Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Primi tractatus
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0080
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<
s
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xml:space
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">Quod ſic ꝓbatur: q2 tēporis in quo adequate per
<
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tranſitur .ef. ab ipſa potentia a. ad tēpus in quo
<
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adequate ꝑtranſitur d. pars nõ eſt ꝓportio g. nec
<
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/>
maior: ergo velocitatis deꝑdite in pertranſitiõe
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ef. partis adequate ad velocitatē deꝑditã in ꝑtrã
<
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ſitiõe d. partis adequate nõ eſt ꝓportio g. nec ma-
<
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ior: quod fuit ꝓbandū. </
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<
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N17DE7
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<
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et antecedens ꝓbatur: q2 velocitas qua adequate
<
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/>
ꝑtranſitur .ef. pars eſt maior velocitate qua ꝑtrã-
<
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/>
ſitur d. pars adequate: et .ef. ad d. eſt proportio g. /
<
lb
/>
ergo tēporis in quo adequate ꝑtranſitur .ef. pars
<
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/>
ad tēpus in quo adequate ꝑtranſitur d. pars non
<
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eſt ꝓportio g. nec maior. </
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<
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xml:space
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">Cõſequentia patꝫ: quia ſi
<
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velocitas qua adequate ꝑtranſitur .ef. pars eſſet
<
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/>
equalis velocitati qua ꝑtranſitur d. pars: iam tē-
<
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/>
poris in quo ꝑtranſitur .ef. ad tēpus in quo ꝑtrã-
<
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/>
ſitur d. pars eſſet ꝓportio g. (que videlicet eſt inter
<
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/>
illas partes .ef. et d. / vt conſtat) / igitur ſi velocitas
<
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qua ꝑtranſitur .ef. pars eſt maior velocitate qua
<
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pertranſitur d. pars adequate iam tēporis in quo
<
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/>
adequate ꝑtranſitur d. pars nõ eſt ꝓportio g. nec
<
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maior. </
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<
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xml:space
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">Patet hec cõſequentia / q2 minus tēpus re-
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quiritur ad ꝑtranſeundū ſpaciū .ef. adequate ma
<
lb
/>
iori velocitate quã ad ꝑtranſeundū ipſum adequa-
<
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te aliqua velocitate minori. </
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<
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xml:space
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">Sed iam ꝓbatur an-
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tecedens videlicet / velocitas qua adequate per-
<
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tranſitur adequate .ef. pars eſt maior velocitate
<
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/>
qua adequate ꝑtrãſitur d. pars: q2 velocitas qua
<
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/>
ꝑtranſitur adequate .e. pars ab ipſa potētia a. eſt
<
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/>
equalis vel maior velocitate qua adequate ꝑtran-
<
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/>
ſitur d. pars (cū ex hypotheſi in pertranſitione .e.
