Nam, ut superius dictum est, non sufficitquolibet modo jungere terminos,ut fiant hypotheticae propositiones ex duabus conditionalibus conjugatae.Non enim si quis dicat, si cum homo est, animal est, cum dies est, lucet, talem fecerit propositionem quae duabus conditionibus constet, idcirco quia prior conditio non est secundae causa conditionis, hoc igitur superius positarum propositionum ratio demonstrat,quemadmodum fit, ut conditionem conditio consequatur. Quae cum ita sint de earum dicendum est syllogismis. Fit igitur ex prima propositione syllogismus hoc modo: si cum est a, est b, cum sit c, est d. Atqui cum sit a, est b, cum igitur sit c, erit; vel ita, atqui cum sit c, non est d, cum igitur sita, non est b. Posse vero hanc esseassumptionem superius descriptapropositionum naturademonstrat.Item ex secunda propositione, si cum est a, est b, cum sit c, non est d. Atqui cum sit a, est b, cum igitur sit c, non est; vel ita, atqui cum sit c,est d, cum igitur sit a, non est b. Ex tota, si cum sit a, est b, cum non sit c, est d. Atqui cum sit a est b, cum igitur non sit c, est; vel ita, atqui cum non site, non est d, cumigitursita, non est b. Item ex quarta, si cum sit a, est b, cum non sit c, non est d. Sed cum sit a, est b, cum igitur non sit c, non; vel ita, atqui cum non sit c, est d, cum igitur sit a, non est t.
For, as was said above, it is not sufficient to join terms in any way whatever for hypothetical propositions to be made from two combined conditionals. For if someone says, "if when a man is, an animal is, when day is, it is light," he has not for that reason made a proposition consisting of two conditions, because the prior condition is not the cause of the second condition. Therefore the account of the propositions set out above demonstrates how it comes about that a condition follows a condition. Since these things are so, one must speak of their syllogisms. From the first proposition, then, a syllogism is made in this way: if when a is, b is, when c is, d is. But when a is, b is; when c is, therefore, it will be; or thus: but when c is, d is not; when a is, therefore, b is not. That this assumption can hold, the nature of the propositions described above demonstrates. Likewise from the second proposition: if when a is, b is, when c is, d is not. But when a is, b is; when c is, therefore, it is not; or thus: but when c is, d is; when a is, therefore, b is not. From the whole: if when a is, b is, when c is not, d is. But when a is, b is; when c is not, therefore, it is; or thus: but when c is not, d is not; when a is, therefore, b is not. Likewise from the fourth: if when a is, b is, when c is not, d is not. But when a is, b is; when c is not, therefore, it is not; or thus: but when c is not, d is; when a is, therefore, it is not.
Ex quinta propositione fiunt quatuor collectiones, ita namque termini proponuntur, ut utrobique fiat rata conclusio hoc modo: si cum est a, non est b, cum sit c, est d. A tqui cum sit a, non estb, cum igitur, sit c, est; vel ita, atqui cum sit a, est b, cum igitur sit c, non est; vel ita, atqui cum sit c, non est d, I cum igitursit a, est; vel ita, atqui eum sit c, est d, cum igitur sit a, non est b. Ex sexta, si cum esta, non est 6, cum sit c, non est d. Atqui cum sit. a, non est b, cum igitur sit,non est; vel ita, atqui cum sit c, non est d. Cum igitur sit a, est b. Ex septima item fiunt quatuor syllogismi hoc modo, si cum est a, non est b, cum non sit c, est d. Atqui cum est a, non estb, cum igitur nonsit c, est d; vel ita, atqui cum sit a, est b, cum igitur non sit c, non est, vel ita, atqui cum non sit c, non est d, cum igitur sit a, est; vel ita, atqui cum non sit c, est d, cum igitur a sit, non est b. Ex octava propositione, si cum est a, non est b, cum non site, non est d. Atqui cum sit a, non est b, cum igitur non sit c,est; vel ita, atqui cumnonsitc,estd,cum igitur site, est b.
