Alvarus, Thomas, Liber de triplici motu, 1509

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                <p xml:id="N1AD53">
                  <s xml:id="N1AD63" xml:space="preserve">
                    <pb chead="De motu penes cauſã in medio vniformiter difformi inuariato." file="0112" n="112"/>
                  igitur tranſeundo ſecundam medietatem non mo-
                    <lb/>
                  uetur ab f. proportione: ergo non mouetur cõtinuo
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                  vniformiter / quod fuit probandum. </s>
                  <s xml:id="N1AD8F" xml:space="preserve">Conſequentia
                    <lb/>
                  patet ex ſecundo correlario quinte concluſionis ſe-
                    <lb/>
                  cundi capitis ſecunde partis. </s>
                  <s xml:id="N1AD96" xml:space="preserve">Nam quod ibi dici-
                    <lb/>
                  tur de rationalibus quantitatibus de quibuſcū
                    <lb/>
                  ex eadem quinta concluſione facile demonſtrari va­
                    <lb/>
                  let. </s>
                  <s xml:id="N1AD9F" xml:space="preserve">Et ſic patet correlarium.
                    <note position="left" xlink:href="note-0112-01a" xlink:label="note-0112-01" xml:id="N1ADC3" xml:space="preserve">quõ ↄ̨clu­
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                    ſiones de­
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                    cimi et vn­
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                    decimi ca­
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                    pitū dñt
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                    reſtringi</note>
                  </s>
                  <s xml:id="N1ADA7" xml:space="preserve">¶ Et ex hoc habes do-
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                  cumentum notandum /  predicte concluſiones duo­
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                  rum precedentium capitum intelliguntur cum po-
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                  tentie mouentur in medio vniformiter difformi per­
                    <lb/>
                  fecte q̈drato, vel quadrilatero vniformis latitudi-
                    <lb/>
                  nis et profunditatis continuo. </s>
                  <s xml:id="N1ADB4" xml:space="preserve">¶ Utrum autem ta-
                    <lb/>
                  lia media requirantur ad predictas cõcluſiones ve­
                    <lb/>
                  rificandas, ita  cum nullis aliis mediis potentie
                    <lb/>
                  poſſint moueri ſecundum tenorem predictarum cõ-
                    <lb/>
                  cluſionum quam cum illis tu ipſe inquiras.</s>
                </p>
                <note position="left" xml:id="N1ADD3" xml:space="preserve">argumē-
                  <lb/>
                tū calcu.</note>
                <p xml:id="N1ADD9">
                  <s xml:id="N1ADDA" xml:space="preserve">Secundo contra tertium correlariū
                    <lb/>
                  quinte concluſionis decimi capitis arguitur ſic. </s>
                  <s xml:id="N1ADDF" xml:space="preserve">q2
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                  b. potentia in caſu illius correlarii aliquando vni-
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                  formiter mouetur dato  motus ille perpetuo con­
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                  tinuetur: igitur non cõtinuo intendit motum ſuum /
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                  et per conſequens correlariū falſuꝫ. </s>
                  <s xml:id="N1ADEA" xml:space="preserve">Conſequentia
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                  patet / et arguitur antecedens: quia motus ipſius b.
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                  quando ſimul incipit moueri ab eodem puncto cuꝫ
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                  a. ſolum finite diſtat a gradu velocitatis quo mo-
                    <lb/>
                  uetur a. et a. continuo vniformiter mouetur: et b. con­
                    <lb/>
                  tinuo intendit motum ſuum: et ſic perpetuo mouebū­
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                  tur: ergo velocitas ipſius b. tandem deneniet ad eq̈­
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                  litatem velocitatis motus a. et b. / tunc vniformiter
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                  mouebitur / igitur propoſitum. </s>
                  <s xml:id="N1ADFD" xml:space="preserve">Patet conſequētia /
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                  quia non eſt dabilis latitudo inter motum maiorē
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                  et minorem quin illa per continuam intenſioneꝫ mi­
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                  noris tandem valeat acquiri vt ſatis cõſtat: igitur
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                  b. in tempore finito poteſt acquirere latitudinē mo­
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                  tus per quam motus ipſius a. excedit motum ipſiꝰ
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                  b. </s>
                  <s xml:id="N1AE0C" xml:space="preserve">Sed  tunc b. vniformiter mouebitur probatur.
                    <lb/>
                  </s>
                  <s xml:id="N1AE10" xml:space="preserve">quia tūc b. mouebitur ab eadē proportione: et ita ve­
                    <lb/>
                  lociter ſicut a. mouetur ī illo puncto quia a. ſemper
                    <lb/>
                  mouetur vniformiter: et per conſequens ſequitur / 
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                  in illo puncto erit b. potentia tanta quanta fuit a.
