Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Primi tractatus
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91
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tem equalē vel maiorē magis reſiſtentiã quã potē-
<
lb
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tia vt .10. / et per cõſequēs ↄ̨tinuo potentia illa vt .16.
<
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maiorē proportionē deperdit per acquiſitionē re-
<
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ſiſtentie quã potentia vt .10. </
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<
s
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xml:space
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">Patet hec conſequētia
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ex ſecūda ſuppoſitione octaui capitis huiꝰ. </
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<
s
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xml:space
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uis em̄ hec potentia varietur: nichilominus ex par
<
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te acquiſitionis reſiſtentie tantã ꝓportionē vel ma
<
lb
/>
iorem deperdit ac ſi maneret cõtinuo īuariata: igi
<
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tur cõtinuo maiorē ꝓportionē deperdit / quod fuit
<
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probandum.</
s
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<
s
xml:id
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xml:space
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<
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ꝓbationē admiſſo caſu nego maiorē: et ad ꝓbatio-
<
lb
/>
nem nego antecedens videlicet / continue maiorē
<
lb
/>
ꝓpõrtionē deperdit: et cum ꝓbatur concedo antece
<
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/>
cedens / et nego cõſequentiã: ſed bene ſequitur / ma
<
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iorē reſiſtentiã ꝓportiõabiliter acquirit. </
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>
<
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xml:space
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em̄ deperdat cõtinue ꝓportionē maiorē per acqui-
<
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ſitionē reſiſtentie tamen ſemper aliquã ꝓportionē
<
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acquirit per intenſionē potentie. </
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<
s
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xml:space
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preserve
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bene ꝓbaret ꝓpropoſitū ſi potentia non intenderetur</
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>
</
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<
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<
s
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xml:space
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">Sed contra / quia tunc ſequeretur /
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ſi potentia illa remitteretur cõtinuo ipſa nõ poſſet
<
lb
/>
vniformiter remittere motū ſuū illud mediū tran-
<
lb
/>
ſeundo: ſed cõſequens eſt contra correlariū ſecūde
<
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/>
ↄ̨cluſionis octaui capitis huiꝰ / igitur ſolutio nulla
<
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/>
</
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>
<
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xml:space
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">Probatur ſequela / q2 tūc talis potentia continuo
<
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moueretur velocius alia potentia maiore nõ varia
<
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ta difformiter remittente motū ſuū idem medium
<
lb
/>
tranſeundo verſus extremū intenſius: igitur con-
<
lb
/>
tinuo maiorē ꝓportionē deperderet: et per conſe-
<
lb
/>
quens velocius continuo remitteret motū ſuū quã
<
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/>
potentia maior vt .10. nõ variata: et ſic nõ vniformi
<
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ter. </
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>
<
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xml:space
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">Cõſequentia tamen ptꝫ ex ſecūda ſuppoſitione
<
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octaui capitis preallegata. </
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<
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xml:space
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">Sed ãtecedens arguit̄̄
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videlicet / potentia illa vt .16. cõtinuo velociꝰ mo-
<
lb
/>
ueretur: et pono potentiã vt .16. ſimul cum potentia
<
lb
/>
vt .10. ad principiū vltime quarte puta ad punctum
<
lb
/>
vt .4. / et pono potentiã vt .8. q̄ nõ variata ꝑtrãſeūdo
<
lb
/>
c. mediū īuariatū cõtinuo vniformiter remittit mo-
<
lb
/>
tū ſuū ad punctū ītrīſecū eiuſdē vltime q̈te / ad qḋ ha
<
lb
/>
bet ꝓportionē irrationalē ſubduplã duple: et mo-
<
lb
/>
ueantur ſic oēs ille potentie ſimul ab eodē inſtanti /
<
lb
/>
quo poſito ptꝫ / maior potentia variata puta vt
<
lb
/>
16. cõtinuo velocius mouebitur quã potentia vt .10.
<
lb
/>
qm̄ potentia vt .16. incipit moueri a multo maiori
<
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/>
proportione: igitur propoſitum. </
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>
<
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">Hec em̄ a dupla
<
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ſexquialtera: illa autem a quadrupla ſuum motum
<
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inchoat / vt patet ex caſu.</
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>
</
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<
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xml:space
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">Reſpõdeo negando ſequelã / ad pro-
<
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bationē nego / potentia vt .16. continuo velocius
<
lb
/>
mouebitur quã potentia vt .10. maior nõ variata / et
<
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/>
cū ꝓbatur admiſſo caſu nego antecedens. </
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<
s
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">Dico em̄ /
<
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illa potentia maior vt .16. variata antea quã de-
<
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euniat ad finē ab in infinitū parua ꝓportione mo-
<
lb
/>
uebitur qm̄ ipſa ſic cõtinue remittente cū altera re
<
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/>
mittente motū ſuū ad nõ gradū: neceſſe eſt ipſã ad
<
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/>
nõ gradū remittere ſimiliter motū ſuū: et ſic ab in
<
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īfinitū parua ꝓportiõe moueri / vt ſepiꝰ ſupra argu
<
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/>
gutū eſt.
