Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N15C22" level="3" n="1" type="other" type-free="tractatus">
              <div xml:id="N18B2D" level="4" n="9" type="chapter" type-free="capitulum">
                <p xml:id="N18F57">
                  <s xml:id="N18F72" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0092" n="92"/>
                  et ſic conſequenter: igitur ꝓpoſitum. </s>
                  <s xml:id="N18F8A" xml:space="preserve">Arguitur an-
                    <lb/>
                  tecedens / quoniam qualitas acquiſita in ſecunda ꝑ­
                    <lb/>
                  te propoſtiouali eſt equalis qualitati acquiſite in
                    <lb/>
                  medietate prime partis proportionalis </s>
                  <s xml:id="N18F93" xml:space="preserve">(Uolo em̄
                    <lb/>
                   acquirat vniformiter) et aquiritur in duplo mino­
                    <lb/>
                  ri tempore quam ſit illa medietas prime partis ꝓ-
                    <lb/>
                  portionalis / vt conſtat intelligenti quintum caput
                    <lb/>
                  prime partis: igitur ī duplo velocius acquiritur il­
                    <lb/>
                  la qualitas in ſecunda parte ꝓportionali quam in
                    <lb/>
                  prima. </s>
                  <s xml:id="N18FA2" xml:space="preserve">Et iſto modo arguatur de qualitate acquiſi­
                    <lb/>
                  ta in tertia parte ꝓportionali reſpectu qualitatis
                    <lb/>
                  acquiſite in ſecunda. </s>
                  <s xml:id="N18FA9" xml:space="preserve">Bene tamen concedo pro reſo­
                    <lb/>
                  lutione argumenti /  illa poña verſus extremum in­
                    <lb/>
                  tenſius deueniendo in infinitum velociter intendi-
                    <lb/>
                  tur / vt probat argumentum.
                    <note position="left" xlink:href="note-0092-01a" xlink:label="note-0092-01" xml:id="N18FC2" xml:space="preserve">1. correl.</note>
                  </s>
                  <s xml:id="N18FB7" xml:space="preserve">¶ Ex quo ſequitur pri-
                    <lb/>
                  mo /  ſtat aliquid in infinitum velociter augeri ac-
                    <lb/>
                  quirendo preciſe quantitatem pedalem in hora.</s>
                </p>
                <p xml:id="N18FC8">
                  <s xml:id="N18FC9" xml:space="preserve">Patet hoc ſupponendo /  hora diuidatur per par­
                    <lb/>
                  tes proportionales proportione quadrupla, aut
                    <lb/>
                  quintupla (in idem redit) et vnum corpus in prima
                    <lb/>
                  parte ꝓportionali acquirat ſemipedale, et in ſecun­
                    <lb/>
                  da quartam partem pedalis, et in tertia octauaꝫ, et
                    <lb/>
                  ſic conſequenter in ſubdupla ꝓportione. </s>
                  <s xml:id="N18FD6" xml:space="preserve">quo poſi-
                    <lb/>
                  to manifeſtū ē (vt patet ex ſolutione argumenti) / 
                    <lb/>
                  illud corpus in infinitum velociter augetur: et tamē
                    <lb/>
                  ſolum finite augetur acquirendo adequate quan-
                    <lb/>
                  titatem pedalem in hora: </s>
                  <s xml:id="N18FE1" xml:space="preserve">Nam acquirit infinita cõ­
                    <lb/>
                  tinue ſe habentia in ꝓportione dupla: igit̄̄ reſiduū
                    <lb/>
                  a primo eſt equale primo / vt patet ex ſecundo corre-
                    <lb/>
                  lario tertie concluſionis quinti capitis preallega-
                    <lb/>
                  to: et primo acquiſitum eſt ſemipedale: ergo totum
                    <lb/>
                  eſt pedale.
                    <note position="left" xlink:href="note-0092-02a" xlink:label="note-0092-02" xml:id="N18FFC" xml:space="preserve">2. correl.</note>
                  </s>
                  <s xml:id="N18FF3" xml:space="preserve">¶ Sequitur ſecundo /  aliquid in infini-
                    <lb/>
                  tum tarde intenditur: et tamen finite intenditur.</s>
                </p>
                <p xml:id="N19002">
                  <s xml:id="N19003" xml:space="preserve">Probatur ponendo /  hora diuidatur per partes
                    <lb/>
                  ꝓportionales ꝓportione dupla: et in prima parte
                    <lb/>
                  ꝓportiõali aliquod corpus acquirat quatuor gra­
                    <lb/>
                  dus, et in ſecunda vnum, et in tertia vnam quartam
                    <lb/>
                  vnius gradus: et ſic conſequenter procedendo per ꝑ­
                    <lb/>
                  tes ꝓportionales proportione quadrupla. </s>
                  <s xml:id="N19010" xml:space="preserve">quo po­
                    <lb/>
                  ſito manifeſtum eſt /  illud corpus in infinitum tar­
                    <lb/>
                  de intenditur: quoniaꝫ in ſecunda parte proportio­
                    <lb/>
                  nali in duplo tardius quaꝫ in prima, et ī tertia ī du­
                    <lb/>
                  plo tardius quam in ſecunda, et ſic conſequēter: igi­
                    <lb/>
                  tur in infinitum tarde intenditur. </s>
                  <s xml:id="N1901D" xml:space="preserve">Probatur ante-
                    <lb/>
                  cedens / quoniam in ſecunda parte tale corpꝰ acqui­
                    <lb/>
                  rit ſubduplam intenſionem ad intenſionem acqui-
                    <lb/>
                  ſitam in medietate prime partis: et medietas prime
                    <lb/>
                  et ſecunda ſunt equales: igitur ī equali tempore ſub­
                    <lb/>
                  duplam intenſionem acquirit / et per conſequens in
                    <lb/>
                  duplo tardius intenditur. </s>
                  <s xml:id="N1902C" xml:space="preserve">Et ſic ꝓbabitur de qua-
                    <lb/>
                  litate acquiſita in tertia, et de quacun alia reſpe-
                    <lb/>
                  ctu qualitatis acquiſite in parte precedenti eaꝫ im­
                    <lb/>
                  mediate. </s>
                  <s xml:id="N19035" xml:space="preserve">igitur propoſitum. </s>
                  <s xml:id="N19038" xml:space="preserve">Sed  finite intenda-
                    <lb/>
                  tur patet: quia preciſe in toto tempore illo acquirit
                    <lb/>
                  quin gradus cum tertia. </s>
                  <s xml:id="N1903F" xml:space="preserve">Nam in prima parte ꝓ-
                    <lb/>
                  portionali acquirit quatuor gradus: et in ſecunda
                    <lb/>
                  vnum: et ſic conſequenter ꝓcedendo per partes pro­
                    <lb/>
                  portionales proportione quadrupla: ergo reſiduū
                    <lb/>
                  ab acquiſito in prima eſt ſubtriplum ad illud / vt pa­
                    <lb/>
                  tet ex ſecundo correlario preallegato: ſed acquiſi-
                    <lb/>
                  tum in prima eſt quatuor graduum: igitur acquiſi-
                    <lb/>
                  tum in omnibus ſequentibus a prima eſt gradꝰ cū
                    <lb/>
                  tertia: et ſic totum eſt quin graduum cuꝫ tertia / qḋ
                    <lb/>
                  fuit probandum.
