est aliqua causa,aut non, post hæc scientes quia est aliqua, quid igitur bæc sit, quærimus. Causa enim ipsius esse non hoc,aut hoc, sed simpliciter substantiam,aut non simpliciter,sed aliquid eorum quae sunt per se, aut secundum accidens, medium est.","english":"And why it fails, and why the earth is moved, we seek these things in this way. But some things we seek in another way, as whether the centaur is or is not, or God—this, I say, simply whether it is or is not, but not whether it is white or not. But when we know that it is, we seek what it is, as what therefore is God, or what is man. The things, therefore, that we seek, and which, when we find them, we know, are these and so many.\n\nCHAPTER II.\n\nThat every question concerns the middle term.\n\nBut we seek, when we seek that it is, or whether it is simply, whether there is a middle term of it or not; but when we know either that it is, or whether it is, either in part or simply, we again seek why it is, or what it is, and then we seek what the middle term is. But I say \"that it is\" or \"whether it is,\" either in part or simply. In part, indeed, as whether the moon fails or increases; for if there is something or there is not something, in such matters we seek; but simply whether the moon is or is not, or night. It happens, therefore, in all questions that we seek either whether there is a middle term, or what the middle term is. For the cause is the middle term, and in all things this is sought, as whether the moon fails, whether there is some cause or not; after this, knowing that there is some cause, we seek what therefore this is. For the cause of its being this or that, but simply of its substance, or not simply, but of some one of the things that are per se or according to accident, is the middle term.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":79,"ref":"p79","source":"Dico autem simpliciter quidem subjectum ut lunam, aut terram, aut solem, aut triangulum, quid autem esse defectum, aequalitatem aut inaequalitatem, si in medio sit, aut non.In omnibus enim bis manifestum est quod idem sit quod quid est, et propter quid est, Ut quid est defectus? privatio luminis a luna terræ objectu. Propter quid est defectus, aut propter quid deficit luna? propter defectum luminisobjecta terra.Quid estconsonantia? ratio numerorum in acuto et gravi. et propter quid consonat acutum gravi?propter id quod ration em habet numerorum etgrave etacuturn. Utrum est consonare acutum est grave? Utrum sit in numeris ratio eorum? Accipientes autem quia est, quid igitur est ratio quærimus.Quod autem sit medii quæstio, ostenditur quandocunque medium est sensibile.Quærimus enim nonsentientesutde defectu si eSt,aut non.Si vero essemus super lunam, non util(ue quaereremus neque si fit,neque propter quid fil,sed simul manifestum utique esset utrumque,ex eo enim quod sentimus etuniversale factum est nobis notum,Sensus enim quod nunc objicitur, etmanifestum est quod nunc deficit,ex his autem univeraale utique factum est. Sicut igitur duximus quod quid est scire idem est et propter quid est, boc autem aut est simpliciter, et non eorum quae insunt aliquid est, aut quae insunt, ut quoniam duo recti Bunt,au quoniam majus aut minus est.","english":"I say that the subject simply is, for example, the moon, or the earth, or the sun, or a triangle; but what the fact is—a defect, equality or inequality, whether it is in the middle or not. For in all these cases it is clear in two ways that what it is and why it is are the same. For what is a defect? The privation of light from the moon by the interposition of the earth. Why is there a defect, or why does the moon suffer defect? Because of the loss of light when the earth is interposed. What is consonance? The ratio of numbers in the high and the low. And why does the high sound with the low? Because both the low and the high have a ratio of numbers. Whether the high sounds with the low, and whether there is in them a ratio of numbers? But when we have grasped that it is, we then seek what the ratio is. That the inquiry concerns the middle term is shown whenever the middle term is perceptible. For we seek, not perceiving, as concerning a defect, whether it is or not. But if we were above the moon, we would not seek either whether it occurs or why it occurs, but both would at once be manifest; for from what we perceive, the universal would have become known to us. For the sense is of what is now interposed, and it is manifest that it now suffers defect; but from these things the universal would have come about. Therefore, as we have said, to know what it is is the same as to know why it is; and this is either simply, and is not something of the things that are present, or it is of the things that are present, as that two are right angles, or that it is greater or less.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":80,"ref":"p80","source":"Quod igltur omnia quae quæruntur medii quaestio sint,manifestum est.\n\nCAPUT III.\n\nDiscrepatio quod demonstratio et definitio non ejusdem sint.\n\nQuomodo autem quod quid est demonstratur. et quis modus introductionis,et quid est definitio, et quorum, dicemus, primum opponentes de ipsis. Principium autem sit futurorum, quod quidem sit maxime proprium habitis rationibus Dubitabit autem aliquis utrum sit idern,et secundum idem defi. nitione scire et demonstratione scire, aut sit impossibile. Definitio enim ipsius quod quid est esse videtur; quod autem quid est omne universale et prædicaLivurn est; syllogismi autem Bunt,alii quidem privativi, alii vero non universales, sicut in secunda figura privativi omnes sunt, in tertia vero non universales.Post ea neque eorum quae in prima figura prædicativorum omnium est definitio,ut quoniam omnis triangulus duobus rectis habet æquales. Hujus autem ratio est, quoniam scire demonstrabile est demonstrationem habere,quare si in talibus est demonshatio,est manifestum quod non utique erit eorum definitio.Sciet enim utique aliquis et secundum definitionem,non babensdemonstrationem, nihil enim prohibet non simuI babere.Sufficit autcm!ides et ex inductione.","english":"That all things which are sought are a question of the middle term is evident.\n\nCHAPTER III.\n\nThe disagreement that demonstration and definition are not of the same thing.\n\nIn what way, however, the what-it-is is demonstrated, and what is the mode of introduction, and what is definition, and of what things, we shall say, first setting out objections concerning these matters. And let this be the starting point for what follows, which is indeed most proper to the accounts already held. Someone will doubt whether it is the same to know by definition and to know by demonstration, and according to the same thing, or whether it is impossible. For definition seems to be of the what-it-is itself; but the what-it-is is altogether universal and predicable; but syllogisms are some privative, others not universal, as in the second figure all are privative, but in the third not universal. After this, neither is there definition of all the predicative [syllogisms] in the first figure, as that every triangle has [angles] equal to two right angles. The reason for this is that what is demonstrable is to have a demonstration; wherefore if there is demonstration in such things, it is evident that there will certainly not be definition of them. For someone will certainly know also according to definition, not having demonstration; for nothing prevents not having them at the same time. But belief is sufficient also from induction.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":81,"ref":"p81","source":"nihil enim definientes aliquando cognoscemus,neque eorum quæ per se sunt, neqtte quae secundum accidens.Amplius,si definitio substantiae quaedam cornitio est,bujusmodi manifestum est quod non sintsubstantiæ,quoniamquidem igitur non est definitio omnis cujus est demonstratio, manifestum est.Quid autem cujus est detlnitio,nunquid omnis demonstratio est,aut non? una quidem jam ratio et de hoc eadem est,unius enim inquantum unum est una scientia, quare si utique scire demonstrabile est demonstrationem habere,accidit quoddam impossibile, definitionem enim babens si ne demonstratione sciet.Amplius,principia demon. slrationum sunt definitiones,quorum non esse demonstrationes monstratum est prius:autenirn erunt principia demonstrabilia,et principiorum principia, et hoc in infinitum abibit; aut primae defi-mtiones erunt indemonstrabiles. Sed utrum si non omnis ejusdem, sed alicujus ejusdem sit definitio et demonstratio, an impossibile sit; non enim ejusdem demonstratio cujus est definitio, definitio quidem ipsius quid est,et substantiae est,sed demonstrationes omnes videntur supponere,et accipientes quod quid est,ut mathernaticæquhl unitas,et quid impar, et similiter alix.","english":"For if we define, we shall never know anything—neither things that are per se nor things that are per accidens. Moreover, if a definition is a certain cognition of substance, it is evident that such things as these are not substances. That, therefore, there is not a definition of everything of which there is a demonstration is evident. But of what there is a definition, is there demonstration of everything, or not? The same account already applies to this as well; for of one thing, insofar as it is one, there is one science. Wherefore, if to know a demonstrable thing is to have a demonstration, a certain impossibility results: for one who has a definition will know without demonstration. Moreover, the principles of demonstrations are definitions, and it has been shown earlier that there are no demonstrations of these; for either the principles will be demonstrable, and there will be principles of principles, and this will proceed to infinity, or the first definitions will be indemonstrable. But whether, if the definition and demonstration are not of every same thing, but of some same thing, it is impossible—for the demonstration is not of the same thing of which there is the definition; the definition is of the what-it-is and is of substance, but all demonstrations seem to assume and take up the what-it-is, as in mathematics [they assume] unity, and what odd is, and similarly in other cases.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":82,"ref":"p82","source":"Amplius,ornnis demonstratio aliquid de aliquo rnonstrat,ut quia est,aut non est; in definitione autem nibil alterum de altero prædicatur, ut neque quod animal de bipede, neque hoc de anirnali,neque de plano figura,neque enim est planum figura,neque figura planumAmplius,alterum quod quid est,et quia rnonstrare,definitio enim qmd est ostendit, sed demonstratio quia est hoc de hoc, aut non est.Alterius autem altera demonstratio est,nisi sit tanquam pars quasdam totius (boc autem dico quod ostensum est duobus rectis æquales habere de isoscele, si omnis ostensus est triangulus, pars enim hoc est, iliad totum); hæc autem ad invicem non sese habent sic,et quia est,et quid est, non enim alterumest alterius pars.Manifestum itaque quoniam neque cujus definitio,omnis hujus demonstratio,neque cujus omnis sit demonstratio, et hujus omnis sit definitio.Quare omnino ejusdem nullius contin git utraque habere.Manifestum est itaque quod neque definitio et demonstratio neque idem erunt. neque alterum in altero,et namque subjecta similiter se haberent,. Haec ergo usque huc addubitata sunt.","english":"Further, every demonstration shows something of something, namely that it is or is not; but in a definition nothing else is predicated of another, neither that animal is predicated of biped nor this of animal, nor figure of plane—for plane is not figure, nor figure plane. Further, it is one thing to show what something is and another to show that it is; for a definition shows what something is, but a demonstration shows that this belongs to this or does not. Moreover, one demonstration is of one thing and another of another, unless it be as certain parts of a whole (and this I mean: that having angles equal to two right angles is shown of the isosceles, if every triangle has been shown [to have them]; for this is a part, that the whole); but these do not stand to one another in this way—both that it is and what it is—for neither is one a part of the other. It is evident, therefore, that neither is there demonstration of everything of which there is a definition, nor is there definition of everything of which there is demonstration. Therefore it cannot happen at all that both belong to the same thing. It is evident, therefore, that neither will definition and demonstration be the same, nor the one in the other; for then their subjects would stand in a similar relation. These matters, then, have been raised as difficulties up to this point.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":83,"ref":"p83","source":"CAPUT IV.\n\nSyllogismo duplante non demonstrari quid est de eo CUJUS est.\n\nIpsius autem quid est utrum syllogismus sit, et demonstratio aut non, sicut nunc ratio supposuit. Syllogismus enim aliquid de aliquo monstrat per meriium,sed quid est,propriurn quidem eat.et in eo quod quid est pra'dicatur, hoc autem necesse est converti.Si enim ipsi proprium est a, maniFestum quoque et ipsi b, et hoc ipsi c,quare omnia sunt ad invicem; at vero et si a in eo quod quid est omni inest, et universaliter de omni in eo quod quid est dicitur, necesse est a in eo quod quid est de dici; si vero non sic accipit aliquis duplicans, non necesse erit a in eo quod quid est prædicari de c, sed si a de in eo quod quid est. non autem de quocunque in eo quod quid est,ipsurn autem quid est utraque habebunt, de hoc erit utique et de in eo quod quid eat.Si igitur quod quid est at quid eratesseutraque habent,in medio termino erit prius quod quid erat esse, et omnino si est monstrare quid est homo, sa homo, a vero quod quid est, sive animal bipes,sive ali quid aliud. Si ergo syIlogizatur a de c, necesse est a de omni prædicari; hujus autem erit alia media ratio,quare et hoc eriquod quid est homo, accipit igitur quod op!lrtet ostendere,etenirn est quod quid est hominis.Oportet autem in duabus propositionibus, et prim is, et immediatis considerare maximo enim manifestam quod dicitur,fit.","english":"CHAPTER IV.\n\nThat the what-it-is is not demonstrated of that whose it is by a doubling syllogism.