Tractatus

Tertio nihil eſt in gn̄e qd̓ nō ſit in aliqͣ ſpēꝝ. gͦ nihil eſtcōtingēs cōe ad nccāriū ⁊ ad nō nccāriū niſi ſit aut incōtingēti nccārio. aut in ꝯtingēti nō nccārio. ⁊ ſic nulla eſt ꝯcluſio de cōtingenti ꝓ poſſibili in cōe ad vtrunqꝫiſtoꝝ q̄ diſtincta ſit a ꝯcluſionibꝰ ſpēalibꝰ que ſunt decōtingēti ꝓ nccārio. ⁊ de cōtingēti ꝓ nō nccārio Sodicte ꝯiugatōes ſunt inutiles. ad ꝯtīgēs ꝓ nccārio tm̄et ad ꝯtingēs ꝓ nō nccārio tm̄. tn̄ vtiles ſunt ad ꝯtingens in cōi ꝓ poſſibili ſicut qn̄ due ꝓpōnes ſumūtur deineē quaꝝ vna eſt de ineē ſimpl̓r. ⁊ altera de ineē nō. qͣꝫuis tm̄ tal̓ ꝯiugatio inutil̓ ſit qͣꝫtū ad ꝯcluſionē de ineſimpliciter ⁊ ſil̓r qͣꝫtū ad ꝯcluſionē de ineſſe vt nūc. ē tn̄vtilis ad ꝯcluſionē de ineē in cōi ſumptū Ad obiectain oppoſitū Ad primū eſt dd̓m. ꝙ ꝯtingēs in cōi ſetur ex forma illaꝝ ꝯiugationū. ꝯtingēs āt ꝓ nccārio inſpēali ſeqͥt̉ grā termīoꝝ ſb̓ tali forma acceptoꝝ. ⁊ ſic cōiugatio formaliter ꝯcludit ꝯtingēs ꝓ poſſibili grā aūtmaterie. ſequitur contingēs in ſpēali qd̓ eſt hoc vel illd̓et qͣꝫuis ſatis ꝓbatū eſt in obiectis. ꝙ dcā ꝯiugatio ſitinutil̓ ad ꝯcludendū hoc vel illud in ſpēali tn̄ ex hoc nonſequit̉ quin vl̓is ſit ad ꝯcludendū ꝯtingēs in cōi. ſicutdcm̄ eſt de ꝓpōnibꝰ de ineē. Et ꝑ idē patꝫ rn̄ſio ad aliudquo argutum fuit nihil eſt in gn̄e qd̓ nō ſit in aliqͣ ſpet eius quo obici pōt ꝙ a quocūqꝫ remouent̉ om̄s ſpēsalicuiꝰ gn̄is ab illo remouet̉ genꝰ. qꝛ hoc veꝝ eſſet ſi ī toto remouerent̉ ſpēs ab aliqͦ hoc aūt nō fit. qꝛ vtrūqꝫ iſterū grā termīoꝝ ſequit̉ diuiſiꝫ ſꝫ grā forme eſt ꝯn̄a ad cōcluſionem ꝯtingentis ꝓ poſſibili.Si aūt hec quidē vl̓is. illa vero ꝑticularis ſumat̉ dimēſionū qn̄ ad minorē qͥdeꝫ extremitatē vl̓is ponit̉ ⁊ ꝯtingēs. ſiue negatiua ſit ſiue affirmatīa ꝑticularis aūt affirmatiua ⁊ ineē erit ſyll̓s ꝑfectꝰ quēadmodum ⁊cū vl̓es ſunt termini Demōſtratio aūt eadēque et priusHic ph̓s cōiugatōes duas ſuꝑius poſitas declaratin modꝭ ꝑticularibꝰ pͥme figure ⁊ pͥmo pͥmā dicens. ꝙin mōis ꝑticularibꝰ pͥme figure t̓tio ſcꝫ ⁊ qͣrto ſiue maior ſit de ꝯtingenti ⁊ vl̓is. ſiue affiriuatīa ſiue negatiuaet mīor de ineſſę ꝑticularis affirmatīa. tūc fit ſyll̓s perfectus ad cōcludēdum ꝯcluſionē de ꝯtingēti ꝓprie dictoſicut qn̄ ambe ꝓpōes ſunt vl̓es ſicut dcm̄ fuit. Ꝙꝛ auteꝫtal̓ ſyll̓s cōcludēs ꝯcluſionē ꝑticularem in darij vel ferio pdcō mō ſit ꝑfectꝰ on̄dit̉ eodē mō ꝑ dici de om̄i ⁊ dici de nullo in ꝯtingētibꝰ ſicut in vl̓ibus ſupͣ oſtēſum eſtQuādo aūt vl̓is quidē fuerit ad maiorēextremitatē ineē aūt ⁊ nō ꝯtingēs. altera ātꝑticularis ⁊ ꝯtingēs ſiue negatīe ſiue affirmatiue ponāt̉ vtreqꝫ ſiue hec quidā negatꝭua illa v̓o affirmatīa in om̄ibꝰ erit ſyll̓s imꝑfectus. Uerū hi qͥdem ꝑ impoſſibile oſtēdētur illi ꝟo ꝑ ꝯuerſionē ꝯtingentis quemadmodū in prioribꝰ erit aūt ſyll̓s ꝑ ꝯuerſionēet qn̄ vl̓is quidē ad maiorē extremitatē poſita ſignificabit ineē vl̓ nō ineē. Particularis aūt cū ſit priuatīa ſumet ꝯtingere. vt ſi