From the fifth proposition four collections are made; for the terms are set out in such a way that a valid conclusion is produced on both sides, in this way: if when a is, b is not, when c is, d is. But when a is, b is not; therefore when c is, d is; or thus: but when a is, b is; therefore when c is, d is not; or thus: but when c is, d is not; therefore when a is, b is; or thus: but when c is, d is; therefore when a is, b is not. From the sixth: if when a is, b is not, when c is, d is not. But when a is, b is not; therefore when c is, d is not; or thus: but when c is, d is not; therefore when a is, b is. From the seventh likewise four syllogisms are made in this way: if when a is, b is not, when c is not, d is. But when a is, b is not; therefore when c is not, d is; or thus: but when a is, b is; therefore when c is not, d is not; or thus: but when c is not, d is not; therefore when a is, b is; or thus: but when c is not, d is; therefore when a is, b is not. From the eighth proposition: if when a is, b is not, when c is not, d is not. But when a is, b is not; therefore when c is not, d is; or thus: but when c is not, d is; therefore when a is, b is.
Hactenus quidem ex hujusmodi propositionibus, quae a esse proponebant, atque itacætcros terminos affirmando negandoque variabant, ostendimus quifierent syllogismi.Nunc ex his propositionibus quinam syllogismi fiantdicendum est,quæitacæteros terminos varia.nt,ut a quidem non esse proponant.Exnona enim propositione fit syllogismus ita, si cum non est a, est 6, cum sit c, est d. Atqui cum non sit a, est b, cum igitur sit, c, est; vel ita, atqui cum sit c, non est d, cum igitur non sit a, non est 6. Item ex decima, si cum non est a, est b, cum sit c, non est d. Atqui cum non est a, est b, cum igitur c, non est d; vel ita, atqui cum sit c, est d, cum igitur non sit a, non est b. Ex undecima, si cum non est a, est b, cum non sit c, est d. Atqui cum non sit a, est b, cum igitur non sit c, est d; vel ita, at cum non sit c, non est d, cum igitur non sit a, non est b. Ex duodecima, si cum non sit a, est b, cum non sit c, non est d,atqui cum non sit a,est b, cum igitur non eit c, non est d;vel ita, atqui cum non sit c, est d, cum igitur non sit a, non est b. Ex tertia decima, quae quatuor colligit syllogismos hoc modo: si cum non est a, non est b,!:cum sit c, est d.
Up to this point, indeed, from propositions of this kind, which proposed that a is, and in this way varied the other terms by affirming and denying, we have shown what syllogisms come about. Now it must be said what syllogisms come about from those propositions which vary the other terms in such a way that they propose that a is not. For from the ninth proposition a syllogism is made thus: if when a is not, b is, when c is, d is. But when a is not, b is; therefore when c is, d is; or thus: but when c is, d is not; therefore when a is not, b is not. Likewise from the tenth: if when a is not, b is, when c is, d is not. But when a is not, b is; therefore when c is, d is not; or thus: but when c is, d is; therefore when a is not, b is not. From the eleventh: if when a is not, b is, when c is not, d is. But when a is not, b is; therefore when c is not, d is; or thus: but when c is not, d is not; therefore when a is not, b is not. From the twelfth: if when a is not, b is, when c is not, d is not; but when a is not, b is; therefore when c is not, d is not; or thus: but when c is not, d is; therefore when a is not, b is not. From the thirteenth, which collects four syllogisms in this way: if when a is not, b is not, when c is, d is.