\n\nBut whether there is a syllogism and demonstration of the what-it-is itself, or not, as the argument has just now supposed. For a syllogism shows something of something through a middle term, but the what-it-is is proper, and is predicated in the what-it-is, and this must be converted. For if a is proper to b, it is also manifest that b is proper to c, and this to a; wherefore all are related to one another. But indeed if a is present in every instance in the what-it-is, and is said universally of every instance in the what-it-is, it is necessary that a be said of c in the what-it-is; but if someone does not take it thus when doubling, it will not be necessary that a be predicated of c in the what-it-is, but only if a is [predicated] in the what-it-is, yet not of whatever is in the what-it-is; but they will have both the what-it-is itself, and it will be of this and of what is in the what-it-is. If therefore both have the what-it-is and the what-it-was-to-be, the what-it-was-to-be will be first in the middle term, and generally if it is possible to show what man is, [then] man is, but a is the what-it-is, whether animal biped or something else. If therefore a is syllogized of c, it is necessary that a be predicated of every instance; but of this there will be another middle account, wherefore this too will be the what-it-is of man; it therefore takes what ought to be shown, for there is the what-it-is of man. But one ought to consider this in two propositions, and first, and immediate ones; for thus what is said becomes most manifest.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":84,"ref":"p84","source":"Per conversionem quidem igitur j monstrantes quid est anima, aut quid est horno,aut aliud quodlibet eorum quæ sunt,quod est ex principio petunt,ut si quis putet animam esse eamdem sibi ipsi causam vivendi, hoc autem numerum eumdem seipsum moventem, necesse est enim petere animam hoc esse quod numerum esse se ipsum mo-ventem sic sicut idem. Non enim si consequitur a 6, et hoe c, erit in ipso a quod erat esse, sed verum erit dicere solum.Neque si est a quod quid est,et de prædicatur omni, et namque animalis esse prædicatur de hominis esse, verum enim est de omni hominis esse animalis esse, sicut et de omni homine animaI,sed non sic sicut unum esse.Si quidem igitur non sic accipiat,non syllogizatur quod a sit in quod quid erat esse et substantia; si vero sit accipiat, prius erit accipiens in c, quoniam est quod quid erat esse b,quare non demonstratum est, quod enim erat in principio accepit.","english":"Therefore, those who demonstrate what the soul is, or what man is, or anything else of the things that exist, by way of conversion, beg the principle—as if someone should think that the soul is the same cause of living as itself, and this is the same number moving itself. For it is necessary to beg that the soul is this: that it is the same as the number moving itself, in the manner of an identity. For it does not follow that if B follows A, and this is C, then A will contain the what-it-was-to-be, but it will only be true to say so. Nor, if A is the what-it-is and is predicated of every instance, does it follow—for the being of an animal is predicated of the being of a man; for it is true that the being of an animal is predicated of every being of a man, just as it is predicated of every man, but not in the manner of a single being. If, then, one does not take it in this way, it is not syllogized that A is in the what-it-was-to-be and the substance; but if one does take it in this way, the one taking it will first have assumed in C that B is the what-it-was-to-be; wherefore it has not been demonstrated, for he has assumed what was in the beginning.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":85,"ref":"p85","source":"CAPUT V.\n\nNeque idem effici posse per divisivnem syllogismo.\n\nAt vero neque per divisionem via est syllogizare sicut in resolutione circa figuras dictum est.Nequaquam enim necesse fit rem illam esse, cum hæc sint,sed sicut neque inducens demonstrat.Non enim oportet conclusionem interrogare, neque in concedoudo esse, sed necesse est esse cum sint illa, et si non dicat respondens,utrum homo animal est, aut inanimatum? postea accipit animaI,non syllogizat; iterum omne animaI,aut gressibile,aut aquaticum, accepit gressibile, et hominem esse totum animal gressibile, non necesse erit ex dictis, sed accipit et hoc. Differt autem nibil in multis, aut in paucis sic dicere, idem enim est. Non syltogisticus quidem igitur et usus fit sic procedentibus et de contingentibus sylIogizari.Quid enim prohibet et hoc verum quidem omne esse de homine, non tamen quid est, neque quod quid erat esse ostendens. Amplius, quid prohibet aut apponere aliquid, aut auferre, aut excellere sub9tantias,hæc quidem igiturdimittuntur. Contingit autem solvere in accipiendo in eo quod quid est omnia,et quod est consequenter divisionem facere quaesitum prius,et nihil relinquere; hoc autem necessarium esl, si omne in divisione cadit, et nihil relinquit, individuum enim specie oport.etesge.","english":"CHAPTER V.\n\nThat the same cannot be effected by division either, as by syllogism.\n\nBut neither is it possible to syllogize by way of division, as was said in the resolution concerning figures. For it is by no means necessary that that thing be, when these things are, but just as neither does one who proceeds by induction demonstrate. For one ought not to ask the conclusion, nor for it to be in the granting, but it is necessary that it be when those things are, and even if the respondent does not say whether man is an animal or inanimate, afterwards he takes up animal; he does not syllogize. Again, every animal is either walking or aquatic; he has taken walking, and that man is wholly a walking animal—it will not be necessary from what has been said, but he takes up this too. And it makes no difference to speak thus in many things or in few, for it is the same. Therefore, those who proceed in this way are not syllogistic, and the use of syllogizing comes to be about contingent things. For what prevents every one of these from being true of man, yet not showing what he is, nor the what-it-was-to-be? Moreover, what prevents one from adding something, or removing it, or exceeding the substances? These things, then, are dismissed. But it comes about that one solves the matter by taking all things in the what-it-is, and by making the division consequently of the thing sought beforehand, and leaving nothing out; but this is necessary, if everything falls under division and leaves nothing out, for it must be an individual in species.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":86,"ref":"p86","source":"Sed syllogismus tamen non inest,sed si quidem alio modo cognoscere facit, hoc quidem non fuit inconveniens,neque enim inducens forte demonstrat, sed tamen ostendit aliquid.Syllogismum autem non dicit,ex divisione eligens definitionem, sicut enim in conclusionibus,quæ sine mediis sunt,si aliquis dicat quoniam his existentibus necesse est hoc esse, contingitinterrogare propter quid sit,flic etin divisisterminis? ut, quid est bomo? animal mortale, pedes habens,bipe3,sinepemis. Propter quid scit unam. quamque appositionem,et dicit enim, et monstrabit divisione, sicut opinatur quod om[le animal aut rnortaIe,aut immortale sit; hujusmodi autem oratio omnis non est definitio; quare quavis divisione monstravit,scd tamen definitio,non syllogismus fit.\n\nCAPUT VI.\n\nNon monstrari definitionibus; neque definitione contrurii.definitionem sumendo definitionem","english":"But the syllogism is not present in it; yet if it does in some other way make us know, this was not incongruous—for neither does induction perhaps demonstrate, but it nevertheless shows something. However, he does not call it a syllogism—the one who selects the definition by division. For just as in conclusions that are without middle terms, if someone says that when these things exist, this must be, it is possible to ask on account of what it is—so too in the case of divided terms? For example, what is man? A mortal animal, having feet, biped, wingless. On account of what does he know each single addition? For he states it and will show it by division, as he supposes that every animal is either mortal or immortal. But a statement of this sort is not a definition in every case; therefore he has shown it by some sort of division, but it does not become a definition, nor a syllogism.\n\nCHAPTER VI.\n\nThat definitions are not demonstrated; nor is the definition of a contrary [demonstrated] by taking a definition.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[{"kind":"lacuna","severity":"caution","text":"The source is fragmentary here: the edition marks a break or an editorial bracket, and the English carries across it. Treat the bridge as supplied, not translated."}]},{"i":87,"ref":"p87","source":"Sed utrum sit demonstrare quod quid est secundum substantiam ex conditione accipientem quod quid erat esse, quod est ex iis quae sunt in eo quod quid est propriis. Hæc autem in eo quod quid est sola, et proprium est omne, hoc enim est esse ilii. An iterum accepit quod quid erat esse et in hoc? necesseest enim per medium monstrare. Amplius, sicut neque in syllogismo accipitur quod quid est syllogizare, semper enim tota aut pars est propositio,exquibus est syIlogismus,sic neque quod quid est esse oportet esse in syIlogismo, sed seorsum hoc a positis esse.Et ad dubitantem an syllogizatum est,an non est hoc? obviandum,quoniam,hoc enim erat syllogismus, et adhuc quod nec quod quid erat syllogizatum est, quoniam utique, boc enim positum est nobis quod quid erat esse, quare necesse et sine eo quod quid est, sit syllogismus, aut quod quid erat esse syllogizare aliquid.Et si ex conditione monstret, ut si malo inest divisibile esse, in contrario est contrarium esse, in quibuscunque est aliquid eontrarium,lJonum autem malo contrarium est. et indivisibile divisibili; est itaque boni et indivisibile esse.Etenirn hic accipiens quod erat esse, monstrat. Accipitur autem ad monstrandum quod quid erat esse, alterum tamen sit. Etenim in demonstrationibus est hoc quidem de hoc, sed non ipsuLO,ceque cujus est eadem ratio, et convertitur.","english":"But whether it is possible to demonstrate what a thing is according to substance by taking the condition of what it was to be, which is derived from the properties that are in the thing itself as regards what it is. But these are alone in what it is, and every property is proper to it, for this is its being. Or did he again take what it was to be, and also in this? For it is necessary to show through a middle term. Further, just as in a syllogism what a thing is is not taken to be syllogized—for the proposition is always whole or part, from which the syllogism consists—so neither ought the being of what a thing is to be in the syllogism, but this must be separate from the things posited. And to one who doubts whether it has been syllogized or not, this must be met: that this was the syllogism; and further, that what it was to be has not been syllogized, because certainly this was posited for us as what it was to be; wherefore it is necessary that the syllogism exist even without what a thing is, or that something be syllogized as to what it was to be. And if he shows from a condition, as if to be divisible is in evil, the contrary is in the contrary; in whatever things there is something contrary, but good is contrary to evil, and indivisible to divisible; therefore the being of good is also indivisible. For here too, taking what was to be, he shows it. But it is taken for the purpose of showing what it was to be, yet let it be another thing. For in demonstrations this is indeed about this, but not itself, nor of that whose account is the same and which converts.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":88,"ref":"p88","source":"Ad utrosque autem,et secundum divisionem demonstrantem,et ad sic syIlogismum,est eadem dubitatio propter quid est homo animal gressibile bipes, sed non animal et bipes, ex acceptis enim neque una necessitas est unum fieri quod prædicatur,sed utiqce sicutidemhomo erit et musicus et grammaticus.\n\nCAPUT VII.\n\nContendit quid est non posse monstrari.\n\nQualiter igitur definiens demonstrabit substantiam,aut quod quid est? neque enim sicut demonstrans ex certis manifestum esse faciet quod necesse est cum sint illa alterum aliquid esse. Demonstratio enim hoc est,neque sicut inducens per singularia,curn manifesta sint, quoniam omne sic est, eo quod nihil aliter est. Non enim quid est demonstrat, sed quoniam est, aut non est. Quis igitur est alius modus reliquus? non enim demonstrabit sensu, aut digito. Amplius, quomodo monstrabit quod quid est homo? necesse est enim scicntem quid est homo, aut aliud quodcunque, scire quia est. Quod enim non est,nuIlus scit quod quid est, sed quid significat: oratio quidem,aut nomen cum dico tragelaphus,quid autem est tragelaphus, impossibile est scire. At vero si demonstrabit quid est,et quia est, et qualiter eadem ratione dernonstrabit,definito enim unum aliquid, et demonstratio, id autem quod est quid est homo, et esse hominem, aliud est.","english":"But against both—both the one who demonstrates by division and the syllogism so formed—there is the same difficulty: why is man a walking, two-footed animal, but not animal and two-footed? For from the things taken up there is no single necessity that one thing be made of the predicates, but rather, as it were, the same man will be both musical and grammatical.\n\nCHAPTER VII.\n\nHe contends that what a thing is cannot be demonstrated.\n\nIn what way, then, will one who defines demonstrate substance, or what a thing is? For he will not, like one who demonstrates, make it manifest from certain things that it is necessary, when those things exist, that something else be. For demonstration is this: nor again like one who argues by induction through particulars, when these are manifest, that everything is so, because nothing is otherwise. For he does not demonstrate what a thing is, but that it is, or is not. What other mode, then, remains? For he will not demonstrate by sense or by pointing with the finger. Moreover, how will he show what man is? For one who knows what man is, or any other thing whatsoever, must know that it is. For no one knows what a thing is if it is not, but only what it signifies—a phrase, perhaps, or a name—as when I say \"goat-stag\"; but what a goat-stag is, it is impossible to know. But if he will demonstrate what it is, and that it is, and how, he will demonstrate by the same account; for the definition is one single thing, and the demonstration is one single thing, but what man is and that man is are different.