Alvarus, Thomas
,
Liber de triplici motu
,
1509
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<
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De motu penes cauſã in medio vniformiter difformi inuariato.
"
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0112
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n
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112
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igitur tranſeundo ſecundam medietatem non mo-
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uetur ab f. proportione: ergo non mouetur cõtinuo
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vniformiter / quod fuit probandum. </
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>
<
s
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xml:space
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">Conſequentia
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patet ex ſecundo correlario quinte concluſionis ſe-
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cundi capitis ſecunde partis. </
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>
<
s
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xml:space
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preserve
">Nam quod ibi dici-
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tur de rationalibus quantitatibus de quibuſcū
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ex eadem quinta concluſione facile demonſtrari va
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let. </
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>
<
s
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xml:space
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">Et ſic patet correlarium.
<
note
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xml:id
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xml:space
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">quõ ↄ̨clu
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ſiones de
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cimi et vn
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decimi ca
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pitū dñt
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reſtringi</
note
>
</
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>
<
s
xml:id
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xml:space
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preserve
">¶ Et ex hoc habes do-
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cumentum notandum / predicte concluſiones duo
<
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rum precedentium capitum intelliguntur cum po-
<
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tentie mouentur in medio vniformiter difformi per
<
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/>
fecte q̈drato, vel quadrilatero vniformis latitudi-
<
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/>
nis et profunditatis continuo. </
s
>
<
s
xml:id
="
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xml:space
="
preserve
">¶ Utrum autem ta-
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lia media requirantur ad predictas cõcluſiones ve
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rificandas, ita cum nullis aliis mediis potentie
<
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poſſint moueri ſecundum tenorem predictarum cõ-
<
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cluſionum quam cum illis tu ipſe inquiras.</
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>
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xml:id
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xml:space
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">argumē-
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tū calcu.</
note
>
<
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<
s
xml:id
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xml:space
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preserve
">Secundo contra tertium correlariū
<
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quinte concluſionis decimi capitis arguitur ſic. </
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>
<
s
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xml:space
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">q2
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b. potentia in caſu illius correlarii aliquando vni-
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formiter mouetur dato motus ille perpetuo con
<
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/>
tinuetur: igitur non cõtinuo intendit motum ſuum /
<
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/>
et per conſequens correlariū falſuꝫ. </
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>
<
s
xml:id
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N1ADEA
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xml:space
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preserve
">Conſequentia
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patet / et arguitur antecedens: quia motus ipſius b.
<
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/>
quando ſimul incipit moueri ab eodem puncto cuꝫ
<
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/>
a. ſolum finite diſtat a gradu velocitatis quo mo-
<
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/>
uetur a. et a. continuo vniformiter mouetur: et b. con
<
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/>
tinuo intendit motum ſuum: et ſic perpetuo mouebū
<
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/>
tur: ergo velocitas ipſius b. tandem deneniet ad eq̈
<
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/>
litatem velocitatis motus a. et b. / tunc vniformiter
<
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/>
mouebitur / igitur propoſitum. </
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>
<
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">Patet conſequētia /
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quia non eſt dabilis latitudo inter motum maiorē
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et minorem quin illa per continuam intenſioneꝫ mi
<
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noris tandem valeat acquiri vt ſatis cõſtat: igitur
<
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b. in tempore finito poteſt acquirere latitudinē mo
<
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/>
tus per quam motus ipſius a. excedit motum ipſiꝰ
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b. </
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>
<
s
xml:id
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xml:space
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">Sed tunc b. vniformiter mouebitur probatur.
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</
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>
<
s
xml:id
="
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xml:space
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">quia tūc b. mouebitur ab eadē proportione: et ita ve
<
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/>
lociter ſicut a. mouetur ī illo puncto quia a. ſemper
<
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/>
mouetur vniformiter: et per conſequens ſequitur /
<
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in illo puncto erit b. potentia tanta quanta fuit a.
