Alvarus, Thomas, Liber de triplici motu, 1509

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              <div xml:id="N19FD6" level="4" n="11" type="chapter" type-free="capitulum">
                <p xml:id="N1A438">
                  <s xml:id="N1A43C" xml:space="preserve">
                    <pb chead="De motu penes cauſã in medio vniformiter difformi inuariato." file="0106" n="106"/>
                  iori proportione velocius continuo creſcente quaꝫ
                    <lb/>
                  ſit proportio a qua altera continuo mouetur: potē­
                    <lb/>
                  tia que velocius continuo creſcit velocius continuo
                    <lb/>
                  mouetur in maiori proportiõe ꝙ̄ ſit ꝓportio a qua
                    <lb/>
                  mouetur minor. </s>
                  <s xml:id="N1A454" xml:space="preserve">Probatur / ſit a. potentia que c. me­
                    <lb/>
                  dium vniformiter difforme ad non gradum termi-
                    <lb/>
                  natum pertranſeat: vniformiter continuo mouēdo
                    <lb/>
                  ab f. proportione per ſue potentie a non gradu vni­
                    <lb/>
                  forme crementum: ſit b. potentia que idem c. medi­
                    <lb/>
                  um pertranſeundo a non gradu potentie in h. pro-
                    <lb/>
                  portione maiori f. in maiori proportione quam f.
                    <lb/>
                  continuo velocius creſcat vniformiter continuo mo­
                    <lb/>
                  uens. </s>
                  <s xml:id="N1A467" xml:space="preserve">tūc dico /  b. potentia mouetur velocius ꝙ̄ ip­
                    <lb/>
                  ſa potentia a. in maiori proportione velocius quã
                    <lb/>
                  ſit f. </s>
                  <s xml:id="N1A46E" xml:space="preserve">Quod ſic probatur / quia b. mouetur velociꝰ ̄
                    <lb/>
                  a. et non mouetur velocius in f. ꝓportione adequa-
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                  te: nec in minori ꝙ̄ f. / igitur b. mouetur velocius in
                    <lb/>
                  in maiori ꝓportione ꝙ̄ ſit f. </s>
                  <s xml:id="N1A477" xml:space="preserve">Conſequentia patet cū
                    <lb/>
                  maiore. </s>
                  <s xml:id="N1A47C" xml:space="preserve">Et probatur minor / quo ad primam parteꝫ
                    <lb/>
                  quia ſi b. mouetur velocius a. in f. ꝓportione: ſequit̄̄
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                  ex correlario ſuppõis /  ↄ̨tinuo reſiſtētie ipſiꝰ b. ad
                    <lb/>
                  reſiſtentiam ipſius a. eſt f. proportio adequate: et vl­
                    <lb/>
                  tra reſiſtentie ipſius b. ad reſiſtentiã ipſiꝰ a. ↄ̨tinuo
                    <lb/>
                  eſt proportio f. / igitur ipſius b. ad reſiſtentiam ipſi-
                    <lb/>
                  us b. eſt h. proportio: </s>
                  <s xml:id="N1A48B" xml:space="preserve">Patet conſequentia / quia re-
                    <lb/>
                  ſiſtentia ipſius b. et ipſa poña a. ſunt equalia: quia
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                  vtrum habet f. proportionem ad vnum tertiū pu­
                    <lb/>
                  ta ad reſiſtentiam ipſius a. per te: et ipſius b. ad a. ē
                    <lb/>
                  h. proportio / g̊. ipſius b. ad reſiſtentiam ipſius b. ē
                    <lb/>
                  h. proportio: igitur de primo ad vltimum patet cõ-
                    <lb/>
                  ſequentia. </s>
                  <s xml:id="N1A49A" xml:space="preserve">Et vltra ipſius b. ad reſiſtentiam ipſius
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                  b. eſt h. proportio a qua mouetur ipſa b. potentia
                    <lb/>
                  continuo: et h. proportio eſt maior f. proportione in
                    <lb/>
                  maiori proportione quam ſit f. proportio ex hypo­
                    <lb/>
                  theſi: igitur b. mouetur velocius a. in maiori ꝓpor-
                    <lb/>
                  tione velocius quam ſit f. / quod eſt probandum. </s>
                  <s xml:id="N1A4A7" xml:space="preserve">Iã
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                  probatur ſecunda pars minoris videlicet /  b. non
                    <lb/>
                  mouetur in minori proportione velocius quam ſit
                    <lb/>
                  f. </s>
                  <s xml:id="N1A4B0" xml:space="preserve">Quod ſic probatur / quia ſi b. mouetur in minori
                    <lb/>
                  proportione velocius ipſa a. potentia quam ſit f. / ſe­
                    <lb/>
                  quitur ex correlario ſuppoſitionis /  continuo re-
                    <lb/>
                  ſiſtentie ipſius b. ad reſiſtentiaꝫ ipſius a. eſt minor
                    <lb/>
                  proportio quam f. et vltra reſiſtentie ipſius b. ad re­
                    <lb/>
                  ſiſtentiam ipſius a. eſt minor ꝓportio quam ſit f. et
                    <lb/>
                  b. habet ad a. ꝓportionem h. ex hipotheſi. </s>
                  <s xml:id="N1A4BF" xml:space="preserve">igitur b.