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":89,"ref":"p89","source":"Postea per demonstrationem dicimus necessarium esse demonstrare omne quia est, nisi substantia sit, esse autem non substantia ulla est, non eoirn est genus, quod est, demonstratio itaque eri quia est, quod quidem et nunc faciunt scientiæ; quid enim significat triangulus, accipit geometra, quia autem est, demonstrat. Quid igitur monstrabit definiens, quid est triangulus? sciens itaque aliquis difinitione quid est, si est non sciet, sed impossibile. Manifestum est et secundum nunc modos terminorum, quod non monstrant definientes quia est. Si enim et est ex medio aliquod æquale, sed propter quid est quod definitur, et propter quid est circulus quæritur, esset enim utique et montis aenei dicere ipsum, neque enim quia possibile sit esse quod dicitur assignant termini, neque quod illud est cujus dicunt esse definitionem, sed semper licet dicere et propter quid. Si ergo definiens monstrabit aut quid est, aut quid significat nomen, sed non est ullo modo ejus quod quid est, erit utique definitio ratio nominis, idem significans, sed non conveniens est. Primum quidem quia et non substantiarum esset definitio, et eorum quæ non sunt, significare enim est et quae non sunt. Amplius, ornnes orationes di!initiones erunt; essetenino utique nomen ponere cuilibet orationi, quare terminis utique disputabimus omnes, et Ilias definitio erit.","english":"After this, through demonstration, we say it is necessary to demonstrate that every thing is, unless it is a substance; but to be is not any substance, for there is no genus of the things that are. Therefore demonstration is of the fact that it is, which indeed the sciences now do; for what a triangle signifies the geometer assumes, but that it is, he demonstrates. What, then, will the one who defines show—what a triangle is? Therefore someone knowing by definition what it is will not know if it is, but this is impossible. It is evident also according to the modes of terms now discussed that those who define do not show that it is. For if there is also some equal [line] from the middle, yet why is it what is defined, and why is a circle sought? For it would surely be possible also to speak of a bronze mountain, for the terms do not establish that what is said is possible to be, nor that it is that of which they say it is the definition, but it is always permitted to say also why. If, therefore, the one who defines will show either what it is or what the name signifies, but it is in no way [a definition] of the essence, then the definition will be an account of the name, signifying the same thing, but this is not fitting. First, indeed, because there would be a definition also of non-substances, and of things that are not—for it is possible to signify also things that are not. Further, all accounts will be definitions; for it would be possible to assign a name to any account whatever; wherefore we shall dispute with all terms, and the Iliad will be a definition.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":90,"ref":"p90","source":"AmpIiug, neque una scientia demontrat utique quia hoc nomen ejus quod quid est esse ostendit, neque igitur definitiones hoc asssignant. Ex his igitur neque deftnitio et syllogismus idem videtur esse, neque ejusdem syllogismus et definitio. Adhuc autem quod neque definitio nihil demonstrat, neque monstrat, neque quod quid est, neque definitione, neque demonstratione cognoscere est.\n\nCAPUT VIII.\n\nQuid est, monstrari per aliud quid est.\n\nIterum autem speculandum estquid eorum dicitur bene,et quid non bene, et quid est definitio, et ejus quod quid est, unquid quodam modo est demonstratio, aut definitio, aut nullo modo. Quoniam (sicut diximus) idem est scire quod quid est, et scire causam ipsius si est, ratio autem hujus est quoniam est aliqua causa, et haec, aut eadem aut alia est, et si utique alia est, autdemonstrabilis est, aut indemonsLrabil is. Si igitur est alia, etcontingit demonstrari, necesse est mediam causam esse, et in figura prima. monstrari; universale enim et praedicativum est quod demonstratur. Dnus quidem modus nunc exquisitus est per aliud quod quid est est monstrare horum enim quod quid est necesse est medium esse quid est, et propriorum proprium. Quare hoc quidem monstrabit, illud vero non eorumquod quid erat esse ejusdem rei. Hic quidem igitur modus quod non sit demonstratio dictum est prius, sed est syliogismuslogicus ipsius quid est.","english":"Again, neither does one science demonstrate that this name shows what it is to be, nor therefore do definitions assign this. From these considerations, then, neither does definition seem to be the same as syllogism, nor is the syllogism and the definition of the same thing. Moreover, neither does definition demonstrate anything, nor does it show, nor is it possible to know what it is either by definition or by demonstration.\n\nCHAPTER VIII.\n\nWhat it is, is shown through another what it is.\n\nAgain, it must be considered what of these things is said well and what not well, and what definition is, and whether what it is is in some way a demonstration, or a definition, or in no way. Since (as we have said) to know what it is is the same as to know the cause of it, if it exists, and the reason for this is that there is some cause, and this is either the same or another, and if indeed it is another, it is either demonstrable or indemonstrable. If, therefore, it is another, and it happens to be demonstrated, it is necessary that the middle cause be shown in the first figure; for what is demonstrated is universal and predicable. One mode has now been examined—to show what it is through another; for of these it is necessary that the middle term be what it is, and that it be proper to proper attributes. Wherefore this will show one thing, but that will not be of the what-it-was-to-be of the same thing. This mode, then, has been said before not to be a demonstration, but it is a logical syllogism of what it is.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":91,"ref":"p91","source":"CAPUT IX.\n\nDe,quid est, et quod est.\n\nQuo autem modo contingat dicemus, iterum dicentes ex principio. Sicut enim propter quid quærimus, habentes quia est, aliquando autem et simul manifesta fiunt, sed neque prius propter quid possibile est cognocere, quam quia, manifestum est quod similiter et quod quid erat esse non sine quia est; impossibile est enim scire quid est, ignorantes si est. Hoc autem si est aliquando quidem, sed secundum accidens habemus, aliquando vero habentes quid ipsius rei,ut tonitruum,quoniam sonus quidam est nebularum, et defectum, quoniam privatio quaedam luminis, et bominem, quoniam animal quoddam est, et animam, idem seipsum movens. Sed quæcunque quidem secundum accidens scimus quia sunt necesse est illa nullo modo se habere ad quid est, neque enim quia sunt scimus, quaerere aut quid est, non haben. tes quia est, nihil quærere est, secundum quæcunque autem habemusquid facile est: quare quernadmodum habemus quia est, sic habemus et ad quid est. Quorum igitur habemus aliquid, quod quid est, primum quidem sit defectus in quo a, luna in quo c, oppositio terrae in quo b. Utrum quidem deficit, an non, quaerere est,nunquid est, an non. Hoc autem nibil differt quærere, quam si est ratio ipsius, et si sithoc, etil]ud dicimus esse, aut utriuscontradictionis est ratio, utrum habendi duos rectos, aut non habendi?","english":"CHAPTER IX.\n\nOn \"what it is\" and \"that it is.\"\n\nIn what way this comes about we shall state, speaking again from the beginning. For just as we seek the reason why, when we already have the fact that it is, and sometimes these become manifest at the same time—but it is not possible to know the reason why before [knowing] that it is—so it is manifest that [we cannot know] what it was to be without [knowing] that it is; for it is impossible to know what something is while being ignorant whether it exists. Now this \"that it is\" we sometimes have in a certain way, but [only] incidentally, while at other times we have something of the thing itself, as thunder, that it is a certain sound of the clouds, and eclipse, that it is a certain privation of light, and man, that he is a certain animal, and soul, that it is the same thing moving itself. But whatever things we know to exist only incidentally, it is necessary that these stand in no way toward \"what it is\"; for not even because we know that they are do we seek what they are, since not having [the knowledge] that it is, to seek [what it is] is to seek nothing. But in whatever cases we have something [of the thing], it is easy; wherefore in whatever way we have \"that it is,\" in that way we also have [something] toward \"what it is.\" Of those, then, of which we have something of \"what it is,\" first let eclipse be that in which [is] a, the moon that in which c, the opposition of the earth that in which b. Whether it is eclipsed or not, to seek is [to ask] whether it is or not. But this differs in nothing from seeking whether there is a account of it, and whether, if this is so, we say that that is, or whether it is the account of either side of the contradiction—whether of having two right angles or of not having [them]?","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":92,"ref":"p92","source":"Cum autem inveniamussimul ipsum quia, et propter quid scimus, si per media sit, si vero non, quia scimus, propter quid autem non. Sit ergo luna e, defectus a, lunam plenam, umbram non posse facere, nullo noHtrumin medio existente manifesto, in quo b, si ergo in est b, quod est non posse facere umbram, cum nullus nostrum in medio sit, in hoc quidem a, quod est deficere, quia deficit manifestum est, sed propter quid, nondum, sed quia defectus quidem est scimus, quid autem est, nescimus. Cum autem manifestum est quia a in fit, sed propter quid est? quaerere quidem est, utrum objectio, aut conversio lunæ autautexstinctio Iuminis;boc autem ratio alterius termini, utin his, ipsiusa,estenim defectus, objectio terree. Quid autem est tonitruus? ignis exstinctioin nube. Propter quid tonat? propterexstin. gui ignem in nube. Sit nubes c, tonitruum a, exstinctio ignis b, in igitur nube est b, exstinguitur enim in ipsa ignis, huic autem inest a, et est ratio b, ipsius a primi termini; si autem iterum hujus aliud medium sit, ex reliquis erit rationibus. Ut igitur accipitur quid est, et fit notum, dictum est. Quare syIlogismus quidem ipsius quod quid est non fit, neque demonstratio manifestum tamen est per syllogismum demonstrationem, quare neque sine demonstratione est cognocere quid est, cujus est causa alia, neque est demonstratio ipsius, sicut et in dubitationibus diximus.","english":"But when we discover both the fact and the reason why at the same time, we know them together if the explanation comes through middle terms; but if not, we know the fact and not the reason why. Let, then, the moon be E, the failure of light A, the moon being full and unable to cast a shadow, with none of us standing in the way, manifestly, be B. If, then, B belongs to E—that is, the inability to cast a shadow when none of us stands in the way—then A, which is the failure of light, is manifestly present; but the reason why is not yet known. We know that the failure of light exists, but we do not know what it is. But when it is manifest that A belongs to E, and we ask why, we seek whether it is the obstruction of the earth, or the turning of the moon, or the extinguishing of its light. This, however, is the account of the other term, namely of A: for the failure of light is the obstruction of the earth. What, then, is thunder? The extinguishing of fire in a cloud. Why does it thunder? Because the fire in the cloud is extinguished. Let the cloud be C, thunder A, the extinguishing of fire B. Then B is in C, for the fire is extinguished in it; and A belongs to this, and the account of B is the account of A, the first term. But if there is again another middle term of this, it will be from the remaining accounts. In what way, then, the what-it-is is grasped and becomes known has been stated. Therefore it is manifest that there is no syllogism of the what-it-is, nor demonstration; yet it is made known through a syllogism, though not through a demonstration. Hence neither is it possible to know the what-it-is of a thing whose cause is something else, without a demonstration, nor is there a demonstration of it, as we also said in the difficulties.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":93,"ref":"p93","source":"CAPUT X.\n\nDe definitione quid est, et propter quid.\n\nEst autem quorumdam quaedam causa altera, quorumdam autem non est: quare manifestum quoniam eorum quae sunt quid est, alia quidem sine media, ut principia sunt, quae quia sunt et quae quid sunt, supponere oportet, aut alio quidemaritbmeticus facit.Et modo facere uamquequid manifesta,est, quod et quia est, sed babeatium meunitatem supponit, diumet quorumestquædamaltera causA substantiæ, et ipsius esse, est per demonstrationcm (sicut diximus) ostendere, non demonstrare. Definitio autem quoniam quidem dicitur ratio ipsius quod quid ipsius quodest, manifestum et quoniam aliqua erit ratio quidam significat nomen, aut ratio altera, ponens: ut quii sigl1ificat quod quid est secundumnomina quod triangulus est, quod quidem habentes qui est, quærimus propter quid est. Difficile autem sic sunt, causa autem dictaest accipere quæ nescimus quia est est prius difficultatis, quia naquesiest, neque si nonscimus, sed aut hoc secundum accidens. Oratio autem una est dupliciter: hæc quidem conj unctione, ut Ilias; alia vero unum de uno ostendens non secundum accidens, una quidem i;:itur terminus est termini, quæ dicta est.Alius vero terminus est oratio demonstrans propterquid est, quare priorsignificat quidem, demonstrat autem non.","english":"CHAPTER X.