Alvarus, Thomas, Liber de triplici motu, 1509

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              <div xml:id="N19642" level="4" n="10" type="chapter" type-free="capitulum">
                <p xml:id="N19ACD">
                  <s xml:id="N19B17" xml:space="preserve">
                    <pb chead="De motu penes cauſã ī medio vniformiṫ difformi īuariato." file="0100" n="100"/>
                  portione deperdita ab ipſa potentia a. et continuo
                    <lb/>
                  proportio deperdita ab ipſa potentia a. eſt adhuc
                    <lb/>
                  maior proportione deperdita ab ipſa potentia b.
                    <lb/>
                  </s>
                  <s xml:id="N19B2A" xml:space="preserve">Patet igitur correlarium.</s>
                </p>
                <note position="left" xml:id="N19B2D" xml:space="preserve">4. correĺ.</note>
                <p xml:id="N19B31">
                  <s xml:id="N19B32" xml:space="preserve">¶ Sequitur quarto:  illa potentia b. que tardius
                    <lb/>
                  remittitur deueniens verſus non gradum talis me­
                    <lb/>
                  dii ſiue reſiſtentie: in infinitum velociter mouebi-
                    <lb/>
                  tur: in infinitum velociter intendit motum ſuum.
                    <lb/>
                  </s>
                  <s xml:id="N19B3C" xml:space="preserve">Patet hoc correlariū / et capio gradū quē habebit
                    <lb/>
                  talis potentia b. in fine: et ſit vt .2. (gratia exempli) /
                    <lb/>
                  et arguo ſic / quãdo potentia b. erit in gradu reſiſten­
                    <lb/>
                  tie vt vnū in illa reſiſtentia terminata ad nõ gradū
                    <lb/>
                  mouebitur a ꝓportione dupla, et in ſubduplo gra­
                    <lb/>
                  du reſiſtentie mouebitur a dupla ꝓportione ad du-
                    <lb/>
                  plam puta a quadrupla, et in ſubduplo ad illum a
                    <lb/>
                  proportione octupla, et ſic in īfinitū ꝓcedendo per
                    <lb/>
                  ꝓportiões denoīatas a numeris pariter paribus /
                    <lb/>
                  igitur ab infinita ꝓportione mouetur b. veniendo
                    <lb/>
                  verſus nõ gradū talis reſiſtentie: et ꝑ cõſequens in
                    <lb/>
                  infinitū velociter mouetur. </s>
                  <s xml:id="N19B55" xml:space="preserve">Et ſic ptꝫ ſecunda pars
                    <lb/>
                  correlarii videlicet /  in infinitū velociter intendit
                    <lb/>
                  motum ſuū. </s>
                  <s xml:id="N19B5C" xml:space="preserve">Ptꝫ igr̄ correlariū.
                    <note position="left" xlink:href="note-0100-01a" xlink:label="note-0100-01" xml:id="N19BD3" xml:space="preserve">5. correĺ.</note>
                  </s>
                  <s xml:id="N19B64" xml:space="preserve">¶ Sequitur quinto / 
                    <lb/>
                  ſi aliq̈ potētia / q̄ mouet̄̄ vniformiṫ mediū vniformi-
                    <lb/>
                  ter difforme terminatū ad nõ gradū pertranſeun-
                    <lb/>
                  do per continuū ſue potentie vniforme crementum
                    <lb/>
                  incipiēdo ab extremo remiſſiori, incipiat retrogra­
                    <lb/>
                  de moueri ab extremo intenſiori verſus remiſſius
                    <lb/>
                  vniformiter continuo remittendo potentiaꝫ ſuam
                    <lb/>
                  velocius tamen quam antea intendebat: talis po-
                    <lb/>
                  tentia tardius cõtinuo mouebitur quã antea moue­
                    <lb/>
                  batur tranſeūdo illã reſiſtentiam. </s>
                  <s xml:id="N19B79" xml:space="preserve">Et ſic mouendo,
                    <lb/>
                  velociꝰ quã antea vniformiter potētiã ſuã remittēs
                    <lb/>
                  nõ ſufficit venire ad terminū illius reſiſtētie. </s>
                  <s xml:id="N19B80" xml:space="preserve">Pro-
                    <lb/>
                  batur ſint a. et b. due potētie equales / q̄ ab extremo
                    <lb/>
                  remiſſiori verſus intenſius extremū c. medii vnifor-
                    <lb/>
                  miter difformis terminati ad nõ gradū moueãtur
                    <lb/>
                  continuo vniformiter per ſue potentie continuū et
                    <lb/>
                  vniforme crementū quo ad vſ deueniant ad termi­
                    <lb/>