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                  ad reſiſtentiam eiuſdem b. eſt maior ꝓportio quam
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                  ſit h. </s>
                  <s xml:id="N1A4C6" xml:space="preserve">Patet conſequentia / quia a. eſt maior ꝙ̄ reſi-
                    <lb/>
                  ſtentia ipſius b. (cum a. ad vnum puta ad reſiſten-
                    <lb/>
                  tiam eiuſdem a. habet maiorem ꝓportionem ꝙ̄ re-
                    <lb/>
                  ſiſtentia ipſius b. ad idem tertium) / igitur ipſius b.
                    <lb/>
                  ad reſiſtētiã eiuſdē b. ē maior ꝓportio quã ipſius b.
                    <lb/>
                  ad ipſū a. et ipſiꝰ b. ad ip̄3 a. ē ꝓportio h. / igr̄ ipſiꝰ b.
                    <lb/>
                  ad reſiſtentiam eiuſdeꝫ b. eſt maior proportio quã
                    <lb/>
                  h. </s>
                  <s xml:id="N1A4D7" xml:space="preserve">Et vltra ipſius b. ad reſiſtentiam ipſius b. eſt ma-
                    <lb/>
                  ior proportio quam h. et ab illa proportione b. con­
                    <lb/>
                  tinuo mouetur (cum moueatur a proportione quaꝫ
                    <lb/>
                  habet ad ſuam reſiſtentiaꝫ) / igitur b. mouetur a ma­
                    <lb/>
                  ori proportione ꝙ̄ ſit h. et h. proportio eſt maior f.
                    <lb/>
                  proportione in maiori proportione quam f. ex hy-
                    <lb/>
                  potheſi: igitur b. mouetur velocius a. in maiori pro­
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                  portione quam ſit f. ꝓportio. </s>
                  <s xml:id="N1A4E8" xml:space="preserve">Patet conſequentia /
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                  quia ſi aliquid excedit vnum tertium in aliqua pro­
                    <lb/>
                  portione: omne maius illo excedit idem tertiū ī ma­
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                  iori ꝓportione (vt conſtat) / ſed ſic eſt in ꝓpoſito  h.
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                  ꝓportio eſt maior f. ꝓportione in maiori ꝓportio-
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                  ne ꝙ̄ ſit ipſa f. ꝓportio: et ꝓportio a qua mouet̄̄ b. ē
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                  maior h. / ergo ꝓportio a qua mouetur b. eſt maior
                    <lb/>
                  f. ꝓportione in maiori proportione quam ſit f. et ſic
                    <lb/>
                  habetur  b. mouetur velocius in maiori ꝓportio-
                    <cb chead="De motu penes cauſã in medio vniformiter difformi inuariato."/>
                  ne quam ſit f. / quod fuit ꝓbandum. </s>
                  <s xml:id="N1A4FE" xml:space="preserve">Et ſic patet con­
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                  cluſio.
                    <note position="right" xlink:href="note-0106-01a" xlink:label="note-0106-01" xml:id="N1A52A" xml:space="preserve">1. correl.</note>
                  </s>
                  <s xml:id="N1A508" xml:space="preserve">¶ Ex quo ſequitur primo /  ſi a. poña minor
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                  in caſu concluſionis moueatur continuo a ꝓportio­
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                  ne ſexquitertia et b. poña maior creſcat in duplo ve­
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                  locius a. poña minore: tunc b. poña maior mouetur
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                  velocius a. poña minore in maiori ꝓportione ꝙ̄ ſex­
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                  quitertia: in minori tamen ꝓportione velocius quã
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                  dupla. </s>
                  <s xml:id="N1A517" xml:space="preserve">Secunda pars huius correlarii patet ex pri­
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                  ma concluſione huius: et prima ex hac concluſione:
                    <lb/>
                  quoniam proportio dupla in qua b. potentia ma-
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                  ior velocius creſcit quam a. potentia minor: eſt
                    <lb/>
                  maior quam ſexquitertia ad ſexquitertiam immo
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                  maior quam dupla / vt patet ex quīto correlario ter­
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                  tie concluſionis quarti capitis ſecunde partis.</s>
                </p>
                <note position="right" xml:id="N1A530" xml:space="preserve">2. correl.</note>
                <p xml:id="N1A534">
                  <s xml:id="N1A535" xml:space="preserve">¶ Sequitur ſecundo /  ſi a. potentia minor in caſu
                    <lb/>
                  concluſionis moueatur ab aliqua ꝓportione ſuper­
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                  particulari: et b. poña maior continuo creſcat ī tri­
                    <lb/>
                  pla ꝓportione vel in aliqua alia maiore tripla ve-
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                  lociꝰ ꝙ̄ a. poña minor: tunc b. poña maior continuo
                    <lb/>
