Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Primi partis
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0060
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60
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aliquod mobile / hoc eſt aliquam reſiſentiam ali-
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quãta velocitate ſubdupla virtus mouet ſubdu-
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plam reſiſtentiam equali velocitate: hoc eſt. </
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<
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xml:space
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liqua proportio maioris inequalitatis moueat
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aliquam proportionē minoris inequalitatis ali-
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qua velocitate: proportio equalis illi in minori-
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bus terminis mouebit equali velocitate: quod la-
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tius poſtea declarabitur.</
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xml:space
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<
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et improbantur ſecunda et tertia opinio-
<
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nes. de cauſa velocitatis motuum.</
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<
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tem motus ſequi proportionem exceſſus
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potentie motoris ad potentiã rei mote.
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</
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<
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xml:space
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preserve
">Et vult dicere hec opinio / velocitas in motibus
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ſequitur proportionem exceſſus actiuitatis moto
<
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ris ad actiuitatem rei mote. </
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<
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xml:space
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">Ita ſi vnus motor
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ita ſe habeat reſpectu ſui mobilis / actiuitas eiꝰ
<
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excedaṫ actiuitateꝫ mobilis per quatuor gradus /
<
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/>
et actiuitas alterius motoris excedat actiuitatem
<
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/>
ſui modilis per duos gradus: tunc primus mo-
<
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tor mouebit in duplo velocius ſecūdo. </
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<
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xml:space
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">Et iſta opi-
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nio videtur coincidere cum prima dempto / vna
<
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comparat actiuitatem ad reſiſtentiã: et altera acti-
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uitatem ad actiuitatem.</
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ſecunde
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opinioni</
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<
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xml:space
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ſic / quia ſi illa eſſet vera / ſequeretur / aliquod mo-
<
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uens ſucceſſiue moueret ſine reſiſtētia: īmo ita cito
<
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/>
cum reſiſtentia ſicut ſine reſiſtentia / ſed conſequēs
<
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/>
eſt falſum igitur, illud ex quo ſequitur: ſequela ꝓ-
<
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/>
batur et pono caſum / ſit virtus: vt .8. agentis: et
<
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virtus vt quatuor patientis in quo ſit reſiſtentia:
<
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vt .2. / et ſit aliquod aliud paſſum in quo nulla ſit re
<
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ſiſtentia ſed dumtaxat actiuitas vt quatuor: quo
<
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poſito arguitur ſic. </
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<
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xml:space
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">Agens vt .8. eque velociter a-
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git in vtrū iſtorum paſſorum: cum proportiones
<
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actiuitatum ſint equales: et tamen in vno paſſo a-
<
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git cum reſiſtentia: et in alio ſine reſiſtentia igitur
<
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propoſitum.</
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<
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in motu ſequi proportionem reſiſtentiarum inter
<
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ſe: ita ſi ſint duo agentia equalia: et moueãt du-
<
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as reſiſtentias inequales: in quacun ꝓportione
<
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vna reſiſtentia eſt minor alia in eadē proportione
<
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velocius mouetur: vt ſi virtus vt octo moueat re-
<
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ſiſtentiam: vt .4: et reſiſtentiam: vt .3. quia reſiſten-
<
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tia: vt .3. eſt in ſexquitertio minor reſiſtentia: vt .4.
<
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ideo virtus vt .8. in ſexquitertio velocius mouebit
<
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reſiſtentiam vt .3. ꝙ̄ reſiſtentiam vt .4.</
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<
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">Sed contra iſtaꝫ opinionē arguitur
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ſic. </
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<
s
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xml:space
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">Supponendo / ſi aliqua virtus puta vt .8. / ſuf
<
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ficiat mouere aliquod mobile aliquanta velocita
<
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te / eadē virtus ſufficit mouere aliquod aliud mo
<
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bile in duplo tardius, et aliquod in triplo, et aliqḋ
<
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in quadruplo, et ſic in infinitum. </
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<
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">Ita ſi virtus vt
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8. ſufficit mouere aliquod mobile in hora ꝑ leucã:
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eadem virtus ſufficit mouere aliquod maius mo-
<
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bile in hora per mediam leucam: et illamet virtus
<
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ſufficit mouere aliquod maius in hora per tertiã
<
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partem leuce: et aliquod aliud per quartaꝫ: et ſic in
<
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infinitū. </
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>
<
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xml:space
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">quo poſito ſic arguitur / ſi opinio eſſet ve-
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ra ſequeretur / mouens vt .8. poſſet mouere quã-
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tumcun mobile: ſed conſequens eſt falſum: quia
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tunc eſſet infinite actiuitatis: igitur illud ex quo
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ſequitur. </
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<
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">Sequela probatur: et pono / mouens vt
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Capitulū ſcḋm tertiū.