\n\nOn the definition of what a thing is, and on the reason why.\n\nNow of some things there is one kind of cause, of others another; wherefore it is clear that of the things that are, some have their what-it-is without a middle term, as the principles are, which both that they are and what they are one must assume, or in some other way, as the arithmetician does. And in the manner in which each thing is made manifest, it is clear that both that it is and why it is—but for those that have a middle term, it assumes the middle term; and of those of which there is some other cause of the substance and of the very being, it is possible to show through demonstration (as we have said), not to demonstrate. But the definition, since it is indeed said to be the account of the what-it-is of the thing that is, it is clear both that some account will signify the name, or another account, positing: as one that signifies the what-it-is according to names, that a triangle is; for having this, that it is, we seek why it is. But it is difficult to grasp in this way; and the cause has been stated, which we do not know, that it is; for the difficulty is prior, because we do not know whether it is, nor if we do not know it, but either this is according to accident. But an account is one in two ways: this one indeed by conjunction, as the Iliad; the other showing one thing of one thing not according to accident. One indeed, therefore, is a term of the term, which has been stated. But another term is an account demonstrating why it is; wherefore the former signifies indeed, but does not demonstrate.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":94,"ref":"p94","source":"Quæ vero posterior est, manifestum et quoniam erit ut demonstratio ejus quod '(uid est, positione ditferens ademonstratione.Differt enim dicere propter quid tonat, et quid est tonitruus. dicet enim sic quidem propter id quod exstinguitur ignis in nubibus: Quid est tonitruus? sonus exstinctionis ignis in nube. Quare eadem oratio alio modo, et alio dicitur, et sic quidem demontratio continua, sic autem definitio. Amplius, est terminus tonitrui, sonus in nubibus, hæc autem est quae est ipsius quid est, damonstrationis conclusio, quæ autem est immediatorum definitio, positio est ipsius quid est, et indemonstrabilis; estergo definitio una quidem oratio ejus quod quid est, indemonstrabilis; unaverosytlogismus ipsius quid est, casu difFerens a demonstratione; tertia vero est quas est ipsius quid est, demonstrationis conclusio. bianifestum igitur ex dictis est, et dualiter est ipsius quod quid est demonstratio, et quomodo non est, et quorum est, et quorum non est. Amplius autem, definitio quot modis dicitur, et qualiter quod quid est monstrat, et quomodo non, et quorum est, et quorum nou, adhuc autem et ad demontrationem quomodo se habet, et quomodo contingit ejusdem esse, et qualiter non contingit.","english":"But the latter, it is clear also that there will be, as it were, a demonstration of what a thing is, differing in position from a demonstration. For it is one thing to say why it thunders, and another to say what thunder is. For one will say in this way: because the fire in the clouds is extinguished; but what is thunder? A sound of the extinguishing of fire in the cloud. Therefore the same account is spoken in one way and in another: in one way as a continuous demonstration, in another as a definition. Further, there is a term of thunder: sound in the clouds; and this is the conclusion of the demonstration of what it is; but the definition of immediates is a position of what a thing is, and indemonstrable. Therefore one definition is an indemonstrable account of what a thing is; another is a syllogism of what a thing is, differing in case from a demonstration; and a third is the conclusion of a demonstration of what a thing is. It is manifest therefore from what has been said both in how many ways there is a demonstration of what a thing is, and how it is not, and of which things it is, and of which it is not. Further, in how many ways a definition is spoken of, and how it shows what a thing is, and how not, and of which things it is, and of which not; and moreover also how it is related to demonstration, and how it happens that there is a demonstration of the same thing, and how it does not happen.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":95,"ref":"p95","source":"CAPUT XI.\n\nPer quodlibet genuf causæ demonstrari posse.\n\nQuoniamautem scire opinamur cum eciamus causam causæ autem quatuor sunt: una quidem quod quid erat esse; una vero cum hoc sit, necesse est hoe esse; altera autem quae aliquid primo movit; quarta vero cujusgratia omnes hæ per medium monstrant. Et hoc enim quod cum sit boc, necesse est esse, una quidem accepta propositione non est, dua. bus autem ad minus, boc autem est, cum unum medium habeant, hoc ergo uno accepto, conclusionem necesse est esse. Manifestum est autem et sic, propter quid est rectus in semicirculo? aut quo existente rectus est? Sit ergo reCtus in quo a, media duorum rectorum in quo h, qui est in semi. circulo in quo c, ipsius a igitur rectum esse in c, qui est in semicirculo, causa est b, hoc enim ipsi a aequale est, qui vero est c, ipsi b. Duorum enim rectorum dimidium est, existeute igitur dirnidio duorum rectorum, a in est, hoc autem erat in semicirculo rectum esse. Hoc autem idem i est ei quod quid erat esse, cum hoc significaret oratione, at vero et ipsius quod quid erat esse causa monstrata est media. Hoc autem propter quid Medorum bellum factum est Atheniensibus? quae causa est præliari Athenienses? quuniam in Sardes cum Erethriis commiserunt, propter hoc euim motum est.","english":"CHAPTER XI.\n\nThat demonstration can be given through any kind of cause.\n\nSince we think we know when we know the cause, and there are four causes: one is what it was to be; one, that when this is, it is necessary that this be; another, that which first moved; and the fourth, that for the sake of which—all these are shown through the middle term. For that \"when this is, it is necessary that this be,\" is not [established] when one proposition is assumed, but when at least two are assumed; and this holds when they have one middle term. So when this one is assumed, the conclusion is necessarily [produced]. It is clear also in this way: why is a right angle in a semicircle? Or, when what exists, is it a right angle? Let the right angle be that in which A is, the two right angles [be] that in which B is, and the angle in the semicircle that in which C is. Therefore the cause of A, that is, the right angle, being in C, that is, in the semicircle, is B. For B is equal to A, and C is [equal] to B. For it is half of two right angles. Therefore, when the half of two right angles exists, A is in C. But this was [the fact] that a right angle is in the semicircle. And this is the same as what it was to be, since the account signifies this. But also the cause of what it was to be has been shown through the middle term. But why was the Median war made against the Athenians? What is the cause of the Athenians fighting? Because they went with the Eretrians against Sardis. For it was moved on account of this.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":96,"ref":"p96","source":"Primum si bellum in quo a, priores committentes in alios b, Atheniensibus, est igitur in c, prius enim est committerre,Atheniensibus, a autem in b, debellaverunt enim prius injustos, est itaque in; a, debellari prius incipientes, autem in c, sive in atheniensibus, priores enim inceperunt, medium itaque hic causa primum movens. Quorumcunque vero causa est cujus gratia. ut propter quid ambulat? ut sanus fiat. Propter quid domus est? ut salventur vasa. Hoc quidem gratia hujus quod est sanari, illud vero gratia hujus quod est salvari, et propter quid oportet post cœnam ambulare, et cujus gratia oportet, nihil differt. Sit ambulare post cœnam, in quo c, non eminere cibos, in quo b, sanari in quo a. Sit igitur in eo quod est post coenam ambulat, esse facere non supereminere cibos juxta os ventris, et hoc esse sanum, videturenim inesse ipsi ambulare quod est c, non eminere cibos. In autem a, hoc quod est sauativum, quae igitur causa est, in quod a sit, quod est gratia cujus? non eminere, hoc autem est sicut illius ratio,a enim sic reddetur, propter quid inest c? quoniam hoc est sanari, hoc.sic habere. Oportet autem commulare rationes, et sic singula magis apparebunt. Generationes autem econtrario hic et in causis secundum motum: ibi enim medium oportet primum fieri, hic autem ipsum extremum, ultimum autem gratiacujus.","english":"First, if the war in which A is the prior engagement of one party against another, B is the Athenians, then it is in C; for the prior thing is the engagement against the Athenians, and A is in B; for they waged war first against the unjust, and so it is in A to be first to begin waging war, and this is in C, that is, in the Athenians; for they began first. Here, then, the middle term is the first moving cause. But in those cases where the cause is that for the sake of which: for example, why does he walk? So that he may become healthy. Why is there a house? So that the vessels may be preserved. This indeed is for the sake of this, namely being healthy; that is for the sake of this, namely being preserved. And why one ought to walk after dinner, and for the sake of what one ought to do so, make no difference. Let walking after dinner be C, the not having the food rise up be B, being healthy be A. Let it be, then, that in walking after dinner there is the doing of this, that the food does not rise up to the mouth of the stomach, and that this is being healthy; for walking appears to have in it this, namely C, that the food does not rise up. And A is this, namely the healthful thing. What, then, is the cause, in the sense of that for the sake of which A is present? The not rising up; and this is, as it were, the account of that. For A will be explained thus: why is C present? Because this is being healthy, namely to be so disposed. But one ought to combine the accounts, and thus each point will appear more clearly. In the case of generation, however, the order is the reverse here and in the causes according to motion: for there the middle term must come to be first, but here the extreme itself, and the last is that for the sake of which.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":97,"ref":"p97","source":"Contingitaulem idemet gratia cujus esse et ex necessitate, ut per lucerna pellem lumen egredi; etenim ex necessitate disgreditur, quod in parvl est partibitius, et per majores poros, si quidem lumen fit disgrediendo,et gratia cu ju,sut non offendamus.Nonne igitur si esse contingit, et fieri contigit? sicut si tonat exstincto igne, necesse est sizire et sonare, et (quemadmodum Pythagonci dicunt) minarum causa iis qui sunt in tartaro, quatenus timeant. Plurima autem hujusmodi sunt, et maxime in iis quæ natura subsistunt, et in constantibus hæc quidem propter hoc natura facit, illa vero ex necessitate. Necessitas autem est duplex, hæc quidem secundum naturam et aptitudinem, hæc vero violenta et contra aptitudinem, sicut lapis ex necessitate et sursum et deorsum fertur, sed non propter eamdem necessitatem. Sed in iis quæ sunt ab intelligentia, alia quidem nequaquam sunt ab eo quod per se frustra est, ut domus aut effigies neque ex necessitate sunt, sed propter hoc. Alia vero a fortuna suut,ut sanitas,et saIus,maxime in quibus cunque contingil,et sic et aliter cum non a fortuna generatio sit. Quare finio bonus alicujus gratia fit, aut natura,aut arte;a fortuna autem nihil propter aliquid fit.","english":"It happens also for the sake of this same thing, both to be and from necessity, as through a lantern the skin lets light pass; for it passes out of necessity, since it is in small parts and through larger pores, if indeed light comes to be by passing out, and for the sake of this, that we not be offended. Is it not, then, that if to be happens, also to come to be happens? As if it thunders when fire is extinguished, it is necessary to hiss and to sound, and (as the Pythagoreans say) for the sake of threatening those who are in Tartarus, so that they may fear. But very many things of this sort are, and especially in those things that subsist by nature, and among constant things, these indeed nature makes for the sake of this, but those from necessity. But necessity is twofold: this indeed according to nature and aptitude, but that violent and contrary to aptitude, as a stone is borne both upward and downward from necessity, but not for the sake of the same necessity. But in those things that are from intelligence, some indeed are in no way from that which is in vain by itself, as a house or a likeness, nor are they from necessity, but for the sake of this. But others are from fortune, as health and safety, especially in whatever things it happens, and thus and otherwise when generation is not from fortune. Wherefore the end of some good comes to be for the sake of something, either by nature or by art; but nothing from fortune comes to be for the sake of something.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":98,"ref":"p98","source":"Eadem autem causa est et et in iis quæ fiunt, et in factis, et futuris, quæ vere est iis quae sunt, medium enim causa est; verumtamen in iis quæ sunt quae est, in iis autem quae fiunt quæ fit, factis autem facta,et futuris futura. Ut propter quid factus est defectus,propter id quod in medio facta est terra, fit enim propter id quod fit, erit autem et propter id quod erit in medio,et est autem propter id quod est. Ut quid est crystalJus,accipiatur quoniam aqua congelata est. Aqua in quo c, congelata in quo a,rausa media in quo t,defeclus caloris penitus,est igitur in quidern b,in hoc autem congelatum esse, quod est in quo est a,6t autem crystallu?, cum fiat b, fac!us est autem facto, erit autem futuro b.Sic quidem igitur causa,etcujuscausaest, simul fit cum fit, et est cum est, et in eo quod factum est, et futuro eodem modo.