a quidem om̄i bineſt. b aūt alicui c. ꝯtingitnō ineē. Cōuerſa eī b cẜm ꝯtingere fit ſyll̓sHic poīt ſcd̓am ꝯiugatōnē ſiue regulā dicēs In modis ꝑticl̓aribꝰ pͥme figure. ſi maior fuerit vl̓is ⁊ de ineē.et mīor ꝑticularis de ꝯtingenti. ſiue ambe fuer̄it affirmatiue ſiue ambe fuerint negatīe. ſiue vna fuerit affirmatiua ⁊ alia negatiua ſꝑ ſequit̉ ꝯcluſio de ꝯtingēti ꝓpoſſibili ⁊ fit ſyll̓s imꝑfectꝰ qͥ ꝑficit̉ ꝑ reductōeꝫ quo adalios ſyll̓os ⁊ ꝑ ꝯuerſionē ꝯtingentis ẜm oppoſitas qͣlitates quo ad aliquos ⁊ qͥdā vtroqꝫ mō ⁊ illa t̓tia viamelior eſt ſicut ſupͣ dcm̄ fuit in modis vl̓ibꝰ. ꝑ ꝯuerſionem aūt ꝑficit̉ iſte ſyllogiſmꝰ qn̄ maior ē vl̓is affirmatiua vel negatīa de ineſſe vel nō ineē. ⁊ mīor ꝑticularisde cōtingēti. Exemplū eſt. vt ſi a ꝯtīgit oī b ineē. ſicut ēin darij vel nō ineſt ſicut eſt in ferio. b aūt ꝯtingit alicuic nō ineſſe affirmatīe. tūc ꝯuerſa mīore ꝓpōne q̄ fuit priuatiua ẜm ꝯuerſionē de ꝯtingenti in oppoſitā qͣlitateꝫfit ſyllogiſmꝰ vel in darij vel in ferio.Qn̄ aūt nō ineſſe ſumet̉ ꝑticulariter poſita. nō erit ſyll̓s. Termī quidē ineſſe aīal albū nix. nō ineē aūt albū aīal pix. ꝑ infinituꝫem̄ ſumēda demonſtratioHic ph̓s ponit ꝯiugatōes inutiles p̄miſſaꝝ. qͣꝝ prima eſt hec. Si mīor eſt de ineē ꝑticl̓arꝭ negatīe. ⁊ maiorde ꝯtīgenti nō erit ſyll̓s ad inferendū ꝯcl̓onē de ꝯtīgētiEt hoc on̄dit maīfeſte in t̓mīs inſtātiarum Termī em̄inſtantiaꝝ ad cōcluſionē affirmatiuā ſyllogiſandā ſtiiſti. albū aīal nix. ex qͥbus ſic format̉ ſyll̓s. Om̄e aīmalcōtingit eſſe albū. q̄dā nix nō eſt aīal. gͦ oīs nix ꝯtingēter eſt alba. maīfeſtū eſt ꝙ nō ſequit̉ tal̓ ꝯcluſīo qꝛ oīsnix de ncc̄itate eſt alba. Termī vero ad ſyllogiſandumcōcluſionē de nō ineē ſiue negatīuā ſunt iſti. albū aīmalpix. ſic arguendo. Om̄e aīal ꝯtingit eſſe albū q̄daꝫ pixnō eſt aīal. nō ſeqͥtur ꝯcluſio de ꝯtigenti. gͦ nullā picemcōtingit eſſe albam. qꝛ de neceſſitate nulla pix eſt albaIn talibꝰ aūt minor eſt negatīa de ineſſe. debet ſumi ꝓbatō ex indefinito qꝛ duas cās hꝫ ſue ꝟitatis tal̓ ꝓpoſitio. qꝛ ſicut dcm̄ fuit qd̓ ſequit̉ ad an̄s ſeqͥtur ad ꝯn̄s. etcū talis de ꝯtingenti nō ſequit̉ ad vl̓em q̄ eſt vl̓is negatiua nō ſequit̉ etiā ad ꝑticularē negatiuā que ſeqͥtur ꝑlegē ſb̓alternarū ad vl̓em ꝑ modū ſuꝑius dictum de demonſtratione ex indefinito.Si aūt vl̓e quidē ponat̉ ad minorem extremitatē. ꝑticulare aūt ad maiorē. ſiue priuatiuā ſiue affirmatiuā ſiue ꝯtingēs ſiue ineſſe. vtrūuis nullo mō erit ſyll̓sHic ponit aliā ꝯiugatōem inutilē dicēs. ſi maior eſtꝑticularis ⁊ mīor vl̓is ſiue affirmatīa ſiue negatīa ſiue de ꝯtingēti ſiue de ineē nō valet ſyll̓s. qꝛ ſꝑ eſt inutiliscōiugatio ad inferendū ꝯcluſionē de contingentiNec cū ꝑticulares vl̓ indefinite ꝓpōes ſumant̉ fiue ꝯtingere ſumpte ſiue ineē ſiue permutatim nec ſic erit ſyll̓s. Demōſtratio aūteadē q̄ in prioribꝰ Termī āt cōes ineē quidē ex ncītate aīal albū hō. nō ꝯtīgere v̓o al̓albū tunica Maīfeſtū igit̉ vl̓i poīto ad maiorē extreītatē ſꝑ fit ſyll̓s. ad minorē autemnunqͣꝫ vllo modo-