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">1. correĺ.</
note
>
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<
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xml:space
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">¶ Ex quo ſequit̄̄ / ſi aliqua potētia varia
<
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ta moueretur vniformiter cõtinuo remittēs motuꝫ
<
lb
/>
ſuū ad nõ gradū cū alia nõ variata: et moueret̄̄ cõ-
<
lb
/>
tinuo a ꝓportiõe in cētuplo vel millecuplo vel quã-
<
lb
/>
tūcun volueris maiori: ipſã ab in infinitū parua
<
lb
/>
ꝓportiõe mouebit̄̄ antea quã deueniat ad finē quã
<
lb
/>
quecū potētia quãtacū parua nõ remittēte mo
<
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/>
tum ſuū ad nõ gradū idē mediū trãſeūdo. </
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">Hoc ptꝫ
<
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ex ꝓbatione concluſionum precedentis capitis.</
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</
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<
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="
Capitulum nonū.
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<
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<
s
xml:id
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xml:space
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preserve
">Tertio principaliter cõtra eandē cõ-
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cluſione arguit̄̄ ſic / q2 ſi illa eſſet vera / ſeq̄ret̄̄ a. potē
<
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/>
tiã maiorē variatã in īfinitū intēdi: ſed ↄ̨ſequēs eſt
<
lb
/>
falſū: igit̄̄ illud ex quo ſequit̄̄: falſitas cõſequentis
<
lb
/>
apparet manifeſte: qm̄ tūc nõ cõtinuo remittet mo
<
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/>
tum ſuū. </
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<
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">Plus em̄ aliquãdo accreſceret ſibi de pro
<
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portiõe ꝑ intēſionē ſue potentie quã deꝑderet̄̄ ꝑ re-
<
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ſiſtentie acquiſitionē. </
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<
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xml:space
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">Seq̄la tamē ꝓbat̄̄ / qm̄ in īfi-
<
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nitū vetociter intendit̄̄ ipſa a. potētia: igit̄̄ ipſa in
<
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īfinitū ītendit̄̄. </
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<
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">Aneecedēs ꝓbat̄̄: qm̄ in īfinitū velo-
<
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citer ꝓportiõabiliter accreſcet ſibi reſiſtētia / vt ptꝫ
<
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/>
ex ꝓbatiõe quīte cõcluſiõis ſeptimi capitis huiꝰ: et
<
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/>
ipſa cõtinuo vniformiter remittit motū ſuū: igit̄̄ in
<
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/>
īfinitū velociter accreſcit ſibi potentia. </
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>
<
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<
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nota ex cõcluſiõe: et ꝓbat̄̄ ↄ̨ña / qm̄ ſi ſolū finite velo-
<
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/>
citer accreſceret ſibi potētia: et reſiſtētia in īfinitum
<
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/>
velociter ei accreſceret ſequeret̄̄ / nõ ſemꝑ eque ve
<
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/>
lociter deꝑderet ꝓportionē: et ꝑ ↄ̨ñs nõ vniformiter
<
lb
/>
remitteret motū ſuū: igit̄̄ ſi cõtinuo vniformiter re
<
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/>
mittit motū ſuū: et in īfinitū velociter ꝓportiõabi-
<
lb
/>
liter acquirit̄̄ ſibi reſiſtētia: ſequit̄̄ / potētia eiꝰ in
<
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/>
īfinitū velociter intēdit̄̄. </
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>
<
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">Patet hec ↄ̨ña / qm̄ oppo-
<
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ſitū cõſcqrētis cū altera parte ãtecedētis īfert op-