\n\nCAPUT XII.","english":"The same cause applies both in things that come to be and in things that have come to be, and in future things, which truly is [the case] for things that are; for the middle term is the cause. Yet in things that are, it is the cause that is; in things that come to be, the cause that comes to be; in things that have come to be, the cause that has come to be; and in future things, the cause that will be. For example, why has a defect [of light] come about? Because the earth has come to be in the middle; for it comes to be because of what comes to be, and it will be because of what will be in the middle, and it is because of what is. For example, what is crystal? Let it be taken that it is congealed water. Water, in which [is] c; congealed, in which a; the middle term, in which b; the complete absence of heat, [is the cause]. Therefore it is in b, and in this, namely to be congealed, which is in that in which a is; and crystal is when b comes to be; it has come to be by a past [cause], and it will be by a future b. In this way, then, the cause and that of which it is the cause come to be at the same time when it comes to be, and are when it is, and in what has come to be, and in the future in the same way.\n\nCHAPTER XII.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":99,"ref":"p99","source":"De fieri et facto esse.\n\nIn iis autem quae non simul sunt, nunquid sit in continuo tempore? sicut videtur nobis alia eorum causa esse,ut facti esse altera facta,et futuri futura, et ejus quod fit,si aliquid antea factumest.Est igitur a posterius facto syIlogismus, principium autem et horum quæ factasunt,unde etin iis quae fiuntsimiliter, a priori autem non est,ut quoniam hoc factum est,quod hoc posterius factum est, et in futuro similiter est,Heque enim infinito autfinito erit tempore, quare quoniam hoc verum tet dicere factum esse, hoc verum est dicere factum esse posterius.In medio autem falsum esset dicere hoc jam altero facto, eadem autem ratio est et in futuro. Neque quoniam boc factum est,boc erit; medium pnim si. mul genitum oportet ps-e,factorum facturn,futuroo rum futurum, cum iis quae fiunt fieri, cum iis quæ sunt esse, sed futurum esse,et esse, non contingit simul esse geniturn.AmpIius,neque infinitum contingit esse tempus medium, neque finitum; falsum enim erit dicere in media. Speculandum ergo quid est continens? ul post id quod factum est, sit fieri in rebus? an manifestum est quod non continuum cum facto esse, quod fit? neque factum cum post facto esse?Termini enim suntatomi,sicut igitur neque sunt puncta ad invicem copulata, neque quae facta sunt, utraque enim indivisibilia sunt.","english":"On coming to be and having come to be.\n\nBut in things that are not simultaneous, is there [a cause] in continuous time? For it seems to us that the cause of these is different, as the cause of having come to be is different from that of coming to be, and of what will be from future things, and of what is coming to be, if something has come to be beforehand. Therefore there is a syllogism from a thing having come to be later, but the principle also of these things that have come to be, whence also in things that come to be similarly; but from a prior thing there is not, as that because this has come to be, that has come to be later, and similarly in the future. For neither in infinite nor in finite time will it be, wherefore because it is true to say this has come to be, it is true to say this has come to be later. But in the middle it would be false to say this already when the other has come to be; and the same account holds also in the future. Nor [is it true] that because this has come to be, this will be; for the middle term must be generated at the same time—of things that have come to be, one that has come to be; of future things, one that will be; with things that come to be, to come to be; with things that are, to be—but to be going to be and to be cannot be generated at the same time. Moreover, neither can the middle time be infinite nor finite; for it would be false to say [so] in the middle. One must consider, then, what is the continuous thing, so that after what has come to be there may be a coming to be in things? Or is it manifest that what comes to be is not continuous with having come to be? Nor is what has come to be [continuous] with what has come to be afterwards? For the terms are atomic; just as, therefore, points are not joined to one another, neither are things that have come to be; for both are indivisible.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":100,"ref":"p100","source":"Neque igitur quod fit cum eo quod factum est propter idem quod enim fit, divisibile esi; quod autem factum est,indivisibiIe est.Sicut igitur linea ad punctum se habet, sic quod fit ad quod factum est, sunt enim infinita facta in eo quod 6t,manifestum autem magis est in universaIibus.De motuoportetdicerede his. De eo igitur quomodo cum eo quod consequenter fit generatione se habeat media causa,intantum acceptum sit,nfcesse enim et in his rnediam,et primam immediata essr,ut a lacturn,quoniam factum est posteriua autem factum,a autem prius.Principium igitur est c, propterid quod proximum est ipsi nunc, quod est principium ternporis,serl factum est,si factum est,cum igiturdf'actum est, necesse est et a factum esse: causa autem est c, enim facto, necesse est factum esse,c autem facto, necesse est a prius fuisse. Si autem accipiens aliquod medium stabit alicui immediatum. an semper extra cadet propter infinitum?non enim continuum factum cum faclo,quemadmodum dictum est,sed incipere tamen est necesse a medio,et ab ipso nunc primo Similiter autem est et in eo quod erit;si enim verum est dicere quoniam erit d,DEcesse est prius verum dicere quoniam a erit,hujus autem causa est c, siquidem enim erit, prius erit, si vero erit,prius a erit. Similiterautem et infinita est decisio et in his;non enim erunt quae erunt continua ad invicem,principium autem et in his sine medioaccipiendum est.","english":"Nor, then, is that which is coming to be, together with that which has come to be, divisible on account of the same thing; for that which is coming to be is divisible, but that which has come to be is indivisible. Therefore, as a line is related to a point, so is that which is coming to be related to that which has come to be; for there are infinitely many things that have come to be in that which is coming to be, and this is more evident in universals. Concerning motion, one must speak of these matters. Concerning, then, how the intermediate cause is related in generation to that which follows, let this much be accepted; for it is necessary that in these too there be a middle and a first immediate term, as, for example, that a has come to be because it has come to be afterward, but that which has come to be is prior, and a is prior. The principle, then, is c, because it is nearest to the now, which is the principle of time, [namely] that it has come to be, if it has come to be. When, therefore, it has come to be, it is necessary that a also has come to be; and the cause is c; for when this has come to be, it is necessary that it has come to be; but when c has come to be, it is necessary that a was prior. But if, taking some middle term, one comes to a stop at something immediate, or does it always fall outside on account of the infinite? For that which has come to be is not continuous with that which has come to be, as has been said; but it is necessary to begin from a middle term and from the now itself first. And similarly it is also in that which will be; for if it is true to say that d will be, it is necessary first to say that a will be; and the cause of this is c; for if this will be, it will be prior; but if it will be, a will be prior. And similarly the division is also infinite in these; for the things that will be will not be continuous with one another; but the principle in these too must be taken as immediate.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":101,"ref":"p101","source":"Habent autem sic sein operibus.Si facIa est domus, necesse est decisos esse lapides,etfacturn esse hec propter quid est,quoniam necesse est fundamentum factum esse, si quidem et domus facta est, si vero fundamentum est,prius lapides esse factos necesse ist; iterum si erit domus, similiter prius erunl parietes (demonstratur autem per medium similiter), erit enim fundamentum prius.\n\nCAPUT XIII.\n\nin iis quæ circularem.circulo gignuntur demonstratiollem esse\n\nQuoniam autem videmus in iis quæ fiunt,circulo quamdam generationem ease.et contingit boc esse, si quidem consequanturad invicem medium et termini, in his enim converti est, optensum autem es hoc impriæis quod convertuntur conclusiones circulo autem hoc est.In operibus autem videtur sic,depluta terra, necesse est vaporem fieri, boc autem facto, nubem, bac autem facta,aquarn, hac vero facta,necesse est terram deplutam esse. Hoc autem erat ex principio, quare circulo circuivit, cum enim unum borum quodlibet est alterum est,et cum illud alterum et cum hoc prirnurn.Sunt autem quædam quæ fiunt universaliter,semper enim et in omni aut sic se ha.","english":"For in works things stand thus. If a house has been made, it is necessary that the stones have been cut, and that this has come to be; and the reason why is that it is necessary that the foundation has been made, if indeed the house too has been made; but if the foundation is, it is necessary that the stones have been made first; again, if there will be a house, similarly there will first be walls (and this is demonstrated similarly through the middle term), for the foundation will be first.\n\nCHAPTER XIII.\n\nThat in things which are generated in a circle there is demonstration\n\nSince we see in things that come to be a certain circular generation, and it is possible for this to be so, if indeed the middle term and the extremes follow one another; for in these there is conversion, and it has been shown above all that the conclusions are converted in a circle, and this is [the circle]. But in works it appears thus: the earth having been moistened, it is necessary that vapor come to be; this having been made, cloud; this having been made, water; this having been made, it is necessary that the earth have been moistened. But this was from the beginning; therefore it has gone around in a circle, for when any one of these is, the other is, and when that other is, the first. But there are certain things that come to be universally, for always and in every case either thus they stand.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":102,"ref":"p102","source":"bent, aut fiunt; alia vero quidem semper non, sed sicut frequenter 5unt,ut non omnis homo masculus habet barbam,sed est sicut frequenter.Talium igitur necesse est et medium sicutfrequenteresse.Si enim a de prædicatur universaliter,et hoc de universaliter necesse est, et a de sernper,et de omn prædicari,hoc enim est universaliter,et de omni,et semper,sed suppositum est sicut frequenter esse;necesse est ergo medium sicut frequenter esse quod est in quo b. Erunt ergo et eorum principia frequenter sine medio, quæcunque ut plurimum sic sunt, aut fiunt.\n\nCAPUT XIV.\n\nQuo pacto definilio vesliganda sit..\n\nQuomodo quidem sit quod quid est in terminos assignandum,et qualiter demonstratio,aut definitio sit ipsius, aut non, dictum est prius.Quomodo autem oportet venari in eo quod quid est prædicantia, nunc dicemus.Eorumigiturquæinsuntsemper unicuique, quaedam sc: extendunt in plus, non tamen extra genus.","english":"...or come to be; but others not always, yet as it happens for the most part, as not every man has a beard, but it is so for the most part. Of such things, therefore, it is necessary that the middle term also be as it happens for the most part. For if A is predicated universally of B, and this universally of C, it is necessary that A be predicated always and of every one; for this is what is universal, and of every one, and always. But it has been supposed that it is as it happens for the most part; it is necessary, therefore, that the middle term, which is that in which B is, be as it happens for the most part. Therefore the principles of these things will also be for the most part without a middle term, whatever things are or come to be thus for the most part.\n\nCHAPTER XIV.\n\nHow a definition is to be sought out.\n\nIn what way that which a thing is should be assigned in terms, and how demonstration or definition of it exists or does not, has been said earlier. But in what way one ought to hunt for the predicates in that which a thing is, we shall now say. Of those things, then, which are always present in each thing, some extend more widely, yet not outside the genus.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":103,"ref":"p103","source":"Dico autem in plus esse quæcunque insuntquidem unicuique universaIiter,at non vero et alii, ut est aliquid quod omni trinitati inest,sed et non trinitati;sicut quod est, inest trinitati,sed et non numero, sed impar inest omni trinitati, et in plus est, et namque ipsi quinario inest,sed non extra genus, quinarius quidem numerus est, nullum autem extra numerum, impar est.Hujusmodi igitur accipiendasunt usque ad hoc, quousque tot accipiantur primum quorum unumquodque in plus sit,omniu autem non in plus,banc enim necesse est subslantiam rei esse. Ut trinitati inest omni, numerus imparprimus utrobique,et sicut quod est non mensurari numero,et sicut non componi ex numeris.Hoc itaque jam trinitas eat, numerus impar primus,et sic prirnus.Horum enim unumquodque illa quidem imparibus omnibus insunt,ultimum autem et duaIitati,omnia autem nulli.Quoniam autem osten sum a nobis in superioribus, quod necessaria quidem sunt in eo quod quid est prædicantia,universalia autem necessaria sunt, trinitati autem,et cuilibet alii sic accipiuntur in eo quod quid est accepta, sic ex necessitate quidem erit trinitas haec.","english":"I say that \"in more\" are whatever things belong to each thing universally, but not truly also to others, as there is something that belongs to every trinity, but also to what is not a trinity; such as that which is, belongs to trinity, but also to what is not number; but odd belongs to every trinity, and is in more, for it also belongs to the five itself, but not outside the genus—the five is indeed a number, and nothing outside number is odd. Things of this sort, therefore, are to be taken up to this point, until as many are taken first of which each one is in more, but all together are not in more; for this must be the substance of the thing. As to trinity belongs every number that is odd and primary in both respects, and as that which is not measured by number, and as not composed of numbers. This, then, is already trinity: a number odd, primary, and in this way primary. For each of these belongs to all odd numbers, but the last also to duality, but all together to nothing. Since, however, it has been shown by us in the earlier passages that the things predicated in the what-it-is are necessary, and universals are necessary, but for trinity and for anything else such things are taken as are accepted in the what-it-is, thus from necessity trinity will be this.