<
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/>
partis adequate moueatur a. potētia cū equali vĺ
<
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/>
minori reſiſtentia quã in pertranſitione d. partis
<
lb
/>
adequate) et ipſi velocitati qua ꝑtranſitur .e. pars
<
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/>
adequate additur extēſiue adhuc maior velocitas
<
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/>
in pertranſitione f. partis minus reſiſtentis / vt cõ
<
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/>
ſtat: igitur tota velocitas qua ꝑtranſitur .ef. pars
<
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adequate eſt maior tota velocitate qua pertranſi-
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tur d. pars adequate: quod fuit oſtēdendū. </
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<
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hec cõſequentia: q2 ſi alicui latitudini intenſionis
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addatur extēſiue aliqua latitudo maioris intēſio
<
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nis .etc̈. totalis illa latitudo aggregata ex addita
<
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et preexiſtenti efficitur maioris intēſionis: vt ſi la-
<
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titudini vniformiter difformi q̈rto vſ ad octa-
<
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uum addatur vna alia maioris intēſiõis puta ab
<
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/>
octauo vſ ad duodecimū: aggregatū ex eis effi-
<
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cit̄̄ maioris intēſiõis / vt cõſtat. </
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>
<
s
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xml:space
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">Et ſic ptꝫ ſuppoſitio</
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</
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ma ṗma
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ↄ̨cĺo. cal.</
note
>
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<
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</
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<
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xml:space
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">Ubi aliqua potentia non variata vniformiter re-
<
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mittit motū ſuū ad nõ gradū mediū īuariatū trã-
<
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ſeūdo: aliqua maior ꝑ ſui cõtinuã intenſionē idem
<
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mediū īuariatū trãſeūdo valet motū ſuū vniformi
<
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ter ad gradū remittere. </
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>
<
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">Probat̄̄: ſit b. potētia que
<
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īuariata c. mediū īuariatū trãſeūdo vniformiter
<
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ad nõ gradū motū ſuū remittat: ſit a. potentia
<
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/>
maior q̄ ab eodē puncto c. medii incipiēdo moueri
<
lb
/>
cū ipſo b. ab in duplo maiori ꝓportiõe īcipiat mo
<
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/>
ueri quã b. et cõtinuo in duplo velociꝰ moueat̄̄ quã
<
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/>
b. ꝑ variationē ipſiꝰ a. potētie (q2 alias medio īua
<
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/>
riato hoc nequit fieri / vt ptꝫ ex quarta ↄ̨cluſiõe pre
<
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/>
cedētis capitis): tūc dico / a. potētia ↄ̨tinuo vni-
<
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/>
formiter remittit motū ſuū ad gradū ↄ̨tinuo intē-
<
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/>
tendo potentiã ſuã. </
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>
<
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">Quod ꝓbatur ſic: q2 a. poten-
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tia cõtinuo vniformiter remittit motū ſuū trãſeū-
<
lb
/>
do illud mediū: et per nullū tēpus ſtabit inuariata
<
lb
/>
aut remittet potentiã ſuã idē mediū trãſeūdo: igit̄̄
<
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/>
cõtinuo vniformiter remittit motū ſuū, cõtinuo in
<
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/>
tendendo potentiã ſuã. </
s
>
<
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">Cõſequētia ptꝫ ex ſe: et ꝓba
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tur maior / q2 a. potentia cõtinuo in duplo velocius
<
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Capitulū octauū.
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mouetur quam b. potentia / vt ptꝫ ex hypotheſi: et b.
<
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potētia cõtinuo vniformiter remittit motū ſuum:
<
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igitur a potētia idem mediū tranſeūdo vniformi-
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ter remittit motū ſuū cõtinuo. </
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<
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xml:space
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tia ex ſecūda parte prime ſuppoſitionis. </
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<
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xml:space
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">Iam pro
<
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batur minor / q2 ſi a. per aliquod tēpus ſtat īuaria-
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ta vel remittit potentiã ſuam: detur illud et ſit g. et
<
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pars pertranſita ab ipſa .a. potentia in g. tēpore
<
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/>
adequate ſit .ef. et pars ꝑtranſita ab ipſa b. poten
<
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/>
tia in eodē g. tēpore ſit d. / et manifeſtū eſt / ipſius
<
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/>
ef. ad ipſam d. partē eſt ꝓportio dupla, cū ſemper
<
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/>
a. moueatur in duplo velocius ipſa potentia b. / vt
<
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/>
ptꝫ ex hypotheſi: quo poſito arguitur ſic: latitudi
<
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nis motus deperdite ab ipſa b. potētia tranſeūdo
<
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ef. partē adequate, ad latitudinē motus deꝑditã
<
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/>
ab ipſa b. potētia tranſeūdo d. partē adequate in
<
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g. tēpore eſt maior ꝓportio quã dupla que eſt īter
<
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illas partes .ef. et d. / ergo latitudinis deperdite ab
<
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/>
a. potētia ſtante vel remittente potentiã ſuam trã-
<
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ſeundo .ef. partē in g. tēpore adequate ad velocita
<
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tem deperditã ab ipſa b. potentia tranſeundo d.