Atqui cum non sit a, non est b, cum sit c, est d; vel ita, atqui cum non sit a.est b, cum igitur c, non est; vel ita,atqui cum sit c, est d,cum igiturnon sit a, non est 6; vel iLa,atqui cum sit c, non est d, cum igitur non sit a,est b.ltem ex quarta decima, si cum non est a, non est b, cum sit c, non est d. Atqui cum non est a,non est b,cum igitur sit c, non est d; vel ita,atquicum sit c,est d,cum igitur non sit a, est b. Quinta decima rursus quatuor colligit syllogismos, hoc modo: si cum non est a,non est 6, cum non sit c, est d.Atqui cum non sit a, non est b, cum igitur non sit e, est d; vel ita, atqui cum non sit a, est b, cum igitur non sit c,est d;vel ita, atqui cum non sit c, non est d, cum igitur non sit, a, est; vel ita, atqui cum non sit c,est d,cum igitur non sit a, non est b. Ex sexta decima propositione;si cum non sit a,non est b, cum non c, non est d. Atqui cum non sit a, non est b, cum igitur ron sit c, non est d; vel ita atqui cum non sit c, est d. Cum igitur non sit a, est b.Ex quibus omnibus quadragintaconclusiones fiunt.Sedecim quidem assumpta prima conditione, ita utin prima propositione est posita.Sedecim vero assumpta secunda conditionecontrario modo atque in propositione est collocata.
But when a is not, b is not, when c is, d is; or thus: but when a is not, b is, when therefore c is, it is not; or thus: but when c is, d is, when therefore a is not, b is not; or thus: but when c is, d is not, when therefore a is not, b is. Likewise from the fourteenth: if when a is not, b is not, when c is, d is not. But when a is not, b is not, when therefore c is, d is not; or thus: but when c is, d is, when therefore a is not, b is. The fifteenth again collects four syllogisms, in this way: if when a is not, b is not, when c is not, d is. But when a is not, b is not, when therefore c is not, d is; or thus: but when a is not, b is, when therefore c is not, d is; or thus: but when c is not, d is not, when therefore a is not, it is; or thus: but when c is not, d is, when therefore a is not, b is not. From the sixteenth proposition: if when a is not, b is not, when c is not, d is not. But when a is not, b is not, when therefore c is not, d is not; or thus: but when c is not, d is. When therefore a is not, b is. From all these forty conclusions are made. Sixteen indeed by assuming the first condition, as it is placed in the first proposition. Sixteen truly by assuming the second condition in the contrary way and as it is set out in the proposition.
Octo vero ex quinta, septima,tertia decima et quinta decima propositionibus fiunt assumptisprimisquidem conditionibus contrario modo,atquein propositione proferebantur secundis vero conditionibus eodem modo assumptis, ut in propositione fuerant collocatæ. Ut igitur omnium propositionumconclusionumque ratio clarescat,omnes hujusmodi enuntiationes cum propriis proposuimus exemplis.
Si cum sit a homo, est medicus, cum sit animatum, est artifex.
Si cum sit a homo, est niger, cum sit animatus, non est albus.
Si cum sit a animatum, est medicus, cum non sit inanimatum, est artifex.
Si cum sit a homo, est niger, cum non sit v inanimatus, non est albus.
Si cum sit a homo, non est aeger, cum sit animatus, est sanus.
Si cum sit a homo, non est artifex, cum sit animatus,non est medicus.
Si cum sit a animal, non est sanus, cum non sit inanimatum, est aegrum.
But eight [syllogisms] are made from the fifth, seventh, thirteenth, and fifteenth propositions, with the first conditions indeed assumed in the contrary way to that in which they were set forth in the proposition, but with the second conditions assumed in the same way as they had been placed in the proposition. Therefore, so that the account of all the propositions and conclusions may be clear, we have set forth all enunciations of this kind with their own examples.
If when a is a man, he is a physician, then when he is animate, he is a craftsman.
If when a is a man, he is black, then when he is animate, he is not white.
If when a is animate, he is a physician, then when he is not inanimate, he is a craftsman.
If when a is a man, he is black, then when he is not inanimate, he is not white.
If when a is a man, he is not sick, then when he is animate, he is healthy.