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":104,"ref":"p104","source":"Quod autem substantia sit, ex his manifestum est, necesse est enim nisi hoc sit trinitatis esse, ut genus aliquod esse;boc autem nominatum est,aut non nominatum erit igitur in plus quam trinitati inexistens.Concessum enim hujusmodi sit esse genus, ut quod insit quidem secundum potentiamin plus,si igitur nulli inest alii quam atomis trinitatibus,hac utique erit trinitatis esse;supponaturenim hoc substantia unius cujusque esse, quae in atomis ultimum praedicatum, quare similiter et alii cuilibet,sic demonstratorum quidem, illi esse erit. Congruum autem est cum totum aliquod negotietur aliquis departiri genus in atoma specie prima,ut numerum in trinitatem, et dualitatem, postea sic illorum definitiones accipere tentare, ut rectae lineæ, et circuli, et recti anguli. Post hæc autem accipientemquod genus sit, ututrum quantitatum,autqualitatum,proprias passiones speculari per communia prima, compositis enim exatomis convenientia,ex definitionibus erunt rnanifesta,propterea quod principium est omnium definitio,et quod simplex est, et simplicibus per se inesse convenientia soIis,aliis autem secundum ilia.","english":"That it is a substance is clear from these considerations; for unless this were so, it would be necessary either that being a trinity be some genus, or that this be named, or else it will be unnamed and thus present in more things than the trinity. For let it be granted that such a thing be a genus, so that it is present indeed in potentiality in more things. If, therefore, it is present in no other things than the atomic trinities, this will surely be the being of the trinity; for let this be supposed to be the substance of each thing, which is the last predicate in atoms. Wherefore similarly also for any other thing, of things demonstrated in this way, that will be its being. It is fitting, moreover, when someone treats of some whole, to divide the genus into first atomic species, as number into trinity and duality, and afterwards thus to attempt to receive their definitions, as of the straight line, the circle, and the right angle. After this, however, one who has grasped what the genus is—whether of quantities or of qualities—should contemplate the proper affections through the common first principles; for the things fitting things composed of atoms will be manifest from the definitions, because definition is the principle of all things, and what is simple, and things fitting simples per se belong to simples alone, but to others according to those.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":105,"ref":"p105","source":"Sed divisiones quæ sunt secundum differentias,utiles sunt ad hoc adeundum, ut tamen monstrant, dictum est prius.Utiles autem erunt sic utique solum ad colligendum quod quid est,et videbitur utique nibil monstrare, sed mox decipere omnia,tanquam si ex princi pio acceperit aliquis sine divisione. Differt autem aliquid primum et posterius prædicamentorum prædicari, ut. est dicere animal mansuetum bipes, vel bipes animal mansuetum; si enim omne ex duobus est,et unum quid sit animal mansuetum,iterurn ex hoc et diiferentiahomo aut quodlibet unum sit, necesse est dividentem petere.AmpIius, nihil relinquendum in eo quod quid est,sic solummodo contingit,cum enim primum accipiatur genus,si quidemalicujus inferiorum aliquam divisionum accipiat,non incidet omne in hoc,ut non omne animal, aut totum pennatum est,aut divisum pennis, sed pennatum,animal omne.Hujusenirn differentia haec est. Prima autem differentia est animalis, in quam omne animal incidit. Similiter autem et in unoquoque aliorum, et in iis quae extra genera, et quae sub ipsis sunt, utinave,in quaest omnis avis, et in pisce, in quo omnis est piscis. Sic igitur vadenti promptum estscirequoniam nihil relictum est, aliter autem relinquere necesse est, et non scire.","english":"But divisions that are made according to differences are useful for this approach, as has been said before, provided that they show it. They will, however, be useful in this way only for collecting what a thing is, and it will seem to show nothing but rather to deceive everything at once, as if someone had taken a starting point without division. But it makes a difference whether the first or the later of the predicaments is predicated, as for example to say \"tame two-footed animal\" or \"two-footed tame animal\"; for if everything is composed of two, and \"tame animal\" is one thing, and again from this and a difference \"man\" or some single thing, then one who divides must necessarily beg the question. Moreover, nothing must be left out in what a thing is, and this is possible only in this way: for when the genus is first taken, if one takes any one of the lower divisions, not everything will fall under it, so that not every animal is either wholly feathered or divided by feathers, but every animal is feathered. For this is the difference of it. But the first difference of animal is that into which every animal falls. Similarly also in each of the others, both in those outside the genera and in those under them, as in the case of bird, in which every bird is, and in fish, in which every fish is. So for one proceeding in this way it is easy to know that nothing has been left out; otherwise one must leave something out and not know.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":106,"ref":"p106","source":"Nibil autem oportet definientem et dividentem omnia scire quæ 5unt,et tamen impopsibiie dicunt esse quidam,differentias cognoscere,quæ sunt ad unumquodque non cognoscentem un umquodque,sine autem differentiis non esseunumquodqusscire,a quo enim non differt,idem esse huic,a quo autem differt, alterum ab hoc. Primum quidem hoc falsum est, non enim secundum omnem differentiam alterum est; multæ enim sunt differentiæ in eisdem specie, sed nonn secundum substantiarn,neque per se.Postea cum accipiantur oppositaetdifferentia,etquod omne incidit hinc aut inde, et accipiat in altero quod quaeritur esse, et hoc cognoscat, nihil differt scire aut non scire de quibuscunque prædicantur aliis differentiæ. Manifestum enim est quod si sic vadens veniat in hæc quorum non est amplius differentia,habebit rationem substantiæ,omne autem incidere in divisionem, sisint opposita quibus aihil interest, non est petitio; necesse est enim omne in altero ipsorum esse, si quidem illius differentia est.Ad probandum autemterminum per divisiones, tria oportet conjecturare, ut accipiantur praedicata in eo quod quid est, et haec ordinate quid primum est, aut secundum,et quoniam haec omnia sint.Est autem unum horum et primum per id quod possumus sicut ad accidens syllogizare, quoniam est et per genus probare.","english":"But the one who defines and divides ought not to know all things that exist, and yet some say it is impossible to know the differences that pertain to each thing without knowing each thing, and that without differences it is not possible to know each thing; for that from which a thing does not differ is the same as it, but that from which it differs is other than it. First, indeed, this is false, for it is not according to every difference that a thing is other; for there are many differences in things of the same species, but not according to substance, nor per se. Next, when opposites and differences are assumed, and that everything falls under one or the other, and one assumes in the one alternative that which is sought to be, and knows this, it makes no difference whether one knows or does not know the other things of which the differences are predicated. For it is evident that if one proceeding in this way arrives at those things of which there is no further difference, he will have the account of the substance; but that everything falls under the division, if the things between which there is no difference are opposites, is not a begging of the question; for it is necessary that everything be in one of them, if indeed it is a difference of that thing. But for proving a term through divisions, three things must be conjectured: that the predicates in the what-it-is be assumed, and these in order—which is first, or second—and that all these exist. And one of these, and the first, is through what we can syllogize as to an accident, that it is, and prove through the genus.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":107,"ref":"p107","source":"Ordinare autem sicut oportet, erit, si primum accipiat, hoc autem erit si accipiatur quod omnibus sequitur,ilIi autem non omnia, necesse est enim aliquod esse hujusmodi, accepto autem hoc,jamidem inferioribus modus,secundum enim,aliorum primum erit, et tertium continuorum remoto enim quod est sursum, continuum aliorum primum erit,simiIiterautem et in aliis.Quod autem omnia bæc sint,manifestum ex hoc quod recipimus, primum quidem secundum divisionem, quoniam omne aut hoc,aut illud est,esl au tem hoc, et iterum hujus totius differentiam,extremi autem non amplius esse differentiam,vel etiam statim cum ultimadiSerentia a toto non differre specie. Hoc manifestum enim est, quoniam neque plus hoc opponitur.","english":"But to arrange them as is fitting will be possible if one takes the first, and this will be if that which follows all is taken; but those do not [follow] all, for it is necessary that there be some such thing. Once this is taken, there is already a limit for the lower ones; for the second will be the first of the others, and the third of those that follow in order. For when that which is above is removed, the first of the others will be continuous, and similarly also in other cases. But that all these are so is manifest from what we have received: first, indeed, with respect to division, since everything is either this or that, and this is so; and again, the difference of this whole; but of the last there is no longer a difference, or even immediately, since the last difference does not differ in species from the whole. For this is manifest, since not even more is this opposed.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":108,"ref":"p108","source":"Omnia enim in eoquod'quid estaccipiunturhornm,neque deficit nihil,aut enim genus,aut differentia utique erit, genus quidem igitur est primum, et cum differentiis hoc acceptum est, differentiæ autem omnes habentur,non enim amplius est posterior.Specie enim utique differret,et uItimum,hocautem dictum est non difl'erre.Quærere autem oportet mtendentem in similia,et indifl'erentia,primum quid omnia idem habeant, postea iterum in altera, quas in eodem quidem genere sunt cum illis, sunt autem ipsis quidem idem specie,ab illis autem altera,cum autem in his accipiatur quid omnino idem, et in aliis simililer,in acceptis iterum intendendum est si idem sit, quousque in unam conveniant rationem. Haec enim erit definitio.Si vero non vadit in unam, sed in duas, aut plures, manifestum est quod utique non est unum aliquod quod prædicatur, sed plura, Ut dico,si quid est magnanimitas quærimus, intendendum est in quosdam rnagnanimos,quosscimus quid habeant unum omnes inquantum sunt huj usmodL Ut si Alcibiades magnanimus,aut Achilles, et Ajax, quid unum omnes habent?","english":"For all things are taken in the what-it-is of these, and nothing is lacking: for it will be either genus or difference. The genus, then, is first, and with the differences this is taken; and all the differences are had, for there is no further posterior one. For it would differ in species, and be last; but this has been said not to differ. But one must inquire, directing attention to things that are similar and undifferentiated: first, what it is that all have the same, then again in another group, those which are in the same genus with those, but are the same in species with them, while others are different from them; and when in these the wholly same thing is taken, and similarly in others, one must again direct attention among the things taken, whether the same thing is present, until they come together into one account. For this will be the definition. But if it does not proceed into one, but into two or more, it is clear that there is not some one thing that is predicated, but several. As I say, if we seek what magnanimity is, one must direct attention to certain magnanimous men, whom we know to have one thing in common insofar as they are of this sort. For example, if Alcibiades is magnanimous, or Achilles, and Ajax, what one thing do all have?","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":109,"ref":"p109","source":"non tolerare injuriati.Hic enim dimicavit,ille insanivit, hic autem interfecitseipsum.Iterum idem est in alteris ut Lysandroj et Socrate,si jam indifferentes esse,et fortunati, etinfortunati; haec duo accipiens intendas quid idem habent, aut impassibilitas quæ est circa fortunas, aut non tolerantia cum injuriantur; si vero nullum sit commune,duæ species erunt utique magnanimitatis. Semperenim estomnis defiaitio universaIis,non enim in quodam oculo dicit sanabile medicus, sed aut in omni, aut in specie determinans.\n\nCAPUT XV.\n\nSpecies facilius quam genera definiri.