Alvarus, Thomas
,
Liber de triplici motu
,
1509
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De motu quo ad cauſã in medio non reſiſtente.
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poſt̄ mouetur velocius: ſemper mouetur velocius /
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quod fuit probandum. </
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<
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xml:space
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">1. correl.</
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<
s
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xml:space
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">¶ Ex hac concluſione ſequitur primo / datis dua-
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bus latitudinibus equalibus reſiſtentie vniformi-
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ter difformis inequaliter extenſis per inequales ꝑ
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tes mediorum non reſiſtentium: et quilibet punctus
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reſiſtentie minus extenſe in aliqua proportione in-
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cipiat vniformiter intendere motum ſuum cõtinuo
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velocius puncto ſibi correſpondente in latitudine
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magis extenſa: poña poſita in reſiſtentia minus ex
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tenſa in aliquo puncto cū quo incipit intendere mo
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tum ſuum velocius continuo mouebitur poña equa
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li poſita in conſimili puncto in latitudine magis ex
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tenſa dūmodo ibi intendat motum ſuum. </
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<
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xml:space
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tur correlarium / quia talis poña poſita in latitudi
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ne minus extenſa incipit velocius moueri: et poſt̄
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ſic mouetur ſemper velocius mouetur ſtante caſu:
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igitur correlarium verum: </
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">Arguitur maior / q2 ſi in
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ciperet tardius vel equaliter moueri: et quilibet pū
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ctus minoris reſiſtentie minus diſtat ab eã ꝙ̄ pun-
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ctus conſimilis diſtat a potentia mota in latitudi-
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ne magis extenſa: et quilibet punctus velocius mo-
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uebitur immediate poſt hoc: ergo citius immedia-
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te poſt hoc aliquis punctus minoris reſiſtentie at-
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tinget in latitudine minus extenſa poñam ibi mo-
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tam quã conſimilis attingat poñam in latitudine
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magis extenſa. </
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<
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">Patet conſequentia ex tertia ſup-
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poſitione: et per conſequens immediate poſt hoc ve
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locius mouebitur alia (cum moueatur cum minori
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reſiſtentia.) </
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<
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">Sed minor eãdem cum minori precedē
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tis concluſionis demonſtrationem exigit. </
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<
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tet correlarium.
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xml:id
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<
s
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xml:space
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">¶ Sequitur ſecundo / datis dua-
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bus: vel quotcū latitudinibus reſiſtētie vniformi
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ter difformis equalis reſiſtentie inequalitater exten-
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ſis et quilibet punctus vnius moueatur eque veloci
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ter ſicut punctus correſpondens in alia: et hoc conti
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nuo vniformiter: poña que mouetur in medio mino
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ri / hoc eſt in minus extenſa reſiſtentia continuo tar-
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dius mouetur ꝙ̄ poña ei equalis que mouetur in la
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titudine magis extenſa et hoc dūmodo ille potētie
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incipiant a conſimilibus punctis. </
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<
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">Probatur cor-
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relarium / quia talis potentia in latitudine minus
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extenſa incipit tardius mouere ꝙ̄ alia in latitudi-
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ne magis extenſa: et poſt̄ mouetur tardius non po
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teſt incipere equaliter moueri: nec velocius: igitur
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continuo tardius mouetur. </
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<
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">Patet conſequentia: et
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tam maior ꝙ̄ minor probantur eodem modo ſicut
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probantur in concluſione precedenti.</
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">3. correl.
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decīa cõ-
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clu. cal.</
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<
s
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xml:space
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">¶ Sequitur tertio / tam in caſu concluſionis quã
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correlariorum continuo in quolibet tempore ade-
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quate terminato ad inſtans initiatiuum motus: ve
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locius intendit motum ſuum poña mota in maiori
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medio ꝙ̄ in minori. </
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">Probatur / quia dato quocū
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tali tempore ſemper in inſtanti terminatiuo illius
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potentia que eſt in maiori medio in caſu concluſio-
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nis eſt cū puncto minus intenſo ſiue mouetur a ma-
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iori ꝓportione ꝙ̄ alia poña in medio maiori / vt pa
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tet ex concluſione: et inceperunt ab equali velocita-
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te: ergo in illo tempore adequate maiorem veloci-
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tatem acquiſiuit potentia mota in maiori medio ̄
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alia mota in minori: et per conſequens velocius ī ta
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li tempore adequate intendit motum ſuum. </
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<
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">Et ſic ꝓ
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batur de alia poñe / que eſt in latitudine minus intē
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ſa in caſu precedentis correlarii reſpectu potentie
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que in caſu eiuſdem correlarii eſt in latitudine ma-
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gis extenſa. </
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">Et hec ſub aliis
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verbis tamen: eſt decima concluſio calculatoris ̄
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uis eam ſic non probet. </
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<
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">¶ Multe alie concluſiones
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poſſent in hac materia adduci, et ex predictis euidē
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De motu quo ad cauſã in medio non reſiſtente.