If when a is a man, he is not a craftsman, then when he is animate, he is not a physician.
If when a is an animal, he is not healthy, then when he is not inanimate, he is sick.
Si cum sit a animatum, non est artifex, cum non sit inanimatum, non est medicus.
Si cum non sit a iDanirnatum, est medicus, cum sit animatum, est artifex.
Si cum non sit a inanimatum, est niger, cum sit inanimatum, non est album.
Si cum non sit a inanimatum, est medicus, cum non sit invitale, est artifex.
Si cum non sit a inanimatum, est album, cum sit invitale, non est nigrum.
Si cum non sit a irrationale, non est aegrum, cum sit rationale, est sanum.
Si cum non sit a inanimatum, non est artifex, cum sit animatum, non est medicus.
Si cum non sit a irrationale, non est sanum, cum non sit inanimatum, e3t aegrum.
Si cum non sit a inanimatum, non est artifex, cum non sit invitale, non est modicus.
Ac de his quidem qui per connexionem fiunthæc dicta sint. Hi vero qui in disjunctione sunt positi illis videntur adjuncti,eorumque modos formasque suscipiunt,quos superius in connexione pusitos ex his propositionibus fieri diximus quae duabus simplicibus j ungerer.tur.Si igitur in disjunctionepropositarum propositionum adcausarum similitudinem monstravero quae in connexione positae ex simplicibus copulatas sunt, quot modi,qualescunque conclusiones sunt in unaquaque illarum, quas per connexionem fiunt propositionum, totetiam in his esse necesse est quae per disjunctionem pronuntiatæ eamdem vim connexionis habere monstratur.
If when a is animate, he is not a craftsman, then when he is not inanimate, he is not a physician.
If when a is not inanimate, he is a physician, then when he is animate, he is a craftsman.
If when a is not inanimate, he is black, then when he is inanimate, he is not white.
If when a is not inanimate, he is a physician, then when he is not invitale, he is a craftsman.
If when a is not inanimate, he is white, then when he is invitale, he is not black.
If when a is not irrational, he is not sick, then when he is rational, he is healthy.
If when a is not inanimate, he is not a craftsman, then when he is animate, he is not a physician.
If when a is not irrational, he is not healthy, then when he is not inanimate, he is sick.
If when a is not inanimate, he is not a craftsman, then when he is not invitale, he is not a physician.
And indeed let these things be said concerning those which are made through connection. But those which are placed in disjunction seem to be joined to them, and they receive the modes and forms of those which, placed above in connection, we said are made from those propositions which were joined from two simples. If therefore in disjunction I show, according to the likeness of the causes, the propositions placed in connection which are copulated from simples, it is necessary that however many modes and of whatever kind the conclusions are in each of those propositions which are made through connection, so many are also in these which are pronounced through disjunction and are shown to have the same force of connection.
Quatuor igitur superius differentias per connexionem enuntiatarum propositionum esse diximus, si ex simplicibus propositionibus copularentur,hoc m'odo si est a, est 6; si non est a, non est 6, si est a non est b; si non est a,est b. Per disjunctionem quoque propositiones quatuor tenent differentias hoc modo: aut est a, aut est b: aut non est a, aut non est b;aut est a, aut non est 6; aut non est a,aut est b. Quarum quidem ea quae prima est et proponit,aut est a,aut est b.ln his tantum dici potest in quibus aUerum eorum esse necesse est, velut in contrariis medietatecarentibus, similisqueest ei propositioni quæ dicit: si non est a, est b. Quae enim proponit aut est a, aut est b, id intelligit, nequesimul utraequeesse posse,et si unum non fuerit,consequi ut sit alterum. Itaque si non sit a, erit b,sed haec una est earum propositionum quas in his quae per connexionem fiunt superius numeravimus. Quicunque igitur syllogismi in eapropositionefiunt, qua; est,si non est a, esl b, hi etiam in ea faciendi sunt quae per disjunctionem proponetur, ut cum dicimus,aut est a, aut est b.