                  nū c. medii: cum igitur fuerint in extremo intenſiori
                    <lb/>
                  incipiant retrograde moueri in eodē inſtanti ab ex­
                    <lb/>
                  tremo intenſiori verſus remiſſiꝰ: et vna puta a. vni-
                    <lb/>
                  formiter et eque velociter mouente ſicut antea et vni­
                    <lb/>
                  formiter et eque velociter adequate remittente po-
                    <lb/>
                  tentiã ſuã ſicut antea intendebat: alia puta b. con-
                    <lb/>
                  tinuo velocius vniformiter remittat potentiã ſuaꝫ
                    <lb/>
                  quã antea. </s>
                  <s xml:id="N19B9D" xml:space="preserve">Quo poſito argr̄ ſic / prima pars corre-
                    <lb/>
                  larii q2 a. et b. in principio motus retrogradi ſunt
                    <lb/>
                  equales: et b. continuo erit minor: igitur continuo
                    <lb/>
                  tardius mouetur ꝙ̄ a. (cū moueantur per eandē re-
                    <lb/>
                  ſiſtentiã) / et per cõſequens tardius mouetur quã an-
                    <lb/>
                  tea mouebatur q2 a. ita velociter mouetur modo ſi­
                    <lb/>
                  cut antea adequate mouebatur b. / vt ptꝫ. </s>
                  <s xml:id="N19BAC" xml:space="preserve">Et ſic ptꝫ
                    <lb/>
                  prima pars. </s>
                  <s xml:id="N19BB1" xml:space="preserve">Secūda pars ꝓbatur / q2 cū b. cõtinuo
                    <lb/>
                  tardius moueatur ꝙ̄ a. / vt ptꝫ ex prima parte huius
                    <lb/>
                  correlarii: et incipiant in eodē inſtanti ab eodē pun­
                    <lb/>
                  cto verſus eandē differentiã moueri, cū ceteris po-
                    <lb/>
                  ſitis in caſu, ſequitur /  cum a. fuerit in termino, b.
                    <lb/>
                  nondū erit in termino: ſed in aliquo puncto intrin­
                    <lb/>
                  ſeco illius reſiſtentie: et tunc iam a. potentia erit re­
                    <lb/>
                  miſſa ad nõ gradū: igitur tunc b. potentia iam erit
                    <lb/>
                  remiſſa ad nõ gradum / vt ptꝫ ex caſu per locū a ma­
                    <lb/>
                  iori: et ſi tunc a. potentia erit remiſſa ad non gradū
                    <lb/>
                  iam non poterit ſic ad non gradum remiſſa vlteriꝰ
                    <lb/>
                  moueri vt deueniat ad terminū illius reſiſtentie / qḋ
                    <lb/>
                  fuit probandum. </s>
                  <s xml:id="N19BCC" xml:space="preserve">Et ſic ptꝫ correlarium.</s>
                </p>
                <note position="left" xml:id="N19BD9" xml:space="preserve">Decima
                  <lb/>
                cõcluſio
                  <lb/>
                calcu.</note>
                <p xml:id="N19BE1">
                  <s xml:id="N19BE2" xml:space="preserve">Quarta concluſio. </s>
                  <s xml:id="N19BE5" xml:space="preserve">Si ab extremo re-
                    <lb/>
                  miſſiori medii vniformiter difformis ad nõ gradū
                    <cb chead="De motu penes cauſã ī medio vniformiṫ difformi īuariato."/>
                  terminati incipiat aliqua potentia moueri a non
                    <lb/>
                  gradu intendendo potentiam ſuam, continuo ve-
                    <lb/>
                  locius et velocius: ipſa continuo intendit motum
                    <lb/>
                  ſuum. </s>
                  <s xml:id="N19BF3" xml:space="preserve">Et ſi tardius et tardius continuo intendatur
                    <lb/>
                  ipſa continuo remittet motum ſuum. </s>
                  <s xml:id="N19BF8" xml:space="preserve">Probatur
                    <lb/>
                  prima pars. </s>
                  <s xml:id="N19BFD" xml:space="preserve">Sit a. potentia que c. medium tranſe-
                    <lb/>
                  undo / vt ponitur in concluſione: continuo velocius
                    <lb/>
                  et velocius intendat potentiam ſuam a non gradu
                    <lb/>
                  etc̈. </s>
                  <s xml:id="N19C06" xml:space="preserve">Tunc dico /  a. potentia continuo intendit mo-
                    <lb/>
                  tum ſuum c. medium tranſeundo. </s>
                  <s xml:id="N19C0B" xml:space="preserve">Quod ſic oſtendi­
                    <lb/>
                  tur / quia a. nun̄ vniformiter mouetur: quia alias
                    <lb/>
                  tunc vniformiter intenderet potentiam ſuam (vt pa­
