Alvarus, Thomas
,
Liber de triplici motu
,
1509
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De motu locali quo ad effectū tꝑe difformi
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168
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ad tempus menſurari habet penes gradum mediū
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xml:space
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nes reductionem ad vniformitatem ſiue penes cal-
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culationem denominationis: et ſi in nõ nullis caſi-
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bus difficile ſit aut impoſſibile naturaliter ad admiſ
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ſim infallibiliter velocitatem menſurare. </
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<
s
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N204C0
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xml:space
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cluſio ſuum colorem apparentiam et probabilita-
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tem ex ſuperioribus ſortitur.</
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<
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xml:space
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mam reſponſum eſt ibi vſ ad vltimam replicã ad
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quã reſpondeo concedendo ſequelam: et negãdo fal
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ſitatē cõſequentis: et cū ꝓbatur / quia alias ſequere-
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tur mobile qḋ continuo īfinite velociter intēdit mo
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tū ſuū infinite tarde moueri: nego illã ſequelã et ad
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ꝓbationē admitto caſū: et ad argumentū cõcedo an
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tecedēs capiēdo ly infinita ī maiore et minore ſin ca
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thegorematice et nego cõſequētiã.
<
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xml:space
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">.1. correl.</
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xml:space
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">¶ Ex quo ſequit̄̄ /
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in caſu poſito quodlibet illoꝝ īmediate poſt hoc
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infinita tarditate mouebit̄̄ et tñ īmediate poſt hoc
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infinita velocitate mouebitur aliquod illorū </
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<
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relarium hoc facile patet ex caſu.
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xml:space
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">2. correl.</
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<
s
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xml:space
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">¶ Sequitur ſecun
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do / in caſu poſito qḋlibet iſtoꝝ īmediate poſt hoc
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in infinitū modicū ſpacium per aliquod tempus ꝑ-
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tranſibit: et tñ īmediate poſt hoc infinite magnum
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ſpaciū ꝑtrãſibit aliquod illoꝝ ꝑ aliquod tempus.</
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<
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">Patet correlariū / quia ſpacia velocitatibus cõmē
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ſurantur.
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xml:space
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">.3. correl:</
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xml:space
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">¶ Sequitur tertio / īmediate poſt hoc in
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finita tarditate mouebitur aliquod illorum: et nul
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lum iſtorum īmediate poſt hoc mouebitur ita tarde
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ſicut a. et a. mouebitur: et ipſuꝫ a. nõ īmediate pꝰ hoc
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infinita tarditate mouebitur. </
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<
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">Probatur correlari
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um et pono caſum / ſint infinita mobilia a. b.c. etc. et
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incipiat a. moueri ab octauo vſ ad non gradum ī
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hora vniformiter difformiter: et b. a gradu duplo
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vſ ad non graduꝫ in prima medietate: et c. adhuc
<
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a gradu duplo ad illum in prima quarta hore vſ
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ad non gradum. </
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<
s
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xml:space
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">et d. a gradu duplo a quo incipit c.
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in prima octaua hore vſ ad non gradum et ſic in ī
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finitum </
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<
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">Quo poſito ſequitur / immediate pꝰ hoc
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infinita tarditate mouebitur aliquod iſtoruꝫ: quia
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immediate poſt hoc erit aliquod iſtorum prope nõ
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gradum motus: et aliud in duplo propinquius non
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gradui: et aliud in quadruplo: et ſic conſequenter / et
<
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nullum iſtorum immediate poſt hoc mouebitur ita
<
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tarde ſicut a. quoniam quodlibet illorum incipit ve
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locius moueri quã a. dempto a. et quodlibet illoruꝫ
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immediate poſt hoc per aliquod tempus mouebi-
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tur velocius quã a. / ergo nullum iſtorum immedia-
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te poſt hoc mouebitur ita tarde ſicut a. in eodem tē-
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pore </
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<
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">Et a. nõ immediate poſt hoc infinita tardi-
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tate mouetur. </
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">Probatur / quia immediate poſt hoc
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mouetur maiori quã vt .6. / igitur non infinita tardi
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tate mouebitur. </
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">Et ſic patet correlariū. </
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<
s
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">¶ Ad ṗmaꝫ
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confirmationē reſponſum eſt ibi vſ ad vltimaꝫ re
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plicam: ad quã reſpondeo negando ſequelam im-
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mo dico / poſſibile eſt eque velociter geometrice
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intendatur vnus motus in tempore finito ſicut al-
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ter remittitur ipſis in principio exiſtentibus equa-
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libus: ſed oportet illum qui intenditur infinitam ve
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locitatem acquirere in illo tempore finito in quo al
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ter motus remittitur ad non gradum. </
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<
s
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">et ad proba-
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tionem ſequele dico / rñſio loquit̄̄ de motu q̇ vſ
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ad certū gradū finite intenditur: et de tali bene con
<
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cedo nõ eſt poſſibile ipſū eque velociter ꝓportio-
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nabiliter intēdi ſicut alter motus ad non gradū re