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8. moueat reſiſtentiam vt .4. per leucã in hora ade
<
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quate: quo poſito tale mouens poteſt mouere ali-
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quod mobile in duplo tardius puta in hora per
<
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mediam leucam, vt patet ex ſuppoſitione: et nõ ni
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ſi mobile vt .8. / vt patet ex opinione: quoniã ꝓpor-
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tio velocitatem ſequitur ꝓportionem reſiſtentiaꝝ
<
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ſed velocitas eſt ſubdupla: ergo reſiſtentia dupla
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</
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<
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">Itē aliquod mobile poteſt mouere illa virtus ſub-
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tripla velocitate: vt patet ex ſuppoſitione: et non
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niſi triple reſiſtentie / vt patet ex opinione: et ſic in
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infinitum: igitur propoſitū. </
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<
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xml:space
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">Et hec ſola ratio ſuffi
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cienter hanc opinionem deſtruit et elidit.</
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<
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">Capitulum tertium / in quo ponitur
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alia opinio et vera.</
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<
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<
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nūc cõmuniter tenetur: et ponit velocita-
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tem motus ſequi ꝓportionē ꝓportionū
<
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hoc eſt proportionē geometricã: vt ſi aliqua virtꝰ
<
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moueat aliquã reſiſtentiã a proportione dupla: et
<
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vna alia moueat eandē reſiſtentiam vel vnã aliaꝫ
<
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(in idem reddit) a proportione quadrupla: talis
<
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virtus mouēs a proportione quadrupla in eadeꝫ
<
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proportione velocius mouet in qua proportione
<
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quadrupla proportio duplam excedit: et quia ex-
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cedit quadrupla duplam in proportione dupla,
<
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vt ptꝫ ex ſexto capite ſecunde partis: ideo quadru
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pla proportio in duplo velocius mouet. </
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<
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qua virtus moueat aliquam reſiſtentiã a propor-
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tione ſexquialtera: et alia mouet eandem reſiſten-
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tiam in proportione tripla: tunc virtus mouens a
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proportione tripla velocius mouet virtute mouē-
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proportione ſexquialtera in ea proportione qua
<
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tripla ſexquialteram exuperat: et quia talis ꝓpor
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tio que eſt inter triplam et ſexquialteram eſt irra-
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tionalis: vt ex ſexto et ſeptimo capitibꝰ ſecūde par
<
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tis facile monſtratur: ideo nec ſpaciū pertranſitū
<
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a ꝓportione tripla excedit ſpaciū pertranſitum a
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proportione ſexquialtera in proportione aliqua
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multiplici, nec ſuperparticulari, nec ſupraparti-
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ente, nec multiplici ſuperparticulari, nec multipli
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ci ſuprapartiente, quod poſtea magis elucidabit̄̄
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</
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<
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">Et pro fundamento et baſi huius opinionis pono
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duas concluſiones.</
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</
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<
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<
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">Prima concluſio / velocitas motꝰ nec
<
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penes proportionem exceſſus potentiarū ad inui-
<
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cem, nec penes proportionem actiuitatū ad inuicē /
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nec reſiſtentiarum inter ſe attenditur. </
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<
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">Probatur
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hec concluſio ex hiis / que in ſuperioribus capitibꝰ
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in impugnationibus triū opinionū dicta ſunt.</
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</
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<
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<
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tuū ſequit̄̄ / et attendi hꝫ penes ꝓportionē propor-
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tionū: ita in quacū proportione vna ꝓportio
<
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eſt maior aut mīor alia: ī eadē ꝓportiõe velocitas
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maior aut minor euadet. </
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<
s
xml:id
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xml:space
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">Et ſi fuerat proportio ꝓ
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portionū rationalis: rationales velocitates erūt
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et ſi irrationalis: cõmenſurari nõ poterunt veloci-
<
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tates taliū motuū. </
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<
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">Probatur hec concluſio ſic / de
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clarata per ſillogiſmum diuiſim eo ordine quo
<
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eam paulus venetus inducit quoniã velocitas et
<
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tarditas motus attendi habet penes ꝓportioneꝫ
<
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exceſſiuū inter ſe, aut penes ꝓportionē actiuitatū
<
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inter ſe, aut reſiſtentiarum, aut penes ꝓportiõe
<
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ꝓportionū: ſed nõ penes .3. prima / vt ptꝫ ex ãterio-
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ri cõcluſione. </
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<
s
xml:id
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xml:space
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">igitur penes quartum / quod fuit pro
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bandum. </
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<
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">Cõſequentia patet a ſufficienti diuiſiõe
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</
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<
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">Nõ em̄ ymaginari valent aliqui alii modi ſaltem
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um apparentia quibus attendi habet motuū ve-
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ocitas et tarditas / igitur diuiſio ſufficiens.</
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