We said above, therefore, that there are four differences of propositions connected by connexion, if they are joined from simple propositions, in this way: if a is, b is; if a is not, b is not; if a is, b is not; if a is not, b is. Through disjunction also, propositions hold four differences in this way: either a is, or b is; either a is not, or b is not; either a is, or b is not; either a is not, or b is. Of these, indeed, the one that is first and proposes "either a is, or b is"—this can be said only in those cases in which it is necessary that one of them be, as in contraries lacking a middle, and it is similar to that proposition which says: if a is not, b is. For the one that proposes "either a is, or b is" understands that both cannot be at the same time, and that if one is not, it follows that the other is. And so if a is not, b will be; but this is one of those propositions which we numbered above among those that come about through connexion. Whatever syllogisms, therefore, are made in that proposition which is "if a is not, b is," these also must be made in that which is proposed through disjunction, as when we say "either a is, or b is.
Fiunt igitur in superiore quatuor modis.Quamlibetenimpartem propositionis assumpseris, sive praecedentem, sive etiam consequentem,sive negativo modo, sive affirmativo, faciet syllogismum.Nam si haec propositio sit,si non est a, est b, sive non sit It, erit b; sive sit a,non erit b; sive non sit b, erit a; sive sit b, non erit a. In propositione quoque disjunctiva idem est. Nam cum dicitur,aut est a,aut est b,siquidem a fuerit, non erit;quod si a non fuerit, erit b; et si non sit, erit a;si non fuerit,non erit a.Id quoque tali declaratur exemplo;nam si sit propositio,aut aeger est, aut sanus,qllidquid horum in assumptione assumptum fuerit,vel negatum,altera pars vel affirmabitur, vel negabiturhoc modo:Nam si sanus est, non est æger: si non est sanus,est asgerjsi aeger est, non est sanus; si non æger est, est sanus. Item ea propositio disjunctiva quae proponit, aut a non est, aut non est, fit quidem de his quae quolibet modo simul esse non possunt, etiamsi non alterum eorum esse necesse sit,similisque est si propositioni connexae per quam ita proponitur, si est a, non est 6. Quae enim sic enuntiat,aut non est a,aut non est b, id nimirum sentit, quod si a sit, esse non possit, id ita probabitur.Cum enim proponitur hoc modo, aut non est a, aut non est b,cum si assumaturesse a,non erit b. Quocirca ei propositioni connexæ similis est quae ita enuntiat, si sit a, non esse b.
Therefore they come about in the four modes above. For whatever part of the proposition you assume—whether the antecedent or even the consequent, whether in negative mode or affirmative—it will make a syllogism. For if this proposition is "if a is not, b is," then whether b is not, b will be; whether a is, b will not be; whether b is not, a will be; whether b is, a will not be. The same holds in a disjunctive proposition. For when it is said "either a is or b is," if indeed a is, b will not be; but if a is not, b will be; and if b is not, a will be; if b is, a will not be. This too is made clear by such an example: for if the proposition is "either he is sick or he is healthy," whatever of these has been assumed or denied in the assumption, the other part will be affirmed or denied in this way: for if he is healthy, he is not sick; if he is not healthy, he is sick; if he is sick, he is not healthy; if he is not sick, he is healthy. Likewise the disjunctive proposition which proposes "either a is not, or b is not" is made indeed concerning those things which cannot be together in any way, even if it is not necessary that one of them be; and it is similar to the connected proposition through which it is proposed thus: "if a is, b is not." For what is enunciated thus, "either a is not, or b is not," surely means this: that if a is, b cannot be. This will be proved thus: for when it is proposed in this way, "either a is not, or b is not," when you have assumed that a is, b will not be. Wherefore it is similar to the connected proposition which enunciates thus: "if a is, that b is not.