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                  potentia in illo puncto: et creſcit vniformiter conti­
                    <lb/>
                  nuo et eq̄ velociter ſicut a. et ex hoc ſicut a. creſcebat
                    <lb/>
                  ibi / et per conſequens mouetur vniformiter ſicut a. /
                    <lb/>
                  quod fuit probandum.</s>
                </p>
                <p xml:id="N1AE21">
                  <s xml:id="N1AE22" xml:space="preserve">Reſpondeo negando antecedens: et
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                  ad probationem concedo antecedens / et nego conſe­
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                  quentiam: et cum probatur / quia nulla eſt latitudo
                    <lb/>
                  finita inter duos motus inequales maiorem vide-
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                  licet et minorem quin illa valeat in tempore finito
                    <lb/>
                  acquiri a minori motu ꝑ continuã eiꝰ maiorationē:
                    <lb/>
                  diſtīguo illud, aut ſi talis minor motus vniformi-
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                  ter continuo intendatur aut velocius et velocius / et
                    <lb/>
                  ſic ego bene concedo illud: aut ſi continuo intenda-
                    <lb/>
                  tur tardius et tardius, et ſic ego nego. </s>
                  <s xml:id="N1AE37" xml:space="preserve">Non em̄ tunc
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                  oportet. </s>
                  <s xml:id="N1AE3C" xml:space="preserve">Poſſibile enim eſt  vnus gradus motus
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                  ſemper ſit in acquiri per infinitum tempus. </s>
                  <s xml:id="N1AE41" xml:space="preserve">Hoc eſt
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                   vnum mobile continuo per infinitum tempus in­
                    <lb/>
                  tendat motum ſuum: et nun̄ acquirat vnum gradū
                    <lb/>
                  motus per quem exceditur a motu velociori ſed be­
                    <lb/>
                  ne quēlibet motum citra. </s>
                  <s xml:id="N1AE4C" xml:space="preserve">Ut ſi in prima hora illius
                    <lb/>
                  infiniti temporis acquirat primaꝫ partem propor­
                    <lb/>
                  tionalem vnius gradus: et in ſecunda ſecundam et
                    <lb/>
                  in tertia tertiam: et ſic cõſequenter.
                    <note position="left" xlink:href="note-0112-02a" xlink:label="note-0112-02" xml:id="N1AE6C" xml:space="preserve">1. correl.</note>
                  </s>
                  <s xml:id="N1AE5A" xml:space="preserve">¶ Ex quo
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                  ſequitur primo /  potentia a. in infinitum tarde in-
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                  tenderet motum ſuum eſto  motus eius perpetuo
                    <lb/>
                  duraret. </s>
                  <s xml:id="N1AE63" xml:space="preserve">Patet quia alias ſequeretur /  in tempo-
                    <lb/>
                  re finito poſſet venire ad equalitatem motus b.</s>
                </p>
                <cb chead="De motu penes cauſã in medio vniformiter difformi inuariato."/>
                <note position="right" xml:id="N1AE74" xml:space="preserve">2. correl.</note>
                <p xml:id="N1AE78">
                  <s xml:id="N1AE79" xml:space="preserve">¶ Sequitur ſecundo /  potentia a. que vniformi-
                    <lb/>
                  ter continuo mouetur non poteſt attingere potētiã
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                  maiorem precedentem ipſam que eque velociter et
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                  vniformiter continuo intenditur ſicut ipſa potētia
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                  a. de qua videlicet ſit mentio ī ſecūdo correlario q̇n­
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                  te concluſionis preallegate. </s>
                  <s xml:id="N1AE86" xml:space="preserve">Probatur / quia a. non
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                  poteſt incipere moueri eque velociter ſicut illa po-
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                  tentia precedens ipſam potentiam a. / ergo ſequitur /
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                   non poteſt attingere ipſam que velocius moue-
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                  tur et precedit. </s>
                  <s xml:id="N1AE91" xml:space="preserve">Conſequentia patet, et arguitur an-
                    <lb/>
                  tecedens: quia ſi mouebitur aliquando eque veloci­
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                  ter ſicut maior precedens: et illa maior precedens
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                  continuo remittit motum ſuum: ſequitur /  a. potē-
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                  tia aliquando cõtinuo certe velocius mouebit̄̄ quã
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                  illa potentia que continuo remittit motum ſuum: et
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                  precedit: et ex conſequenti ſequitur /  a. potentia ali­
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                  quando attinget illam potentiam maiorem prece-
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                  dentem (dato /  perpetuo duraret motus illarū po­
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                  tentiarum in tali medio) / et per conſequens eque ci-
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                  to pertranſiretur aliquod ſpacium a potentia ma­
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                  iore et a potentia minore / quod eſt impoſſibile (cete-
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                  ris deductis) </s>
                  <s xml:id="N1AEAC" xml:space="preserve">Patet conſequentia / q2 omne mobile
                    <lb/>
                  ſequens alteruꝫ qḋ ab aliqua certa ꝓportione con­
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                  tinuo velocius eo mouetur (dūmodo perpetuo ſic
                    <lb/>
                  moueantur) tandem attinget illud vt facile demon­
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                  ſtrari potet.