<
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/>
poſitū alteriꝰ partis eiuſdē ãtecedētis. </
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>
<
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xml:space
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">Sed iã ꝓbo
<
lb
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ãtecedēs / q̄ eſt vna cõditiõalis videlicet / ſi ſolū fini
<
lb
/>
te velociter creſceret ſibi potētia et reſiſtētia in īfini
<
lb
/>
tū velociter ei accreſceret / tã ſeq̄ret̄̄ / nõ ſemꝑ eque
<
lb
/>
velociter deꝑderet ꝓportionē: et ſic nõ vniformiter
<
lb
/>
cõtinuo remitteret motū ſuū: q2 ſi ſolū finite veloci-
<
lb
/>
ter accreſceret ſibi potētia: et reſiſtētia in īfinitū ve-
<
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/>
lociter ei accreſceret: tã ſeq̄ret̄̄ / in īfinitū velocius
<
lb
/>
ꝓportiõabiliter accreſceret ei reſiſtētia quã poten-
<
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/>
tia: et ꝑ ↄ̨ñs in īfinitū maiorē ꝓportionē deꝑderet ꝑ
<
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/>
acquiſitionē reſiſtētie quã acquireret ꝑ acquiſitio-
<
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/>
nē potētie: et ex cõſequēti in īfinitū velociter deper-
<
lb
/>
deret ꝓportionē: et ſic nõ ſemꝑ eque velociter deper
<
lb
/>
deret ꝓportionē nec continuo vniformiter remitte
<
lb
/>
ret motū ſuū: et ſic de primo ad vltimū ptꝫ illa ↄ̨ña
<
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ꝓbanda. </
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<
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xml:space
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">Cõſequētia ptꝫ videlicet / ſi ſolū finite ve
<
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/>
lociter accreſceret ſibi potētia: reſiſtētia in īfinitū
<
lb
/>
velociter ei accreſceret ſequeret̄̄ / in īfinitū velociꝰ
<
lb
/>
ꝓportionabiliter accreſceret ei reſiſtentia quã po-
<
lb
/>
tentia: qm̄ ſi cõtinuo eque velociter accreſceret ſibi
<
lb
/>
reſiſtētia ſicut potētia: velocius ꝓportiõabiliter ac
<
lb
/>
creſceret quã potētia / vt ptꝫ ex octaua ſuppõe q̈rta
<
lb
/>
capitꝪ ſcḋe partꝪ: hoc addito / ↄ̨tinuo potētia ma
<
lb
/>
net maior: ſꝫ modo ī īfinitū velociꝰ accreſcit ſibi re
<
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/>
ſiſtētia quã potētia: g̊ in īfinitū velociꝰ ꝓportiõabi
<
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/>
liṫ accreſcit ſibi reſtētia quã potētia / qḋ fuit ꝓbãdū</
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<
s
xml:id
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xml:space
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preserve
">Reſpõdeo negãdo ſeq̄lã: ad ꝓbatio-
<
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/>
nē nego ↄ̨ñam / q̄ nulliꝰ eſt apparētie. </
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>
<
s
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xml:space
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preserve
">Stat em̄ / ali
<
lb
/>
quid in īfinitū velociṫ intēdi in hora: et tñ ſolū finite
<
lb
/>
intēdi: vt ſatis cõſtat ſi diuiſa hora ꝑ partes ꝓpor
<
lb
/>
tiõales ꝓportiõe q̈drupla: in ṗma illaꝝ acq̇rit̄̄ ali-
<
lb
/>
cui corpori vnꝰ gradꝰ calditatis, et in ſcḋa dimidiꝰ
<
lb
/>
et ī ṫcia, vna q̈rta, et ſic ↄ̨ñter: ꝑ partes ꝓportioãles
<
lb
/>
ꝓportione dupla: tunc manifeſtuꝫ eſt / tota illa ca
<
lb
/>
liditas erit duorum graduum in fine adequate / vt
<
lb
/>
patet ex ſecundo correlario tertie concluſionis quī-
<
lb
/>
ti capitis prime partis: </
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>
<
s
xml:id
="
N18F72
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xml:space
="
preserve
">Ibi enim acquiritur illa q̈-
<
lb
/>
litas per partes ꝓportionales ꝓportione dupla:
<
lb
/>
igitur reſiduuꝫ a prima eſt equale prime: et prima
<
lb
/>
erit vnus gradus: ergo totum eſt duorum graduuꝫ
<
lb
/>
adequate / vt patet ex ſucūdo correlario preallega-
<
lb
/>
to: et tamen in infinitum velociter acquiritur illa ca
<
lb
/>
liditas: quoniam qualitas illa acquiritur in ſecun
<
lb
/>
da parte ꝓportionali in duplo velocius quã in pri
<
lb
/>
ma et in tertia in duplo velocius quam in ſecunda. / </
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>
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