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oꝑationē vniu̓ſalis a ꝑticulari ⁊ hͦ cōpetit etiā phiſice ⁊ ē ꝯmunis ōnibꝫ ſcientijs qꝛ in ōni ſciā p̄termittitur qd̓ ēꝑ accidēs ⁊ accipitur qd̓ eſt ꝑ ſe Et qꝛquidam nō intellexerūt drām duoꝝ vltimorū a primo inciderūt in errore vtponerent mathematica ⁊ vniu̓ſalia aſenfibilibꝫ ſeꝑata vt pictagorici ⁊ platonici Ad primū ergo dicendū ꝙ mathematicꝰ abſtrahens nō cōſiderat rēaliter qͣꝫ ſit Non em̄ intelligit lineā eēſine materia ſenſibili ſed conſiderat lineam ⁊ eꝰ paſſiones fine ꝯfideratione.materie ſenſibilis ⁊ ſic nō ē diſſonātiainter intellectū ⁊ rē. qꝛ etiā ẜm rem idqd̓ eſt de natura linee non depēdet abeo qd̓ facit materiā eē ſenſibilē ſꝫ magis ecōuerſo ⁊ ſic pꝫ ꝙ abſtrahentiū n̄ē mendacium vt dʳ in ij phiſicoꝝ Ad ijdicendū ꝙ materiale diʳ non ſolū illudcꝰ ꝑs ē materia ſed etꝭ illud qd̓ in materia eē habet ſcd̓m quem modū lineaſenſibilis materiale qd̓dam dici p̄t. vn̄per hͦ nō ꝓhibetur quin linea ſine materia intelligi poſſit. non em̄ materiaſenſibilis ꝯꝑatur ad lineam ficꝭ ꝑs ſedmagis ſicut ſb̓iectum in quo eē habetEt ſil̓r ē de ſuꝑficie ⁊ corꝑe non āt mamathematicꝰ ꝯſiderat corpꝰ qd̓ eſt ingenere ſb̓e ꝓut eꝰ ꝑs ē materia ⁊ forma ſed ſcd̓m qd̓ eſt in genere quātitatis tribꝫ dimēſionibꝫ ꝑſcm̄ ⁊ ſic ꝯꝑat̉ad corpꝰ qd̓ eſt in genere ſb̓e cꝰ ꝑs eſtmateria phiſica ſicut accn̄s ad ſb̓iectūAd iij dicendū ꝙ materia nō ē principium diuerſitatꝭ ẜm numerū niſi ẜm ꝙin multas ꝑtes diuiſa ē in ſingul̓ ꝑtibꝫformā recipiens eiuſdē rōis plura indiuidua eiuſdē ſpēi ꝯſtituit Materiaāt diuidi non p̄t niſi ex p̄ſuppoſita qͣꝫtitate qua r̄mota ſb̓a ōnis indiuiſibilisremanet Et ſic pͥma rō diuerſificandiea q̄ ſunt vniꝰ ſpēi ē penes quātitateꝫqd̓ quidē quātitati ꝯpetit inquātum īſui roē ſitum qͣſi drām ꝯſtitutiuā habꝫqd̓ nichil aliud ē qͣꝫ diuiſio ꝑtiū vn̄ etiāabſtracta quātitate a materia ſenſibili ꝑ intellectū adhuc ꝯtingit ymaginari diu̓ſa ẜm numerū vniꝰ ſpēi ſicut ōnes triangulos equilatrios ⁊ plureslineas rcās eqͣles Ad iiij dicēdū ꝙ mathematica non abſtrahit a qͣlibet ma-

teria ſꝫ ſolū a materia ſenfibili ꝑtes ātquātitatis a quibꝫ demōſtratio ſumpta quodāmō ſicut a cā materiali ſumiviʳ non ſunt materia ſenſibil̓ ſꝫ ꝑtinētad materiā intelligibilē q̄ in mathematicis inuenitur vt pꝫ in vij. metha. Adv. dicendū ꝙ motꝰ ſcd̓m naturā ſuā n̄ꝑtinet ad genꝰ quātitatis ſed ꝑticipataliqͥd de natura quantitatꝭ aliūde ẜmꝙ drā motꝰ ex diuiſione ſpacij vl̓ ex diuiſione mobil̓ ſumitur Et iō ꝯſiderare motū non ꝑtinet ad mathematicūſed tn̄ principia mathematica ad motū applicari pn̄t ⁊ id̓o ẜm hoc ꝙ principia quātitatis ad motū applicātᶻ naturalis ꝯfiderat de diuiſionē ⁊ ꝯtinuitate motꝰ vt pꝫ in vi. phiſi. ⁊ in ſcientijs medijs inter mathematicā ⁊ naturalē tractatur de mēſuris motuū ficꝭin ſciā de ſpera mota ⁊ in aſtrologiaAd vi. dicendū ꝙ in ꝯpoſitis ſimpliciaſaluāʳ ⁊ ꝓprietates eoꝝ lꝫ per aliū modū ficꝭ ꝓprie qͣlitates elemētoꝝ ⁊ motꝰ ip̄oꝝ ꝓprie īueniūtur ī mixto qd̓ tn̄ē ꝯpoſitoꝝ ꝓprium niſi īueniʳ in finplicibꝫ Un̄ ē ꝙ quāto ſciā aliqͣ abſtractiora ⁊ ſimpliciora cōſiderat tāto eiꝰprincipia ſunt magꝭ applicabilia alijsſcientijs Un̄ pnͥcipia mathematice ſt̓applicabilia naturalibꝫ rebꝫ nō āt eꝯºꝓpt̓ qd̓ phifica ē ex ſuppoē mathēticeſed nō eꝯͣ vt pꝫ in ii de ce. ⁊ mun. Et in̄ē ꝙ de rebꝫ natualibꝫ ⁊ mathēticꝭ tresordines ſciārū inueniūʳ Quedā em̄ ſt̓pure naturales q̄ ꝯfiderāt ꝓprietatesrerū naturaliū inqͣꝫtū huiuſmodi ſicutphifica ⁊ agricultura ⁊ huiuſmōi Quedā v̓o ſt̓ pure mathētice q̄ det̓minantde quātitatibꝫ abſolute vt geometriade magnitudīe ariſmet̓ca de nu̓o. q̄dāv̓o ſt̓ medie q̄ principia mathētica adres naͣles applicāt vt mufica ⁊ aſtrologia et huiuſmōi q̄ tn̄ magꝭ ſt̓ affinesmathēticis qꝛ in earū ꝯſideratione idqd̓ ē phificū ē qͣſi materiale. qd̓ āt mathematicū ē qͣſi formale ficꝭ mufica cōfiderat ſonos n̄ inqͣꝫᵐ ſt̓ ſoni ſꝫ inqͣꝫᵐ ſt̓ẜm nu̓os ꝓportionales et ſil̓r ē ī alijs⁊ ꝓpt̓ hͦ demrānt ꝯcluſiones ſuas circares nāͣles ſꝫ ꝑ media mathētica Etiō nichil ꝓhibet ſi inqͣꝫtū cū naͣli ꝯīcantmateriā ſenſibilē r̄ſpiciunt inquātum