                    <lb/>
                  tet ex prima concluſione) quod tamen eſt contra hy­
                    <lb/>
                  potheſim. </s>
                  <s xml:id="N19C16" xml:space="preserve">Nec continuo remittit motum ſuum: nec
                    <lb/>
                  aliquando intendit: et aliquando remittit aut econ­
                    <lb/>
                  tra: igitur continuo a. potentia intendit motum ſu­
                    <lb/>
                  um c. medium tranſeundo / quod fuit probandum:
                    <lb/>
                  Cõſequentia cum maiore patet. </s>
                  <s xml:id="N19C21" xml:space="preserve">Et probatur pri-
                    <lb/>
                  ma pars minoris videlicet /  a. nõ continuo remit-
                    <lb/>
                  tit motum ſuum: quia ſi ſic: capio vnam partem il-
                    <lb/>
                  lius temporis per quod continuo remittit termina­
                    <lb/>
                  tam ad principium totius temporis: et ſit propor-
                    <lb/>
                  tio f. quam habet a. ad ſuam reſiſtentiam in inſtan­
                    <lb/>
                  ti medio illius partis. </s>
                  <s xml:id="N19C30" xml:space="preserve">Et arguo ſic / in fine ſecunde
                    <lb/>
                  medietatis illius partis a. habet maiorem propor­
                    <lb/>
                  tionem quam f. ad ſuã reſiſtentiam: igitur propor-
                    <lb/>
                  tio a qua mouetur a. non continuo diminuitur: et
                    <lb/>
                  ꝑ conſequens a. non continuo remittit motum ſuū
                    <lb/>
                  </s>
                  <s xml:id="N19C3C" xml:space="preserve">Patet conſequentia: et probatur antecedens / quia
                    <lb/>
                  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-
                    <lb/>
                  tatis ſecunde inter potentiã et reſiſtentiam eſt pro-
                    <lb/>
                  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
                    <lb/>
                  quarte concluſionis octaui capitis ſecunde partis
                    <lb/>
                  </s>
                  <s xml:id="N19C52" xml:space="preserve">Et probatur antecedens / quia in illa ſecunda me-
                    <lb/>
                  dietate maiorem latitudinē potentie acquirit ꝙ̄ eſt
                    <lb/>
                  tota illa quam acquiſiuit in prima (cum continuo
                    <lb/>
                  velocius creſcat ex hypotheſi) et reſiſtentia minorē
                    <lb/>
                  latitudinem acquirit in illa ſecunda medietate ̄
                    <lb/>
                  eſt tota illa quã acquiſiuit in prima: quia per te tar­
                    <lb/>
                  dius a. mouetur in ſecunda ꝙ̄ in prima: et equales
                    <lb/>
                  partes c. medii tranſeūdo equales latitudines ade­
                    <lb/>
                  quate acquirit ſua reſiſtentia: igitur inter acquiſi-
                    <lb/>
                  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-
                    <lb/>
                  tiam acquirit ꝙ̄ tunc et minorem reſiſtentiã ꝙ̄ tunc
                    <lb/>
                  inter acquiſitum potentie et acquiſitum reſiſtentie
                    <lb/>
                  in ſecunda medietate illius temporis eſt maior pro­
                    <lb/>
                  portio ꝙ̄ f. </s>
                  <s xml:id="N19C79" xml:space="preserve">Iam probo ſecundam partem minoris
                    <lb/>
                  videlicet /  non aliquando intendit: et aliquando
                    <lb/>
                  remittit. </s>
                  <s xml:id="N19C80" xml:space="preserve">Quia ſi poſt̄ intendit remittit motum
                    <lb/>
                  ſuum detur tempus per quod remittit poſt̄ im-
                    <lb/>
                  mediate antea intendebat: et capio vnum inſtans
                    <lb/>
                  in illo tempore remiſſionis in quo habet a. talem
                    <lb/>
                  proportionem qualem habebat antea quando in-
                    <lb/>
                  tendebat motum que ſit f. </s>
                  <s xml:id="N19C8D" xml:space="preserve">Et arguo ſic / in aliquo tē­
                    <lb/>
                  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
                    <lb/>
                  maior proportio quã f. / ergo ſequit̄̄ /  proportio f. </s>
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