\n\nFacile autem est magis singulare definire, quam universale,unde oportet a singularibus in universalia ascendere. Et namque aequivocationes magis latent in universalibus quam in indifferentibus.Sicut autem in demonstrationibus oportetsyllogizari inesse sic et in terminis clarum: hoc autem erit, si per ea quae secundum unumquodque dicuntu!',sit in unoquoque genere definiri separatim, ut simile non omne, sed in coloribus et figuris, et acutum,quod est in voce,et sic in commune erit ire,timentem ne æquivocatio contingat.Si autem nou oportet disputare in methaphoris,manifestum est neque definire rnetaphoris,neque quæcunquedicuntur in metaphoris, disputare enim erit necesse in metaphoris.","english":"For to not tolerate being wronged. For this one fought, that one raged, and this one killed himself. Again the same holds in other cases, as with Lysander and Socrates, if they are now alike in being indifferent and fortunate and unfortunate; taking these two, you should consider what they have in common, either insensibility regarding fortunes, or non-tolerance when wronged; but if there is nothing common, they will surely be two species of magnanimity. For every definition is always universal, for the doctor does not say \"curable\" of some particular eye, but either of every eye or of a species determining it.\n\nCHAPTER XV.\n\nSpecies are defined more easily than genera.\n\nIt is easy to define the more particular rather than the universal, and hence one must ascend from particulars to universals. For equivocations lie more hidden in universals than in things not differing. But just as in demonstrations one must syllogize that something belongs, so also in terms it must be clear: and this will be the case if, through the things said according to each one, one defines separately in each genus, as not every similar thing, but in colors and figures, and sharp, which is in the voice, and so one must go to the common, fearing lest equivocation occur. But if one must not dispute in metaphors, it is manifest that neither must one define by metaphors, nor whatever things are said in metaphors; for it will be necessary to dispute in metaphors.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":110,"ref":"p110","source":"CAPUT XVI.\n\nAnatomen el analogiam terminandis problematis momenlum habere.\n\nUt habeamus proposita,eligere oportet decisiones et divisiones,sic autem eligere secundum subjectum genus commune omnium. Ut si animalia sint quae considerantur, qualia omni animaIi insunt.Acceptis autem his, reliquorum primo qualia omni sequantur, ut si hoc est avis,qualia omni sequantur avi et sic sem-. per illiproxima.Manifestum enim est quoniam habebimusjam dicere propter quid insunt sequentia iis quæ sunt sub communi,ut propter quid homini aut equo insunt.Sit autem animal in quo a, autem sequentia omni animali,in quibus autem sunt e e,sicut quaedam ani malia, manifesturn igitur est propter quod est in d, propter a enim, similiter autem et ill aliis, et semper in aliis eadem est ratio. Nunc quidem secundum ea quae assignantur communia nomina, dicimus. Oportet autem non solum in his considerare,sed et si aliud aliquidvidetur commune existens accipientern,posteaquibus boc inhæreat,et qualia huic sequantur,ut cornua hahentibus habere ventres, et non utrobique dentes esse, item habere cornua quibus sequitur, manifestum enim propter quid in illis est quod dicitur, propter id enim quod cornua habent, inest.","english":"CHAPTER XVI.\n\nThat anatomy and analogy have weight for settling problems.\n\nIn order to have our propositions set out, we must select definitions and divisions, and we must select them in this way: according to the common genus of all the subjects under consideration. For example, if the things considered are animals, [we ask] what belongs to every animal. Having accepted these, [we ask] next what belongs to all the rest, first what follows upon every [member], for example if this is a bird, what follows upon every bird, and so always with the things next in order. For it is clear that we shall then be able to state why the things that follow belong to the things that fall under the common [genus], for example why they belong to man or to horse. Let A be animal, and let the things that follow upon every animal be [the attributes]; and let the things in which they are be C, as certain animals. It is clear, then, why [the attribute] is in D: it is because of A. And similarly in the other cases, and always the same account holds in the others. Now we speak according to the common names that are assigned. But one must consider not only these things, but also, if something else seems to be common, [one must] take it, and afterwards [consider] what things it inheres in, and what things follow upon it—for example, that horned animals have bellies, and that they are not to have teeth on both jaws; and likewise, [consider] what things follow upon having horns. For it is clear why what is stated is present in those things: it is present because of their having horns.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":111,"ref":"p111","source":"AmpIius,alius modus est se,cundum anaIogum eIigere,unum enim accipere non est idem, quod oportet vocare seipsum, et spinam, et os,sunt autem quæ sequuntur,et his,tanquam natura una hujusmodiexistente.Eadem autem proposita sunt,quæ quidem idem medium habent,llt quoniam omniacontrarii status,horum autem quædam genere eadem sunt,quæ cunque habent ditferentias, ex quo aliorum aut aliter sunt, ut propter quid resonat, aut propter quid apparet, et propter quod iris; omnia enim hæc quidem unum propositum sunt genere, omnia enim repercussio sunt,sed specie altera. Alia autem ex eo qUlod medium quidem subalternum medium est,differunt propositorurn,ut propter quid Nilus finiente mense nJagisfluit? propter id quod hibernior est finiens mensis. Propter quid autem hibernior est finiens mensis? propterid quod luna deficit. Hæc enim sic se habent ad invicem.","english":"Further, there is another mode of selecting according to analogy; for to take one thing is not the same as what one ought to call itself, and a spine, and a bone; and the following things are so, these being as it were one nature of this kind. The same propositions are also those which have the same middle term, for example, why every contrary has a state; of these, however, some are the same in kind, whatever have differences, from which they are either otherwise or in another way, as why it resounds, or why it appears, and why the rainbow; for all these are one proposition in kind, for all are a reflection, but differ in species. Others differ in their propositions because the middle term is a subordinate middle term, as why does the Nile flow more at the end of the month? Because the end of the month is more wintry. But why is the end of the month more wintry? Because the moon fails. For these are related to one another in this way.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":112,"ref":"p112","source":"CAPUT XVII.\n\nDe causis et etfeciis, et an unius plures sivit causæ.\n\nDe causa autem,et cujuscausa est dubitabit aliquis, nunquid cum causatum est,et causa est,ut si folia fluunt, aut deficit luna, et causa deficiendi,vel folia cadendi erit,ut si hujus est lata habere folia, deficiendi autem terram in medio esse.Si enim non, aliqua alia erit causa ipsorum, si vero causa sit,et causatum simuI,ut si in medio est terra,deficit,aut, si latum est folium, folia flunnt; si autem sic est, simul utique erunt,et demonstrabuntur per invicem. Sit enim folium fluere in quo a,latum autem folium in quo b,vitis vero in quo::,si igitur in est a,omne enim latum folium habens folio fluit, autem inest b,omnis enim vitis habet lata folia,et ain est, omnis vitis folio fluit: causa est medium. Sed et quoniam latis foliis vitis sit,est propter id quod folio fluit demonstrare. Sit enim latum quidem folium, e autem folio fluere, vitis vero in quo f. In / igitur est e,etenim folio Unit omnis vitis,in e autem est,omne enim fluens folio,latum est folium babens; omnis itaque vitis latum est folium habens, causa autem est folio fluere.Si autem non contingit casus esse ad invicem, causa enim prius est eo cujus est causa,et deficiendi quidem est causa,terram esse in medio,ejus autem quod est in medio terram esse, non est causa deficere.","english":"CHAPTER XVII.\n\nOn causes and effects, and whether one thing has several causes.\n\nConcerning cause, and that of which it is the cause, someone will raise the question whether, when the effect exists, the cause also exists: for example, if leaves fall or the moon wanes, will there be a cause of the waning or of the falling of the leaves—as, if this [tree] has broad leaves, [the cause] of falling is that the earth is in the middle. For if not, there will be some other cause of these things; but if the cause exists, the effect exists at the same time: as, if the earth is in the middle, [the moon] wanes; or, if the leaf is broad, the leaves fall. But if it is so, they will surely exist at the same time and will be demonstrated through one another. For let \"leaves fall\" be that in which A [is present], \"broad leaf\" that in which B [is present], \"vine\" that in which C [is present]. If then A is present in B—for every broad-leaved [plant] sheds its leaves—and B is present in C—for every vine has broad leaves—then A is present in C: every vine sheds its leaves. The cause is the middle term. But also, because the vine has broad leaves, one may demonstrate that it sheds its leaves on account of this. For let \"broad leaf\" be [that in which] E [is present], \"shedding leaves\" [that in which] F [is present], and \"vine\" that in which G [is present]. In G, then, F is present—for every vine sheds its leaves; and in F, E is present—for everything that sheds its leaves has broad leaves; therefore every vine has broad leaves. The cause is the shedding of leaves. But if one cannot have reciprocal predication—for the cause is prior to that of which it is the cause—then the cause of waning is that the earth is in the middle; but of the earth's being in the middle, the waning is not the cause.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":113,"ref":"p113","source":"Si igit,ur per causam demonstratio est, propter quid est, si vero non per causam ipsius,quia,quoniam quidemterrain medio est cognovit, propter qu:d autem non. Quod autem non, deficere causa sit in medio esse, sed hoc, deficiendi manifestum est; in ratione enim deficiendi, inest quod est in medio,quare manifestum est quod per hoc illud cognoscetur, sed, non boc per illud. Į An contingit unius pluresesse causas?et namquE si est idem de pluribus primis prædicari primo,sit a in primo existens, et in alio primo, et hoc sit in d, hoc vero sit in e, erit itaque a in et in e, causa autem quod a sit in dquidcm b,in e autem c;quaro cum causa sit,necesse est rem omnem esse, sed res cum sit, non necesse est esse omne quodcunque sit causa, sed causam quidem necesse est esse, non tamen omnem.An si semper universale propositum, et causa totum quiddam est,et cujus est causa universalo?ut foliofluere intoto quodam determinatum est, et species ipsius sint. Universaliter igitur aut pIantis,aut hujusmodi plantis,quare et medium aequale oportet esse in his et cujus est causa,et converti, ut propter quid arbores folio fluunt, si ergo propterdensitatem humidi,sive folio fluit arbor,opor. tet esse densitatem, sive densitas est non in qualibet, sed in arbore, est folio Quere. Utrum autem contingat non eamdem essecausam ejusdem in omnibus, sed alteram, an non?","english":"If, then, demonstration through the cause is demonstration of the reason why, but if not through the cause itself, it is demonstration of the fact—for instance, one knows that the earth is in the middle, but not why. That the cause of not being in the middle is lacking, however, is evident; for in the account of lacking, that which is in the middle is present, so it is clear that through this that will be known, but not this through that. Whether it is possible for one thing to have several causes? For if the same thing is predicated primarily of several primary things, let A be present in a primary thing, and in another primary thing, and let this be in D, but that in E; then A will be in both D and E, and the cause of A's being in D is B, but of its being in E is C. Therefore, since the cause exists, the thing must also exist; but when the thing exists, it is not necessary that everything whatsoever that is a cause exist—rather, the cause must exist, but not every cause. Or, if the proposition is always universal, is the cause also a whole, and is that of which it is the cause universal? For instance, shedding leaves is determined within a certain whole, and its species exist. Universally, therefore, either of a plant, or of plants of this sort; hence the middle term must also be equal in these, both in respect of that of which it is the cause, and it must convert—as, for example, why do trees shed leaves? If, then, because of the density of moisture, either the tree sheds leaves, the density must exist; or if density is not in any chance thing, but in a tree, then it sheds leaves. But whether it is possible that the same cause is not the cause of the same thing in all cases, but a different one, or not?","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":114,"ref":"p114","source":"an siquidem per se demonstretur,aut non secundum signum aut accidens? non potest esse. Ratio enim extremi, medium; si vero non sic contingit, est autem et cujus causa et cui, considerare secundunn accidens, non tamen videntur proposita esse.Si autem non,similiter se habebit rnedium,siquidem sunt æquivoca,æquivocum medium est,si vero sicut in genere,similiter se habebit, ut propter quid commutabiliter, anaIogurn, alia enim est causa in numeris,et in Iineis,et eadem quidem inquantum lineæ, alia,inquantum autem ha. bens augmentum hujusmodi,eadem,sic in omnibus. Similem autem esse colorem coIori,etfiguram figuræ, aliam esse causam alii,æquivocum enim est simile in bis,hic quidemest fortassissecundum analogiam habere latera et aequales anguIos,in coloribus autem unumsensumesse,autaHquid aliud hujusmodi,quæ autem secundum analogiam sunt eadem,et medium habent secundum analogiam.Habet autem sic consequi causa ad invicem, et cujus est causa,et cui est causa unum quodque quidem accipienti,et cujus est causa in plus est, ut quatuor æquales qui sunt ext.ra,in plus sunt quam triangulus,aut quadrangulus,in omnibus autem ut in aequalibus est, quaecunque pnim,quator aequales qui sunt extra,et medium similiter est.","english":"For if it is demonstrated through itself, is it not according to sign or accident? It cannot be. For the definition of the extreme is the middle term; but if this does not hold in that way, yet there is both that of which it is the cause and that for which it is the cause, to consider according to accident—nevertheless the things proposed do not seem to be so. But if not, the middle term will be related in like manner; if indeed they are equivocal, the middle term is equivocal; but if as in a genus, it will be related in like manner, as the reason why convertibly, by analogy—for the cause is different in numbers and in lines, and the same insofar as they are lines, but different insofar as they have increase of this sort, the same—so in all cases. But for color to be similar to color, and figure to figure, the cause is different for each; for \"similar\" is equivocal in these cases—here perhaps it is to have sides and equal angles according to analogy, but in colors it is for there to be one sensation, or something else of this sort; and those things which are the same according to analogy also have a middle term according to analogy. But the cause is related in this way to one another, both that of which it is the cause and that for which it is the cause: for each one, when taken, that of which it is the cause is more extensive, as the four equal [angles] that are outside are more extensive than a triangle or a quadrilateral; but in all cases as in equals, whatever they are—for the four equal [angles] that are outside, and the middle term is similarly.