                  velocius mouebitur a. poña minore in maiori pro-
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                  portione quam ſit aliqua ꝓportio ſuperparticula­
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                  ris: et in minore ꝓportione ꝙ̄ ſit tripla. </s>
                  <s xml:id="N1A546" xml:space="preserve">Patet ſecū­
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                  da pars correlarii ex prima concluſione huius: et
                    <lb/>
                  prima pars ex hac tertia quia omnis tripla vel ma­
                    <lb/>
                  ior tripla eſt maior quaꝫ ſuperparticularis ad quã­
                    <lb/>
                  libet ſuperparticularem (cum tripla ſit maior ꝙ̄ du­
                    <lb/>
                  pla ad maximam ſuperparticulareꝫ que eſt ſexqui­
                    <lb/>
                  altera) / vt conſtat intelligenti ſecundam partem hu­
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                  ius operis: qui innumera ſimilia correlaria facile
                    <lb/>
                  poterit inferre.</s>
                </p>
                <p xml:id="N1A559">
                  <s xml:id="N1A55A" xml:space="preserve">Quarta concluſio </s>
                  <s xml:id="N1A55D" xml:space="preserve">Duabus potētiis
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                  aliquod medium vniformiter difforme ad non gra­
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                  dum terminatum tranſeuntibus: vniformiter con-
                    <lb/>
                  tinuo mouentibus per earum a non gradu potētie
                    <lb/>
                  continuum et vniforme crementum: vna altera in
                    <lb/>
                  maiori ꝓportione velocius continuo creſcente quã
                    <lb/>
                  ſit ꝓportio a qua altera continuo mouet̄̄ in minori
                    <lb/>
                  tñ ꝓportõe maiori ꝙ̄ ſit illa a q̈ mouet̄̄ alṫa poña q̄
                    <lb/>
                  velocius continuo creſcit: velocius continuo moue­
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                  tur altera, in minori tamen ꝓportione ꝙ̄ ſit ꝓpor-
                    <lb/>
                  tio a qua altera mouetur continuo. </s>
                  <s xml:id="N1A574" xml:space="preserve">Probatur / ſit
                    <lb/>
                  a. poña que c. medium tranſeundo etc. vt ſupra con­
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                  tinuo moueatur ab f. ꝓportione ſit b. poña q̄ idē
                    <lb/>
                  c. medium tranſeundo a non gradu potentie in h. ꝓ­
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                  portione que ſit maior ꝙ̄ f. (maior inquam in mino­
                    <lb/>
                  re tamen ꝓportione ꝙ̄ ſit f.) continuo velocius creſ­
                    <lb/>
                  cat ipſa a. poña: tunc dico /  b. poña mouetur velo-
                    <lb/>
                  cius ꝙ̄ a. in minori tamen ꝓportione velocius quã
                    <lb/>
                  ſit f. </s>
                  <s xml:id="N1A587" xml:space="preserve">Quod ſic probatur / quia b. non mouetur velo­
                    <lb/>
                  cius a. in f. ꝓportione: nec in maiori: ergo b. moue-
                    <lb/>
                  tur velocius a. in minori ꝓportione quam ſit f. / qḋ
                    <lb/>
                  fuit ꝓbandum. </s>
                  <s xml:id="N1A590" xml:space="preserve">Conſequentia patet ex hypotheſi: et
                    <lb/>
                  ꝓbatur maior: quia ſi b. moueretur velocius a in f.
                    <lb/>
                  ꝓportione: reſiſtentie ipſius b. ad reſiſtentiam ipſiꝰ
                    <lb/>
                  a. continuo eēt f. ꝓportio. </s>
                  <s xml:id="N1A599" xml:space="preserve">(Hec conſequentia plerū­
                    <lb/>
                   arguta eſt) et vltra reſiſtentie ipſius b. ad reſiſten­
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                  tiam ipſius a. continuo eſt f. ꝓportio: et ipſius a. ad
                    <lb/>
                  reſiſtentiam ipſius a. eſt f. ꝓportio: igitur reſiſtētia
                    <lb/>
                  ipſius b. et ipſum a. ſunt equalia. </s>
                  <s xml:id="N1A5A4" xml:space="preserve">Conſequentia pa­
                    <lb/>
                  tet / quia habent eandem ꝓportionem ad vnum ter-
                    <lb/>
                  tium: et vltra reſiſtentia ipſius b. et ipſum a. ſunt eq̈­
                    <lb/>
                  lia, et ipſius b. ad ipſum a. eſt h. ꝓportio ex hypothe­
                    <lb/>
                  ſi: igitur ipſius b. ad reſiſtentiam eiuſdem b. eſt h. ꝓ­
                    <lb/>
                  portio. </s>
                  <s xml:id="N1A5B1" xml:space="preserve">Patet conſequentia / quia eiuſdem ad duo
                    <lb/>
                  equalia eſt eadem ꝓportio: et vltra ipſius b. ad reſi­
                    <lb/>
                  ſtentiam ipſius b. eſt h. ꝓportio et a tali mouetur ip­
                    <lb/>
                  ſum b. cum continuo moueatur vniformiter a ꝓpor­
                    <lb/>
                  tione quam habet ad ſuam reſiſtentiam: et h. ꝓpor- </s>
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