Alvarus, Thomas
,
Liber de triplici motu
,
1509
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De motu penes cauſã ī medio vniformiṫ difformi īuariato.
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portione deperdita ab ipſa potentia a. et continuo
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proportio deperdita ab ipſa potentia a. eſt adhuc
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maior proportione deperdita ab ipſa potentia b.
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<
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<
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xml:space
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">¶ Sequitur quarto: illa potentia b. que tardius
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remittitur deueniens verſus non gradum talis me
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dii ſiue reſiſtentie: in infinitum velociter mouebi-
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tur: in infinitum velociter intendit motum ſuum.
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<
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xml:space
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">Patet hoc correlariū / et capio gradū quē habebit
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talis potentia b. in fine: et ſit vt .2. (gratia exempli) /
<
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/>
et arguo ſic / quãdo potentia b. erit in gradu reſiſten
<
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/>
tie vt vnū in illa reſiſtentia terminata ad nõ gradū
<
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/>
mouebitur a ꝓportione dupla, et in ſubduplo gra
<
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/>
du reſiſtentie mouebitur a dupla ꝓportione ad du-
<
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/>
plam puta a quadrupla, et in ſubduplo ad illum a
<
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/>
proportione octupla, et ſic in īfinitū ꝓcedendo per
<
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/>
ꝓportiões denoīatas a numeris pariter paribus /
<
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/>
igitur ab infinita ꝓportione mouetur b. veniendo
<
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/>
verſus nõ gradū talis reſiſtentie: et ꝑ cõſequens in
<
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infinitū velociter mouetur. </
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<
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xml:space
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">Et ſic ptꝫ ſecunda pars
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correlarii videlicet / in infinitū velociter intendit
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motum ſuū. </
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<
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xml:id
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xml:space
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">5. correĺ.</
note
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<
s
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xml:space
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">¶ Sequitur quinto /
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ſi aliq̈ potētia / q̄ mouet̄̄ vniformiṫ mediū vniformi-
<
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ter difforme terminatū ad nõ gradū pertranſeun-
<
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/>
do per continuū ſue potentie vniforme crementum
<
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/>
incipiēdo ab extremo remiſſiori, incipiat retrogra
<
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de moueri ab extremo intenſiori verſus remiſſius
<
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vniformiter continuo remittendo potentiaꝫ ſuam
<
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velocius tamen quam antea intendebat: talis po-
<
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tentia tardius cõtinuo mouebitur quã antea moue
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batur tranſeūdo illã reſiſtentiam. </
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<
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">Et ſic mouendo,
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velociꝰ quã antea vniformiter potētiã ſuã remittēs
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nõ ſufficit venire ad terminū illius reſiſtētie. </
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<
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xml:space
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batur ſint a. et b. due potētie equales / q̄ ab extremo
<
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remiſſiori verſus intenſius extremū c. medii vnifor-
<
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/>
miter difformis terminati ad nõ gradū moueãtur
<
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continuo vniformiter per ſue potentie continuū et
<
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/>
vniforme crementū quo ad vſ deueniant ad termi
<
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/>
nū c. medii: cum igitur fuerint in extremo intenſiori
<
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incipiant retrograde moueri in eodē inſtanti ab ex
<
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tremo intenſiori verſus remiſſiꝰ: et vna puta a. vni-
<
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/>
formiter et eque velociter mouente ſicut antea et vni
<
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/>
formiter et eque velociter adequate remittente po-
<
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tentiã ſuã ſicut antea intendebat: alia puta b. con-
<
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tinuo velocius vniformiter remittat potentiã ſuaꝫ
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quã antea. </
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">Quo poſito argr̄ ſic / prima pars corre-
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larii q2 a. et b. in principio motus retrogradi ſunt
<
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equales: et b. continuo erit minor: igitur continuo
<
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tardius mouetur ꝙ̄ a. (cū moueantur per eandē re-
<
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/>
ſiſtentiã) / et per cõſequens tardius mouetur quã an-
<
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tea mouebatur q2 a. ita velociter mouetur modo ſi
<
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cut antea adequate mouebatur b. / vt ptꝫ. </
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prima pars. </
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">Secūda pars ꝓbatur / q2 cū b. cõtinuo
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tardius moueatur ꝙ̄ a. / vt ptꝫ ex prima parte huius
<
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correlarii: et incipiant in eodē inſtanti ab eodē pun
<
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cto verſus eandē differentiã moueri, cū ceteris po-
<
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ſitis in caſu, ſequitur / cum a. fuerit in termino, b.
<
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nondū erit in termino: ſed in aliquo puncto intrin
<
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/>
ſeco illius reſiſtentie: et tunc iam a. potentia erit re
<
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miſſa ad nõ gradū: igitur tunc b. potentia iam erit
<
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remiſſa ad nõ gradum / vt ptꝫ ex caſu per locū a ma
<
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/>
iori: et ſi tunc a. potentia erit remiſſa ad non gradū
<
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/>
iam non poterit ſic ad non gradum remiſſa vlteriꝰ
<
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moueri vt deueniat ad terminū illius reſiſtentie / qḋ
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fuit probandum. </
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cõcluſio
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calcu.</
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miſſiori medii vniformiter difformis ad nõ gradū
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De motu penes cauſã ī medio vniformiṫ difformi īuariato.