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ter inferri, nihilominus breuitatis cauſa ſuperſe-
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deo in ſequenti capite aliquas ex eis in deductioni
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bus argumentorum probaturus.</
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">Quindecimum caput / quod obiicit ali-
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quibus que dicta ſunt in precedentibꝰ duo
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bus capitibus: inferendo aliquas conclu-
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ſiones de velocitate motus in reſiſtētia dif
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formiter difformi progrediente per medi-
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um non reſiſtens: et in latitudine vniformi
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ter difformi condenſante ſe ad non quãtū
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in medio non reſiſtente.</
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<
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qua eorum que dicta ſunt in tridecimo: et
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quarto decimo capitibus: et ſignanter ter-
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tiam ſuppoſitionem tridecimi capitis baſim / et fun
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damentum omnium dictorum in predictis capiti-
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bus.</
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<
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">Et ideo cõtra eam primo arguitur ſic
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</
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<
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">Non eſt poſſibile latitudinem reſiſtentie acq̇ri par-
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tibiliter quo ad ſubiectum tantum / vt dicit ſuppoſi
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tio / igitur illa falſa. </
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<
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">Conſequentia patet et argui-
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tur antecedens / quoniam ſi illud eſſet poſſibile: ſe-
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queretur / ab inequalibus proportionibus equa-
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les velocitates prouenirent: ſed hoc eſt falſum: et cõ
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tra baſim totius huius operis: igitur illḋ ex quo ſe
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quitur: </
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<
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">Falſitas conſequentis eſt nota, et probatur
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ſequela, et pono caſum / ſint duo media non reſiſtē
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tia equalia: et per vnum illorum extendatur parti-
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biliter quo ad ſubiectuꝫ dūtaxat vna reſiſtentia dif
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formiter difformis cuius prīa medietas ſit vnifor-
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mis continuo vt .2. et ſecunda vt .6. et moueatur qui
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libet punctus eius vniformiter ↄ̨tinuo: puncto ve-
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lociſſime moto, continuo moto a proportione qua
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drupla: et puncto medio a dupla (vt oportet) / et ꝑ ali
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ud medium extendatur a non quanto vna latitudo
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vniformis per totum vt .4. quolibet puncto eius in
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trinſeco mouente vniformiter: et puncto velociſſime
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moto: continuo moto a proportione quadrupla ita
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continuo tales latitudines maneant equales, et
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equaliter moueantur: moueatur cum vtra illa
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rum vna poña vt .8. in eodem inſtanti, ab eodē pun
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cto: per eandem lineam inchoando: </
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argumentor. </
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<
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">poña que mouetur cum latitudine vni
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formi mouetur equaliter omnino: et continuo eque
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velociter cum potentia que mouetur cum latitudi-
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ne difformiter difformi: et tales potentie non poſ-
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ſunt continuo moueri ab eadem proportione cum
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nullus punctus in latitudine difformiter difformi
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ſit equalis reſiſtentie adequate cum aliquo puncto
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reſiſtentie vniformis (quandoquidem quodlibet in
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reſiſtentia vniformi ſit vt .4. et in difformiter diffor
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mi quodlibet eſt vt .2. vel vt .6. adequate) / igitur ab
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inequalibus proportionibus equales velocitates
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proueniunt / quod fuit probandum: </
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<
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patet cum minore: et maior probatur. </
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<
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">quia potētia
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que mouetur cum reſiſtentia vniformi continuo eſt
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in puncto medio illius reſiſtentie: et poña que moue-
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tur cum reſiſtētia difformi ſimiliter ē in medio eiuſ
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dem reſiſtentie difformis: et eque velociter continuo
<
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mouetur mediuꝫ vnius ſicut medium alterius / vt pa
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tet ex caſu: igitur eque velociter continuo mouetur
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cum reſiſtentia vniformi ſicut alia poña cum diffor
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mi / quod fuit probandum. </
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<
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">Conſequentia patet cuꝫ
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minore: et arguitur prima pars maioris / q2 poña
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cū reſiſtentia vniformi vt .4. ↄ̨tinuo mouet̄̄ a ꝓpor-
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tione dupla cum ipſa ſit vt .8. et punctus medius ta
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lis latitudinis etiam continuo mouetur a propor-
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tione dupla ex caſu: et incipiunt moueri ab eodē pū- </
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