In hac vero propositione, duæ tantum complexiones syllogismos procreabant.Nam si esset a, non erat et si esset b, non erat a. Si cum non esset a, non necesse erat esse vel non esse b. Sive autem non esset b, non necesse erat esse vet non esse a. Quocirca et in disjunctiva propositiones totidem syllogismos esse necesse e:-t, totidem vero in collectibiles complexiones; nam cum ita proponitur,aut non est a,aut non est b, ita dicitur, si sit a, non erit b: et si sit a,non erit b. Sive autem non sit a, non necesse erit esse vel non esse b. Sive non sit b, non necesse erit esse vel non esse a,velut in his apparet exemplis. Si enim quis dicat, aut non est album, aut non est nigrum, sed assumat,atqui est album, non erit nigrum; vel rursus, atqui est nigrum,non erit album. Sive album non esse assumpserit, non necesse erit esse vei non esse nigrum; sive nigrum non esse assumpserit, ut si vel non sit album, nullam facietnecessitatem.Itemea propositio per quam ita proponitur, aut est a.aut non est b,dicitur quidem de sibimet adhaerentibus proponiturque in his propositionibus quæ de majoribus ad minora tendunt, similisque est ei propositioni connexæ quae enuntiat,si non est a, non est b.Nam si quis dicit, aut est a, aut non b, si assumat, atqui non est a, modis omnibus non erit b. Si igitur non sit a, non erit b.
In this proposition, however, only two combinations generated syllogisms. For if a was, b was not; and if b was, a was not. But if, when a was not, it was not necessary for b to be or not to be; and again, if b was not, it was not necessary for a to be or not to be. Wherefore also in the disjunctive proposition there must be just as many syllogisms, and just as many in the collective combinations; for when it is proposed thus, either a is not, or b is not, it is said thus: if a is, b will not be; and if b is, a will not be. But if a is not, it will not be necessary for b to be or not to be; and if b is not, it will not be necessary for a to be or not to be, as appears in these examples. For if someone says, either it is not white, or it is not black, but assumes, but it is white, it will not be black; or again, but it is black, it will not be white. But if he assumes that it is not white, it will not be necessary for it to be or not to be black; and if he assumes that it is not black, as, for instance, that it is not white, it will make no necessity. Likewise, that proposition through which it is proposed thus, either a is, or b is not, is indeed said of things adhering to themselves, and is proposed in those propositions which proceed from greater to lesser, and is similar to that connected proposition which declares, if a is not, b is not. For if someone says, either a is, or b is not, and assumes, but a is not, in every way b will not be. If therefore a is not, b will not be.
Id enim hsec disjunctio praemittebat, in hao vero siquidem a negaretur,vel affirmaretur 6,fiebat aliquis syllogismus.Sive autem a affirmaretur,siveb negaretur,nulla eratin conclusione neeessitas:idem provenit in disjunctiva. Nam cum proponitur, aut esta, aut noniest 6, siquidem non sit a,non erit b. Si vero sit b, erit a: quod si sit a, vel non sit b, nihil estnecessarium.ld veroin his terminis approbabimur, si quis ita proponat, aut animal est, aut non homo, si igitur animal non sit, non erit homo; si bomo sit, animal est; sive autern animal sit, non necesse est esse hominem, sive homo non sit, non necesse est animal interire.Ea vero propositio quas dicit,aut non est a, aut est b, in his quae adhaerent proponi potest,et a minoribus all majora contendi, et est similis ei propositioni connexæ quæ dicit: si est a, est b. Namcum itaquis enuntiet,si. quidem assumaturesse a,statim consequitur ut sitb. Bed in hac propositione siquidem affirmaretur esse a, sequebatur ut esset b. Quod si negaretur b, sequebatur ut non esset a.Sive autem negaretur a, sive affirmaretur b,nibil necessariumvidebituraccidere.