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terminati incipiat aliqua potentia moueri a non
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gradu intendendo potentiam ſuam, continuo ve-
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locius et velocius: ipſa continuo intendit motum
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ſuum. </
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ipſa continuo remittet motum ſuum. </
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prima pars. </
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">Sit a. potentia que c. medium tranſe-
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undo / vt ponitur in concluſione: continuo velocius
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et velocius intendat potentiam ſuam a non gradu
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etc̈. </
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">Tunc dico / a. potentia continuo intendit mo-
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tum ſuum c. medium tranſeundo. </
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<
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">Quod ſic oſtendi
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tur / quia a. nun̄ vniformiter mouetur: quia alias
<
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tunc vniformiter intenderet potentiam ſuam (vt pa
<
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tet ex prima concluſione) quod tamen eſt contra hy
<
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potheſim. </
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<
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">Nec continuo remittit motum ſuum: nec
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aliquando intendit: et aliquando remittit aut econ
<
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tra: igitur continuo a. potentia intendit motum ſu
<
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um c. medium tranſeundo / quod fuit probandum:
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Cõſequentia cum maiore patet. </
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<
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">Et probatur pri-
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ma pars minoris videlicet / a. nõ continuo remit-
<
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tit motum ſuum: quia ſi ſic: capio vnam partem il-
<
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lius temporis per quod continuo remittit termina
<
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tam ad principium totius temporis: et ſit propor-
<
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tio f. quam habet a. ad ſuam reſiſtentiam in inſtan
<
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ti medio illius partis. </
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<
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xml:space
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">Et arguo ſic / in fine ſecunde
<
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medietatis illius partis a. habet maiorem propor
<
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tionem quam f. ad ſuã reſiſtentiam: igitur propor-
<
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/>
tio a qua mouetur a. non continuo diminuitur: et
<
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ꝑ conſequens a. non continuo remittit motum ſuū
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</
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<
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">Patet conſequentia: et probatur antecedens / quia
<
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inter acquiſitum potentie et acquiſitum reſiſtentie
<
lb
/>
in ſecunda medietate illius partis temporis eſt ma
<
lb
/>
ior proportio quam f. et in principio illius medie-
<
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/>
tatis ſecunde inter potentiã et reſiſtentiam eſt pro-
<
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/>
portio f. adequate ex caſu: igitur in fine ſecunde me
<
lb
/>
dietatis illius partis ipſa potentia a. habet maio
<
lb
/>
rem proportionem quã f. ad ſuam reſiſtentiã: quod
<
lb
/>
erat inferendum: ↄ̨ſequētia ptꝫ ex tertio correlario
<
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quarte concluſionis octaui capitis ſecunde partis
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</
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<
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">Et probatur antecedens / quia in illa ſecunda me-
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dietate maiorem latitudinē potentie acquirit ꝙ̄ eſt
<
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tota illa quam acquiſiuit in prima (cum continuo
<
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/>
velocius creſcat ex hypotheſi) et reſiſtentia minorē
<
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/>
latitudinem acquirit in illa ſecunda medietate ̄
<
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/>
eſt tota illa quã acquiſiuit in prima: quia per te tar
<
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/>
dius a. mouetur in ſecunda ꝙ̄ in prima: et equales
<
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partes c. medii tranſeūdo equales latitudines ade
<
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/>
quate acquirit ſua reſiſtentia: igitur inter acquiſi-
<
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/>
tum potentie et acquiſitū reſiſtentie in ſecunda me-
<
lb
/>
dietate illius partis temporis eſt maior proportio
<
lb
/>
̄ f. / patet ↄ̨ſequētia / q2 ſi in illa ſcḋa medietate ac-
<
lb
/>
quireret tantam potentiam ſicut in prima, et tantã
<
lb
/>
reſiſtentiam etiam ſicut in prima: tunc inter illa ac
<
lb
/>
quiſita eſſet proportio f. / igitur ſi maiorem poten-
<
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/>
tiam acquirit ꝙ̄ tunc et minorem reſiſtentiã ꝙ̄ tunc
<
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/>
inter acquiſitum potentie et acquiſitum reſiſtentie
<
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in ſecunda medietate illius temporis eſt maior pro
<
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portio ꝙ̄ f. </
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<
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">Iam probo ſecundam partem minoris
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videlicet / non aliquando intendit: et aliquando
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remittit. </
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<
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">Quia ſi poſt̄ intendit remittit motum
<
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ſuum detur tempus per quod remittit poſt̄ im-
<
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/>
mediate antea intendebat: et capio vnum inſtans
<
lb
/>
in illo tempore remiſſionis in quo habet a. talem
<
lb
/>
proportionem qualem habebat antea quando in-
<
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tendebat motum que ſit f. </
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<
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xml:space
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">Et arguo ſic / in aliquo tē
<
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pore immediate ſequente illud inſtans in quo a. ha
<
lb
/>
bet proportionem f. ad ſuam reſiſtentiam inter ac-
<
lb
/>
quiſitum potentie et inter acquiſitum reſiſtētie erit
<
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/>
maior proportio quã f. / ergo ſequit̄̄ / proportio f. </
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