<
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/>
potentia in illo puncto: et creſcit vniformiter conti
<
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/>
nuo et eq̄ velociter ſicut a. et ex hoc ſicut a. creſcebat
<
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ibi / et per conſequens mouetur vniformiter ſicut a. /
<
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quod fuit probandum.</
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>
</
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<
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<
s
xml:id
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xml:space
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">Reſpondeo negando antecedens: et
<
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ad probationem concedo antecedens / et nego conſe
<
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/>
quentiam: et cum probatur / quia nulla eſt latitudo
<
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/>
finita inter duos motus inequales maiorem vide-
<
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/>
licet et minorem quin illa valeat in tempore finito
<
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/>
acquiri a minori motu ꝑ continuã eiꝰ maiorationē:
<
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diſtīguo illud, aut ſi talis minor motus vniformi-
<
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ter continuo intendatur aut velocius et velocius / et
<
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ſic ego bene concedo illud: aut ſi continuo intenda-
<
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tur tardius et tardius, et ſic ego nego. </
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>
<
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">Non em̄ tunc
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oportet. </
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>
<
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xml:space
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">Poſſibile enim eſt vnus gradus motus
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ſemper ſit in acquiri per infinitum tempus. </
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>
<
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xml:space
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">Hoc eſt
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vnum mobile continuo per infinitum tempus in
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tendat motum ſuum: et nun̄ acquirat vnum gradū
<
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motus per quem exceditur a motu velociori ſed be
<
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ne quēlibet motum citra. </
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>
<
s
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">Ut ſi in prima hora illius
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infiniti temporis acquirat primaꝫ partem propor
<
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tionalem vnius gradus: et in ſecunda ſecundam et
<
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in tertia tertiam: et ſic cõſequenter.
<
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xml:id
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xml:space
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">1. correl.</
note
>
</
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<
s
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xml:space
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">¶ Ex quo
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ſequitur primo / potentia a. in infinitum tarde in-
<
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tenderet motum ſuum eſto motus eius perpetuo
<
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duraret. </
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>
<
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xml:space
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">Patet quia alias ſequeretur / in tempo-
<
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re finito poſſet venire ad equalitatem motus b.</
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>
</
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>
<
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De motu penes cauſã in medio vniformiter difformi inuariato.
"/>
<
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xml:id
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xml:space
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">2. correl.</
note
>
<
p
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">
<
s
xml:id
="
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xml:space
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">¶ Sequitur ſecundo / potentia a. que vniformi-
<
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/>
ter continuo mouetur non poteſt attingere potētiã
<
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/>
maiorem precedentem ipſam que eque velociter et
<
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/>
vniformiter continuo intenditur ſicut ipſa potētia
<
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/>
a. de qua videlicet ſit mentio ī ſecūdo correlario q̇n
<
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te concluſionis preallegate. </
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>
<
s
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xml:space
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">Probatur / quia a. non
<
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poteſt incipere moueri eque velociter ſicut illa po-
<
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tentia precedens ipſam potentiam a. / ergo ſequitur /
<
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non poteſt attingere ipſam que velocius moue-
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tur et precedit. </
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>
<
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xml:space
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">Conſequentia patet, et arguitur an-
<
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tecedens: quia ſi mouebitur aliquando eque veloci
<
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ter ſicut maior precedens: et illa maior precedens
<
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/>
continuo remittit motum ſuum: ſequitur / a. potē-
<
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/>
tia aliquando cõtinuo certe velocius mouebit̄̄ quã
<
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illa potentia que continuo remittit motum ſuum: et
<
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precedit: et ex conſequenti ſequitur / a. potentia ali
<
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/>
quando attinget illam potentiam maiorem prece-
<
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/>
dentem (dato / perpetuo duraret motus illarū po
<
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/>
tentiarum in tali medio) / et per conſequens eque ci-
<
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to pertranſiretur aliquod ſpacium a potentia ma
<
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/>
iore et a potentia minore / quod eſt impoſſibile (cete-
<
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ris deductis) </
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>
<
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="
N1AEAC
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">Patet conſequentia / q2 omne mobile
<
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/>
ſequens alteruꝫ qḋ ab aliqua certa ꝓportione con
<
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/>
tinuo velocius eo mouetur (dūmodo perpetuo ſic
<
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/>
moueantur) tandem attinget illud vt facile demon
<
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ſtrari potet.