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mittit̄̄. </
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<
s
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">¶ Ad ſecundã confirmationem que facilis ē:
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rñdeo negãdo ſequelã īmo dico / qñ vnus eſt remiſ
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ſus ad ſubduplū alter eſt remiſſus ad nõ gradū. </
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<
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cū ꝓbatur / non q2 qñ vnus eſt remiſſus ad ſubdu
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De motu locali quo ad effectū tꝑe difformi
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plum perdidit proportioneꝫ duplam: et alter remit
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titur in duplo velocius adequate: ergo debuit per
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didiſſe proportionem quadruplam preciſe q̄ eſt du
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pla duple: nego conſequentiam. </
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<
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">Et ratio eſt / q2 illḋ
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mobile non ſufficit ad illum motum remitti in du-
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plo velocius altero qnia hic non loquimur de velo
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citate geometrica ſed arithmetica que debet attē-
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di penes latitudinem deperditam: et non penes ꝓ-
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portionem deperditam et ſic debet ſemper capi quã
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do dicitur eque velociter, ſi non addatur propor-
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tionabiliter aut geometrice. </
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<
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mationem reſpondeo negando ſequelam: et cum ꝓ
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batur / quia ſemper a. in duplo velocius acquiret la
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titudinem quã b. et hec intenſio procedit in infinituꝫ
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etc. / igitur aliquando a. erit duplus motus ad b. ne-
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go conſequentiam: et cum probatur conſequentia.
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</
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<
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">quia per infinituꝫ latitudo acquiſita ipſi a. excedet
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latitudinem acquiſitam ipſi b. / ergo aliquando mo
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tus a. erit duplus ad motum b. conceſſo anteceden-
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te nego conſequentiam / vt argumentum probat eã
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negandam eſſe. </
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<
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ponſum eſt vſ ad vltimam replicam ad quam reſ
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pondet ſeptima propoſitio primi notabilis huius
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queſtionis cum annotationibus ibi poſitis.</
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<
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cedēdo ſequelã et negando falſitatem conſequentis
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et ad ꝓbationem concedo illi motus ſunt equales
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in principio et equales in fine et equalem latitudinē
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deperdunt in totali illo tēpore cathegorematice: et
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cū infertur / ergo in toto illo tꝑe ſunt equales: nego
<
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illã conſequentiam: quia non mediantibus eis eq̈-
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le ſpaciū pertranſitur / vt patet ex tertia concluſiõe
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tertii notabilis: et ex deductione argumēti. </
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ſolutio ibi poſita. </
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<
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la: et negatur falſitas ↄ̨ñtis vt docet argumentum:
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et ſecundum correlarium tertie propoſitionis ter-
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tii notabilis.</
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</
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<
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do ſequelam. </
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<
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caſu poſito in argumento. </
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<
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">ſed non erit rationalis
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ad intenſionem velocitatis prime partis: </
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<
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requiritur. </
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<
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">Quod tamen totalis ille motus ſit intē
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ſior motu vt ſex vniformi probatur / quia ſi hora eēt
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diuiſa in duas partes equales et in prima illarum
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mobile moueretur vt octo. et in ſecunda vt quatuor
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totus motus eſſet vt ſex (vt notum eſt) ſed motus iſte
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de quo fit mentio in caſu argumenti eſt intenſior:
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cū maior pars quã medietas ſit vt octo et reſidua vt
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4. / ergo ſequitur / ille motus eſt intenſior quã mo-
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tus vt ſex / quod fuit probandum. </
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<
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xml:space
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">Et ad primam re-
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plicam dictum eſt ibi. </
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<
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">Ad vltimam vero reſpondeo
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negando conſequentiam ſicut docet eam negandã
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ſecunda concluſio huius capitis vide eam ibi.</
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<
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ibi vſ ad replicam ad quam replicam cum ſuis cõ
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firmationibus patet reſponſio ex duodecima con-
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cluſione huius capitis cuꝫ ſuis correlariis: </
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<
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">Uide eã
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</
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<
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">Et hec de queſtione et capitulo tertio.</
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<
head
xml:id
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xml:space
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">Capitulum quartum in
<
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quo diſputatiue īquiritur
<
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quõ motus difformis quo
<
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ad ſubiectū et tp̄s ſimul: pa
<
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riter motus mixti veloci
<
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tas cognoſci debeat.</
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>
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="
N20650
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<
s
xml:id
="
N20651
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xml:space
="
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">ABſoluta ſuperioribus capiti-
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bus doctrina perſcrutande motus dif-
<
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mis quo ad ſubiectū et difformis quo ad </
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