For that disjunction premised this: in this one, indeed, if a was denied or affirmed, some syllogism was produced. But whether a was affirmed or b was denied, there was no necessity in the conclusion; the same result occurs in the disjunctive. For when it is proposed, "Either a is, or b is not," if a is not, b will not be. But if b is, a will be. But if a is, or b is not, nothing is necessary. We will be approved in these terms if someone proposes thus: "Either an animal is, or a man is not." If, then, an animal is not, a man will not be; if a man is, an animal is. But whether an animal is, it is not necessary that a man be; or whether a man is not, it is not necessary that an animal perish. But that proposition which says, "Either a is not, or b is," can be proposed in those things which are connected, and can be argued from lesser to greater, and it is similar to that connected proposition which says, "If a is, b is." For when someone thus enunciates it, if indeed he assumes that a is, it immediately follows that b is. But in this proposition, if it was affirmed that a is, it followed that b was. But if b was denied, it followed that a was not. But whether a was denied or b was affirmed, nothing necessary will seem to happen.
Et in ea igitur propositione disjuncta,quaB dicit, aut non est a,aut est b,siquidem fuerit a, erit hi si non fuerit b, non erita.Sive autem non sit a, sive sit b, nulla est necessitas syllogis!!li,ut in hoc declaratur exemplo,aut non est homo,aut animalest.Si igitur assumamus,atqui est homo,erit animal.Si negemus esseanimal,non erit homo; si autem hominem negemus,vel animal affirmemus,nibil necessarium cadet. Quocirca ex his quae superius dicta punt declaratur quot disjunctarum propositionum syllogismi sint, vel quibus ab his quae connexae sunt differentiis segregentur.Quæ enim connexæ sunt quamdam in eo quod est esse vel non esse consequentiam monstrant; quae vero per disjunctionem proponuntur ita sunt,ut sibimet consentire non possint. Invenias quoque per connexionem propositiones,quae id intelligi volunt,ut a se nequeant separari,ut cum ita proponimus,si est a, est b.Id nimirum hæc propositiointelligit,quodsi esse potuerit a,statim con-, sequitur ut sit etiam b. Nulla vero earum quæ in disjunctione sunt ita proponitur, ut simul esse videantur. Cum enim dicimus,aut est a,aut est,aut eaedem propositiones quolibet alio modo variamus, id aut conjuncto quae disjunctiva ponitur, sentit simul eas esse non posse.
And so in that disjunctive proposition which says "either a is not, or b is," if indeed a is, then b will be; if b is not, a will not be. But whether a is not or b is, there is no necessity of a syllogism, as is shown in this example: "either man is not, or animal is." If, then, we assume "but man is," animal will be. If we deny that animal is, man will not be; but if we deny man or affirm animal, nothing necessary will follow. Wherefore from what has been said above it is made clear how many syllogisms there are of disjunctive propositions, or by what differences they are separated from those which are connected. For connected propositions show a certain consequence in respect of being or not being; but those which are proposed by disjunction are such that they cannot agree with one another. You may also find propositions through connection which wish this to be understood, that they cannot be separated from one another, as when we propose thus: "if a is, b is." This proposition certainly understands that if a could be, it follows at once that b also is. But none of those which are in disjunction is proposed in such a way that they seem to be at the same time. For when we say "either a is, or [b] is," or vary the same propositions in any other way, that which is posited as disjunctive in conjunction with this understands that they cannot be at the same time.
Et cum late earum pateat differentia,idcirco nunc de eisdem pauca subjunximus, quoniam totidem syllogismos fieri dicebamus in his propositionibus quae per disjunctionem fierent quot etiam fuerunt in connexis. Et quoniam de omnibus qui quoquo modo possint fieri hypotheticis syllogismis sufficienter dictum est. Hic operis longitudinem terminemus.
And although the difference between them lies widely open, for that reason we have now added a few remarks about the same matters, since we were saying that as many syllogisms are made in those propositions which come about through disjunction as there were also in connected ones. And since enough has been said about all hypothetical syllogisms that can in any way be made, let us here bring the length of the work to an end.