<
note
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="
right
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xlink:href
="
note-0112-03a
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xlink:label
="
note-0112-03
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xml:id
="
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xml:space
="
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">3. correl.</
note
>
</
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>
<
s
xml:id
="
N1AEBC
"
xml:space
="
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">¶ Sequitur tertio / illa potentia ma-
<
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ior precedens continuo tardius remittit motū ſuū:
<
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/>
et ſi perpetuo moueretur per tale medium in infini-
<
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tum tarde remitteret motum ſuum. </
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>
<
s
xml:id
="
N1AEC5
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xml:space
="
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">Probatur hoc
<
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correlarium / quia ſi velocius et velocius remitteret
<
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motum ſuum vel vniformiter continuo: tandem de
<
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ueniret ad equalitateꝫ motus ipſius a. vniformiter
<
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continuo mouentis: et tunc tardius moueretur:
<
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quod ſuperiori correlario improbatum eſt. </
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>
<
s
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">Patet
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igitur correlarium.
<
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="
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="
note-0112-04
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xml:id
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xml:space
="
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">4. correl.</
note
>
</
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>
<
s
xml:id
="
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"
xml:space
="
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">¶ Sequitur quarto / iſta con-
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ſequentia nihil valet a. in īfinitum modicum diſtat
<
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/>
ab aliqua iſtarum potentiarum: et a. qualibet iſtaꝝ
<
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/>
potētiaꝝ verſus eandem differentiam continuo ve
<
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locius mouetur: ergo ſequitur / a. aliquando attī
<
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/>
get alquam illarum potentiarum eſto / perpetuo
<
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motus eius duraret. </
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>
<
s
xml:id
="
N1AEEB
"
xml:space
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">Probatur / et pono /
<
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a. potentia ponatur in puncto initiatiuo c. medii
<
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quod vniformiter continuo mouendo pertranſit ꝑ
<
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/>
ſue potentie ad non gradu continuuꝫ et vniforme cre
<
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/>
mentum: et in quolibet puncto intrinſeco eiuſdem c.
<
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/>
medii ponatur potentia vna que vniformiter conti
<
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nuo a non gradu potentie et eque velociter ſicut a.
<
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/>
creſcat: mouendo verſus extremum intenſius c. me-
<
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dii a ꝓportione ſui ad ſuam reſiſtentiam. </
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>
<
s
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="
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xml:space
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">Quo po
<
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ſito antecedens illius ↄ̨ñe eſt verum: et conſequens
<
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falſum: igit̄̄ correlariū uꝫ. </
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>
<
s
xml:id
="
N1AF05
"
xml:space
="
preserve
">Q, tunc antecedens il-
<
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/>
lius conſequētie eſt verum / patet / quia prima pars
<
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/>
eius eſt ex ſe nota: et ſecunda patet ex quinta conclu
<
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/>
ſione decimi capitis. </
s
>
<
s
xml:id
="
N1AF0E
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xml:space
="
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">Sed conſequens ſit falſum
<
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probatur / quia ſi a. aliquando attingit aliquam il
<
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/>
larum potentiarum: et continuo a. eſt equalis cuili-
<
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/>
bet aliarum potentiarum ex hypotheſi: et quelibet
<
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/>
aliarum poñarum continuo intendit motum ſuum /
<
lb
/>
ſequitur / a. aliquando intendit motum ſuum cum
<
lb
/>
aliqua illarum poñarum mouendo ab eodem pun
<
lb
/>
cto cum ea continuo eque velociter: ſed conſequens
<
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/>
eſt falſum / vt patet ex ſecunda cõcluſione decimi ca
<
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/>
pitis: igitur et antecedens. </
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>
<
s
xml:id
="
N1AF23
"
xml:space
="
preserve
">Item ſi a. aliquando at-
<
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/>
tingit aliquam illarum poñarum ſequitur / eadeꝫ
<
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/>
poña eque cito pertranſiret totum ſicut eius partē
<
lb
/>
ceteris paribus / quod eſt impoſſibile: </
s
>
<
s
xml:id
="
N1AF2C
"
xml:space
="
preserve
">Et ſic patet
<
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/>
correlarium.
<
note
position
="
right
"
xlink:href
="
note-0112-05a
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xlink:label
="
note-0112-05
"
xml:id
="
N1AF7F
"
xml:space
="
preserve
">5. correl.</
note
>
</
s
>
<
s
xml:id
="
N1AF36
"
xml:space
="
preserve
">¶ Sequitur quinto / ad arguendum
<
lb
/>
a. poñam velocius continuo mouentem b. poñam p̄
<
lb
/>
cedentem mouētem tamen tardius aliquando attī </
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>
</
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>
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