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":115,"ref":"p115","source":"Estautem medium ratio primi extremi,ex quo omnes scientiæ per definitionem fiunt; ut folio fluere si militer sequitur viti, et excellit,et ficui pt excelJit,eed non omnia,sed æqual ia sunt;si vero acci[1ias primum medium, ratio fluendi foliisest, erit enim primum quidem in altera, medium, quoniam hujusmodi suntomnia,deinde hujus medium,quoniam succus densatur,autiquiddam aliud hujusmodi. Quid autem est folio fluere? densari in contactu seminis succum.In figuris autem sicassignabit quærentibus consecutionem causæ,et cujus est causa,sit a quidem in omni, autem in unoquoque eorum qua? sunt d,in plus autem, igituruniversale utique ipsis inerit j hoc autem dico universale, quod non convertitur, primum autem universale, cui unumquoque quidem non convertitur, omnia autem convertuntur, et non excedunt, ipsis igitur causa ipsius a est b. Oportet itaque a in plna quam extendi; si vero non, quid magis causa erit boc illius? Si igitur in omnibus e est a, erunt aliquid illa unum omnia aliud quam b.Si enim non, quomodo erit dicere quoniam in quo est e sit a, omni? in quo autem a non omni sit? 6? propter quid enim non eritcausa aliqua ut a sit in omnibus d? sed nunquid et quae sunt e erunt aliquod unum? considerare oportet hoc,et sit e,contingil igitur ej usdem plures causas esse, sed non eisdem specie.","english":"But the middle term is the definition of the first extreme, from which all sciences come about through definition; for example, if the flowing of leaves follows similarly for the vine, and it excels, and for the fig it excels, but not all things, but they are equal; but if you take the first middle term, the definition of the flowing of leaves is the reason, for there will be first, in one, the middle term, that all such things are so, then the middle term of this, that the moisture thickens, or something else of this sort. But what is it for a leaf to flow? For the moisture to thicken at the contact of the seed. In figures, however, he will assign to those seeking the sequence of the cause and that of which it is the cause: let A be in every one, and in each of the things that are D, but in more; therefore the universal will surely be in them. But I call that universal which is not convertible; but the first universal is that to which each one indeed is not convertible, but all are convertible and do not exceed. Therefore the cause of A itself is B. It is necessary, then, that A extend more widely; but if not, what will be the cause of this rather than that? If, therefore, E is A in all things, those things will be some one thing other than B. For if not, how will it be possible to say that in whatever E is, A is in every one? But in whatever A is, it is not in every one? For why will there not be some cause that A is in all D? But will the things that are E also be some one thing? It is necessary to consider this, and let it be E. It happens, therefore, that there are several causes of the same thing, but not the same in species.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[{"kind":"lacuna","severity":"caution","text":"The source is fragmentary here: the edition marks a break or an editorial bracket, and the English carries across it. Treat the bridge as supplied, not translated."}]},{"i":116,"ref":"p116","source":"Ut longæ vitae quadrupedia,non habere cboleram causa est, volatilia autem, sicca esse aut altera aliqua, si autem nalomum non statim veniunt,et non solum unum medium, sed plura, et causæ plures sunt. Utrum autem causa mediorum,quod ad universale primum est, aut quod ad singulare singularibus? Manifestum igitur est ea esse, quae proxima unicuiquecuicausaept,primumenimsub universaIi esse,hæc est causa,ut in d,sit quod est a,causa est c, in quidem igitur essea,causa est c,in autem b, in hoc autem, eadem est. De syllogismo igitur, et de demonstratione, quidque unumquoque est, et quomodo fit,manifestum est,simul autem et de scientia demonstrativa, idem enim est.\n\nCAPUT XVIII.\n\nQuomodo principia cognoscantur,et sit habitus.quis principio rum\n\nDe principiis autem qualiter fiunt cognita,etquis gst cognoscens habitus, hinc est manifestumjdubitantibus prirnum.Quod quidem igiturnon contingit sci re per demonstrationem,non cognoscentem prima principia imrnediata, dictum est prius, immediatorum autem cognitionem utrum eadem est, an non eadem,dubitabit utique aliqnis. Et utrum scientia in utroque est, an nOn,an hujus quidem scientia,ilJius auterr, alterum aliquod genus sit.","english":"That long-lived quadrupeds are without choler is the cause; but that birds are dry, or some other such thing. But if the causes do not come about at once, and there is not only one middle term but several, and the causes are several. But whether the cause of the middle terms is that which is first with respect to the universal, or that which is with respect to the singular for singulars? It is evident, then, that they are those which are nearest to each thing and to each cause; for the first is to be under the universal; this is the cause, as in the case of d, that which is a is the cause, and c is the cause; in respect of essence, then, c is the cause, but in respect of b, and in this, it is the same. Concerning syllogism, then, and demonstration, what each one is and how it comes about, is evident; and at the same time concerning demonstrative science, for it is the same.\n\nCHAPTER XVIII.\n\nHow principles are known, and what habit is. Which of the principles\n\nConcerning principles, however, how they become known, and what the knowing habit is, is evident from this, for those who first raise the question. That it does not happen that one knows through demonstration without knowing the first immediate principles has been said before; but whether the cognition of immediates is the same or not the same, someone will indeed doubt. And whether science is in both, or not, or whether of this one there is science, but of that one some other genus.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":117,"ref":"p117","source":"Et utrum cum non insint habitus, fiant, an cum insint, JateanL Siquidern igitur habemus ipsos,inconveniens est,contingit enim certiores habere cognitiones demonstratione, et Jatere,si autem accipiamus non habentes prius,qualiter utique cognoscamus,et addiscamus ex non praeexistenti cognitione? impossibile enim est, sicntin demonstratione diximus. Manifestum igitur estquoniamnequc; habere possi bile est(neque ignorantibus)etnequo non habentibus habitum fieri.Necesse ast itaque habere quamdam quid em potentiam, non h:Jjusmodi autem habere quae est his honor.bilior secundum certitudinem. Videtur autem hæe omnibusinesseanimalibus,babent Anim connaturalem potentiam judicativam,quam vocant sensum. Cum insit autem sensus,in iis quidem animalium fit mansio sensibil is,in alii\" autern non fit, in qmbuscunque igitur non fit\"aut omnino,aut circa quæ non fit, nec estin his cognitio extra qnod sentiunl;in quibus autem iuest sentientibus habere unum quiddam in anima multis quidem factis hujusmodijamdifFerentia quædam fit, ut in his quamdam sit fieri rationern ex lalium memoria,in aliis vero non. Ex sensu igitur fit memoria, sicut dicimus. Ex memoria autem multoties ejusdem t'acta, experimentum.","english":"And whether they come to be when the habits are not present, or when they are present, is unclear. For if we have them, it is strange—for it follows that we have more certain cognitions than demonstration—and to be unaware, if we do not have them; but if we receive them without having them beforehand, how shall we know and learn from a cognition that did not pre-exist? For it is impossible, as we said in the demonstration. It is clear, therefore, that neither is it possible to have them (nor for those who are ignorant), nor for those who do not have the habit to come to be. It is necessary, then, to have a certain power, but not to have it of such a kind as is more honorable than these in respect of certainty. But this seems to be present in all animals: for they have a connatural power of judgment, which they call sense. But when sense is present, in some animals a persistence of the sensible comes about, but in others it does not; in those, then, in which it does not come about, either altogether or concerning those things about which it does not come about, there is no cognition in them beyond what they sense; but in those in which it does come about, when they have sensed, there is a certain one thing in the soul, and when many such things have been made, a certain difference already comes about, so that in some there is a certain principle of reason from the memory of such things, but in others not. From sense, therefore, memory comes about, as we say. But from memory, when the same thing has been made many times, experience.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":118,"ref":"p118","source":"Multæ enim memoria' numero experimentum est unum, ex experimento aut ex omni quiescente universali in anim;, uno pra'ter multa (quod cum in omnibus unum sit illud idem) artis principium, et scientiæ,si quidem igitur circa generationem artis est,si vero circa ens, scientiæ. Neque igitur insunt determinati habitus, neque abaliis babitibus fiunt notioribus,sed a sensu. Ut in pugna eversione f'acta, uno stanle,alter stetit, postea aller,quousque in principium veniaat,anima autem hujusmodi. cum sit qualis possit pati hoc. Quod autem dictua est, ante, sed non clare dictum est,iterum dicamus;stante enim uno indiSerentium, primum quidem in anima universale est,et namque sentire quidem singulare, sensusautem universalis est, ut bominis non Callia; hominis. Ilerum in his statur,quousque uti im partibilia stentet universalia, ut hujusmodi animal, quousque anima!, et in hoc similiter.Manifestum igiturest quoniam nobis pri nia inductione cognoscere necessarium est, et namque et sensus sic universale facit Quoniam autem circa intelligentiam habituum quibus verum dicimus,alii quidem semper veri sunt, alii recipiunt falsitatem, ut opinio: et ratio, vera antem semper sunt scientia ct.inteIlectus,et nihil est scientia certil1s aliud genus quam intellect liS, principia autem dcmonstralionibus notiora sunt, scientia autem omnis cum ratione est, principiorum scientia quidem non utique erit.","english":"For many memories numerically make one experience, and from experience—or from the universal wholly at rest in the soul, the one beside the many (whichever, being one and the same in all of them, is the principle of art and of science)—if indeed it concerns coming to be, it is of art; but if it concerns being, it is of science. Therefore neither are determinate habits present, nor do they come from other, more known habits, but from sense. As in a battle when a rout has occurred, one man stands fast, then another, and afterwards another, until they come back to the beginning; and the soul is of such a nature as to be able to undergo this. But what was said before, though not clearly said, let us say again: for when one of the indiscernibles has stood fast, first indeed a universal is in the soul—for one perceives the singular, but sense is of the universal, as of man, not of Callias; of man. Again one comes to rest in these, until the indivisible universals stand fast, as of such-and-such an animal, until of animal, and in this likewise. It is evident, therefore, that we must know the first principles by induction; for indeed sense in this way makes the universal. But since concerning understanding—of the habits by which we speak the truth, some are always true, others admit falsehood, as opinion and reasoning; but science and intellect are always true, and no other genus is more certain than science than intellect; and the principles are more known than demonstrations, while all science is with reason—there will surely not be science of the principles.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":119,"ref":"p119","source":"Quoniam autem nihil verius contingit esse scientia quam intellectum, inteI!eclus utique erit principioru Ex his considerantibus et quomam demonstrationis principium non demonstratio, quare neque scientiæ scientia, si igitur nullum aliud praeter scientiam habemus genus verum,intellectus utique eritscientiae principium, et principium quidem principii erit utique: omne autem similiter se habet ad rem omnem.","english":"Since nothing truer than knowledge can be, namely understanding, understanding will assuredly be the principle of principles. From these considerations, and because the principle of demonstration is not demonstration, neither therefore is there knowledge of knowledge. If, then, we have no other true genus besides knowledge, understanding will assuredly be the principle of knowledge, and it will indeed be the principle of principle; but everything is related in like manner to every thing.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]}]}