<
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partē adequate in g. tēpore eſt maior ꝓportio quã
<
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dupla: ſed cõſequens eſt falſum: igitur illud ex quo
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ſequitur. </
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<
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">Probatur cõſequentia: q2 oēs potentie
<
lb
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īuariate idem mediū īuariatū trãſeūtes .etc̈. equa-
<
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/>
lem latitudinē motus deꝑdunt: et ſi aliqua potētia
<
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/>
trãſeundo mediū īuariatū remittendo motū ſuum
<
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/>
etc̈. et remittat potentiã: ipſa maiorē latitudinem
<
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/>
motus deperdit quã ſi ſtaret idem mediū tranſeū-
<
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do / vt conſtat: et ptꝫ ex quarto argumento ſexti ca-
<
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pitis huius. </
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>
<
s
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xml:space
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">Sed falſitas cõſequentis ꝓbatur: q2
<
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ſi latitudinis motus deperdite ab ipſa a. potētia
<
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/>
in g. tēpore ad latitudinē motꝰ deperditã ab ipſa
<
lb
/>
b. potentia in eodē g. tēpore eſt maior ꝓportio quã
<
lb
/>
dupla: et a principio latitudinis motus ipſius a.
<
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ad latitudinem motus ipſius b. erat proportio
<
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duplo: ſequitur / facta tali deperditione: latitu-
<
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/>
dinis motus ipſius a. ad latitudinem motus ipſi-
<
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/>
us b. eſt minor ꝓportio quam dupla: quod eſt con-
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tra hypotheſim. </
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">Conſequentia tamen ptꝫ / ex ſecū-
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da parte quinti correlarii quarte ↄ̨cluſionis octa
<
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ui capitis ſecunde partis. </
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<
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xml:space
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">Iam ꝓbatur antecedēs
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videlicet / latitudinis deperdite ab b. potētia trã
<
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/>
ſeundo .ef. partē adequate ad velocitatē deperdi-
<
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/>
tam etc̈. q2 ipſius .ef. partis ad d. partē eſt propor
<
lb
/>
tio dupla ex caſu: et ipſa potētia b. tranſeūdo quã
<
lb
/>
libet partem exceſſus ipſius .ef. partis minoreꝫ d.
<
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/>
parte mouetur cū maiori reſiſtentia quã tranſeun
<
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do quãlibet partē equalē ipſius d. partis (cū que-
<
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/>
libet pars exceſſus quo .ef. pars excedit d. partem
<
lb
/>
magis diſtat a puncto initiatiuo c. medii a quo in
<
lb
/>
cipit motus quam aliqua pars ipſius d. partis q2
<
lb
/>
per totum illum exceſſum ad minus a potentia b.
<
lb
/>
potentiam precedit) / ergo latitudinis deperdite a
<
lb
/>
b. potentia tranſeundo .ef. partem adequate ad ve
<
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/>
locitatem deperditam ab ipſa b. potentia tranſe-
<
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undo d. partem adequate in g. tempore eſt maior
<
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proportio quam dupla: quod fuit inferendū. </
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<
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<
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tet conſequentia ex tertia ſuppoſitione huius. </
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<
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<
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vero a. potentia remittat motum ſuuꝫ ad gradum
<
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in extremo intenſiori / patet ex ſecundo correlario
<
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quarte concluſionis ſeptimi capitis huius tracta
<
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tus, auxiliante loco a maiori: quia illa potētia cõ
<
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tinuo intenditur. </
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<
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xml:space
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">Et ſic patet concluſio.
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">1. correĺ.</
note
>
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<
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ſequitur. </
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<
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">Q, vbi aliqua potentia non variata vni
<
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formiter continuo remittit motum ſuum ad non
<
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gradū mediū īuariatū trãſeūdo: oīs potentia ma
<
lb
/>
ior ꝑ ſui ↄ̨tinuã ītenſionē idē mediū īuariatū tran-
<
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/>
ſeūdo valet motū ſuū vniformiṫ ad g̈dū remittere.</
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