b Puoꝛum. eiens autem. Hʒ cum in defectu quãtitate irrõnali nũero.vnde poſſ to caſu; duo motꝰ eſſent in celo tm ꝓpoꝛtionẽ quã hʒ dyameter ad coſtã nunꝙᷓ fieret ad inſtãs ↄiũctio ꝓpt᷑ incõueniẽtiã ꝓpoꝛtõis ↄtinui ↄtra aliud qð notũ in nũero nõ eſt nec notũ fieri poteſt cũ multe pꝛo poꝛtiones ſunt in cõtinuis quas nũeroꝝ natura nequaq́ᷓ ſuſtinet.

Sege em̃ erũt termi qbus nõ eſt poſitũ nomẽ.

Nic areſt.docet reducere ꝓpõnes in tmĩos oſtẽdẽs ꝙ nõ opoꝛtet ſꝑ q̃rere tmĩos incõplexos ↄtigit em̃ falli ĩ ſilogiſmo ꝓpt᷑ hmõi reducti⸗ onẽ ⁊ hoc maxie in demõſtratis mathẽatict.vnde exẽplificat in exem plo mathẽatico vt ſi a habere duos rectos ineſt ipic ſcʒ triãgulo eqͥ⸗ cruro ꝑ b.i.ꝑ triangulũ. E vo qð eſtb.i.triangulo nõ eſtncte ĩeſſe a .i.habere duos rectos ꝓpt aliud mediũ.; ĩmediate.ꝑ ſe em̃ tria ngls

bʒ duos rectos vñ int᷑ paſſionẽ ⁊ ciꝰ ſubiectũ nõ eſt aliud mediũ vñ

nõ erit aliud mediũ int a ⁊ b.qñ a de b ſit vᷣmõöſtratũ.i.paſſio de ſuo ſubiecto.nã ꝓpꝛia paſſio triãguli ẽ habere oẽs angulos eq̃les duobꝰ rectis hoc m.Ois triãgulꝰ hʒ tres angulos eq̃les duobꝰ rectis.S Vſogeles ẽ triãgulꝰ.ergo yſogeles hʒ tres angulos eq̃les duobꝰ re/ ctis. Ad reducendũ hmõi ſilogiſmũ ĩ tmĩos incõplexos ſiue ſimpli⸗ ces fallit ĩhmõi ðmõſtratõibꝰ. licʒ demõſtret᷑ in vſochele ꝑ mediũ in ↄplexũ ꝗð eſt triãgulꝰ.ſi tñ deberet demõſtrari de triãgulo hoc erit ꝑmediũ aplexũ ꝑuta ꝑ diffinitõʒ ſubiecti vel paſſionis hoamõ.pᷣmo ꝑ diffinitõʒ paſſiõis Qm̃ĩe hñs ãgulũ extnſecũ duobꝰ intnſec oppoſi tis eqlem.hʒ tres angulos eq̃les duobꝰ rectꝭ ßʒ triãgulꝰ ẽ hmõi.ergo triãgulꝰ hʒ tres ãgulos eq̃les duobꝰ rectt.Sʒ ꝑ diffinitõem ſubiecti hoc mõ.Om̃e qð tribꝰ lineis claudit᷑ hʒ tres angulos eq̃les duobus recte. triãgulꝰeſt hmõi ergo ⁊c̃ vt pᷣus.q̃re opoꝛtet aliꝗñ cape ĩ reſo lutionibꝰ oꝛones ꝓ tmĩs— et paſſiões circũloquũtur t᷑⸗ mĩs et nõ tmĩo. Ad demõſtrãdũ aũt mathẽatice ꝙ triangulꝰ hʒ tres angulos eq̃les duobꝰ recte ſcʒ paſſionẽ hãc de ſuo ſubiecto ꝓtrah at baſis trianguli abc ſcʒ b c in ↄtinuũ ⁊ directũ vſq; in d ꝑ pᷣmã peti tionẽ ⁊ arguat᷑ hoc mõ. A dato puncto c linee a b eq̃diſtantẽ ducere P triceſimapꝛimã pᷣmi geometrie.tʒ a puncto c eſt ducta c f.ergo cfẽ eqͥdiſtãs a b. Oĩm autẽ eqᷓͥdiſtãtiũ lineaꝝ anguli coalterni ſunt eq̃les ꝑ pᷣmã partẽ viceſimenone p̃mi elemẽtoꝝ. Sʒa cf⁊b ac ſunt coalt᷑⸗ ni eqᷣdiſtãtiũ lineaꝝ ab ⁊ cf.ergo coalterni ac f⁊ b acſunt eqles.Et qa oim eqͥdiſtãtiũ lineaꝝ angulꝰ extnſecꝰ angulo intnſeco oppoſito eſt equalis ꝑ ſecũdã ꝑtem viceſimenone p̃mi.Sʒꝭ f c d extnſecꝰ eſt ⁊ a b c intnſecꝰ oppoſitꝰ. ergo anguli fcd⁊ ab gſunt eqles q̃re erit to tus extrinſecus a c d duobus intrinſecis opp̃oſitis a ⁊ b equalis ⁊ ſic demõſtratũ eſt añs maioꝛꝰ. vbi diximꝰ ꝙ om̃e qð haberet ãgulũ extnſecũ duobꝰ intnſect eqlem ⁊c̃. O aũt om̃es tres ſunt eq̃les duo bus rectꝭ ex eo ꝙ angulꝰ extnſecꝰ valeat duos intnſecos. Arguendo hoc mõ.Oĩs linee recte ſuꝑ rectã ſtante duo vtrobiqʒ anguli aut ſũt recti aut duobꝰ rectꝭ eqles.ꝑ tredecimã p̃mi Sʒ ſuꝑ b d rectã ſuper

ſtat a cad angulũ demõſtratũ ext᷑nſecũ a cd cauſans vtrobiqʒ acd iia extnſecꝰ demõſtratꝰ duobꝰ intnſecꝭ triãguli eq̃lis ſcʒ; a ⁊ b ⁊ cau ans alterũa cb qͥ terciꝰ eſt trianguli.ergo ac d extrinſecꝰ cũ a cb va⸗ let duos rectos patet ↄſequẽs maioꝛis.;ʒ; minoꝛ eſt nota cũ triãgulꝰ tali mõ ſit ſubſumptꝰ ĩ demõſtratõe q̃re mãifeſtaẽ ↄcluſio.ꝙ oĩs tri⸗ ãgulꝰ hʒ tres ãgulos eꝗles duobꝰ rectis q̃re mttociẽs ĩ vno ſilogiſ⸗ mo pleſtmi ponũt᷑ loco vniꝰ extremitatt vł medij q qñq; nõ hñt vnũ nomẽ ĩpoſitũ.⁊ ſi debẽt fieri ſꝑ reſolutio ĩ tĩos ĩcõplexos qñq; fieret deceptõ qꝛ ſicut dixi ꝙ paſſio babẽ duos rctõs ponit᷑ in ðmõitratio ne loco maioꝛt extrẽitat q̃ nõ bʒ vnũ nomẽ ĩpoſitũ. aſtat,poſitũ miꝰ