                    <note position="right" xlink:href="note-0112-03a" xlink:label="note-0112-03" xml:id="N1AF73" xml:space="preserve">3. correl.</note>
                  </s>
                  <s xml:id="N1AEBC" xml:space="preserve">¶ Sequitur tertio /  illa potentia ma-
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                  ior precedens continuo tardius remittit motū ſuū:
                    <lb/>
                  et ſi perpetuo moueretur per tale medium in infini-
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                  tum tarde remitteret motum ſuum. </s>
                  <s xml:id="N1AEC5" xml:space="preserve">Probatur hoc
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                  correlarium / quia ſi velocius et velocius remitteret
                    <lb/>
                  motum ſuum vel vniformiter continuo: tandem de­
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                  ueniret ad equalitateꝫ motus ipſius a. vniformiter
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                  continuo mouentis: et tunc tardius moueretur:
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                  quod ſuperiori correlario improbatum eſt. </s>
                  <s xml:id="N1AED2" xml:space="preserve">Patet
                    <lb/>
                  igitur correlarium.
                    <note position="right" xlink:href="note-0112-04a" xlink:label="note-0112-04" xml:id="N1AF79" xml:space="preserve">4. correl.</note>
                  </s>
                  <s xml:id="N1AEDC" xml:space="preserve">¶ Sequitur quarto /  iſta con-
                    <lb/>
                  ſequentia nihil valet a. in īfinitum modicum diſtat
                    <lb/>
                  ab aliqua iſtarum potentiarum: et a. qualibet iſtaꝝ
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                  potētiaꝝ verſus eandem differentiam continuo ve­
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                  locius mouetur: ergo ſequitur /  a. aliquando attī­
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                  get alquam illarum potentiarum eſto /  perpetuo
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                  motus eius duraret. </s>
                  <s xml:id="N1AEEB" xml:space="preserve">Probatur / et pono / 
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                  a. potentia ponatur in puncto initiatiuo c. medii
                    <lb/>
                  quod vniformiter continuo mouendo pertranſit ꝑ
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                  ſue potentie ad non gradu continuuꝫ et vniforme cre­
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                  mentum: et in quolibet puncto intrinſeco eiuſdem c.
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                  medii ponatur potentia vna que vniformiter conti­
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                  nuo a non gradu potentie et eque velociter ſicut a.
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                  creſcat: mouendo verſus extremum intenſius c. me-
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                  dii a ꝓportione ſui ad ſuam reſiſtentiam. </s>
                  <s xml:id="N1AEFE" xml:space="preserve">Quo po­
                    <lb/>
                  ſito antecedens illius ↄ̨ñe eſt verum: et conſequens
                    <lb/>
                  falſum: igit̄̄ correlariū uꝫ. </s>
                  <s xml:id="N1AF05" xml:space="preserve">Q, tunc antecedens il-
                    <lb/>
                  lius conſequētie eſt verum / patet / quia prima pars
                    <lb/>
                  eius eſt ex ſe nota: et ſecunda patet ex quinta conclu­
                    <lb/>
                  ſione decimi capitis. </s>
                  <s xml:id="N1AF0E" xml:space="preserve">Sed  conſequens ſit falſum
                    <lb/>
                  probatur / quia ſi a. aliquando attingit aliquam il­
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                  larum potentiarum: et continuo a. eſt equalis cuili-
                    <lb/>
                  bet aliarum potentiarum ex hypotheſi: et quelibet
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                  aliarum poñarum continuo intendit motum ſuum /
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                  ſequitur /  a. aliquando intendit motum ſuum cum
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                  aliqua illarum poñarum mouendo ab eodem pun­
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                  cto cum ea continuo eque velociter: ſed conſequens
                    <lb/>
                  eſt falſum / vt patet ex ſecunda cõcluſione decimi ca­
                    <lb/>
                  pitis: igitur et antecedens. </s>
                  <s xml:id="N1AF23" xml:space="preserve">Item ſi a. aliquando at-
                    <lb/>
                  tingit aliquam illarum poñarum ſequitur /  eadeꝫ
                    <lb/>
                  poña eque cito pertranſiret totum ſicut eius partē
                    <lb/>
                  ceteris paribus / quod eſt impoſſibile: </s>
                  <s xml:id="N1AF2C" xml:space="preserve">Et ſic patet
                    <lb/>
                  correlarium.
                    <note position="right" xlink:href="note-0112-05a" xlink:label="note-0112-05" xml:id="N1AF7F" xml:space="preserve">5. correl.</note>
                  </s>
                  <s xml:id="N1AF36" xml:space="preserve">¶ Sequitur quinto /  ad arguendum
                    <lb/>
                  a. poñam velocius continuo mouentem b. poñam p̄­
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                  cedentem mouētem tamen tardius aliquando attī­ </s>
                </p>
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