                    <note position="left" xlink:href="note-0092-03a" xlink:label="note-0092-03" xml:id="N19074" xml:space="preserve">3. correl.</note>
                  </s>
                  <s xml:id="N19059" xml:space="preserve">¶ Sequitur tertio /  infinite intē­
                    <lb/>
                  di eſt infinitam qualitatem acquirere vel infinitam
                    <lb/>
                  intenſionem: ſed in infinitum velociter intendi eſt in
                    <lb/>
                  aliquo tempore aliquam qualitatē acquirere ali-
                    <lb/>
                  quanta velocitate: et aliam in duplo maiori veloci-
                    <lb/>
                  tate (ſiue ſit tanta ſiue minor non eſt cura) et aliam
                    <cb chead="Capitulum nonum"/>
                  in triplo maiori: et ſic conſequenter vt poteſt exem-
                    <lb/>
                  plo primi correlarii oſtendi. </s>
                  <s xml:id="N1906B" xml:space="preserve">Conſimiliter diffini-
                    <lb/>
                  as in infinnitum tarde intendi.</s>
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                <note position="right" xml:id="N1907A" xml:space="preserve">4. correl.</note>
                <p xml:id="N1907E">
                  <s xml:id="N1907F" xml:space="preserve">¶ Sequitur quarto /  quamuis poña non variata
                    <lb/>
                  intendens motum ſuum per medium vniformiter
                    <lb/>
                  difforme velocius intendat motum ſuum continuo
                    <lb/>
                  tranſeundo partem minus reſiſtentem quam ma-
                    <lb/>
                  gis reſiſtentem: nichilominus tamen poña non va-
                    <lb/>
                  riata difformiter intendens motum ſuum per me-
                    <lb/>
                  dium difforme per quod poña minor continuo vni­
                    <lb/>
                  formiter intendit motum ſuum: velocius ītendit ip­
                    <lb/>
                  ſa potentia maior non variata motum ſuum tran-
                    <lb/>
                  ſeundo partem magis reſiſtentem quam minus re-
                    <lb/>
                  ſiſtentem. </s>
                  <s xml:id="N19096" xml:space="preserve">Prima pars correlarii patet ex quadra­
                    <lb/>
                  geſima concluſione quinti capitis huius tractatus
                    <lb/>
                  </s>
                  <s xml:id="N1909C" xml:space="preserve">Et ſecunda probatur / quia quacun parte data ꝓ-
                    <lb/>
                  portionabili illius medii procedendo a minoribus
                    <lb/>
                  verſus maiores in qua aliqualiter ītendit talis po­
                    <lb/>
                  tentia maior motum ſuum: in aliqua minore prece­
                    <lb/>
                  dente magis reſiſtente velocius intendebat motum
                    <lb/>
                  ſuum cum in infinitum velociter antea intendebat
                    <lb/>
                  motum ſuum / vt patet ex tertio correlario quinte cõ­
                    <lb/>
                  cluſionis ſeptimi capitis huius tractatus: igitur ve­
                    <lb/>
                  locius intendebat talis potentia motum ſuum cum
                    <lb/>
                  parte magis reſiſtente / quod fuit probandum.</s>
                </p>
                <p xml:id="N190B1">
                  <s xml:id="N190B2" xml:space="preserve">Quarto contra ſecundam concluſio-
                    <lb/>
                  nem octaui capitis arguitur ſic / quia ſi illa eſſet ve-
                    <lb/>
                  ra ſequeretur /  vbi aliqua potentia inuariata ali­
                    <lb/>
                  quod medium inuariatum tranſeundo cõtinuo vni­
                    <lb/>
                  formiter remittit motum ſuum ad non gradum in
                    <lb/>
                  puncto terminatiuo eiuſdem medii in extremo intē­
                    <lb/>
                  ſiori: omnem potentiam maiorem idem mediã trã­
                    <lb/>
                  ſeundo adequate vniformiter continuo poſſe remit­
                    <lb/>
                  tere motum ſuum ad non gradum in eodem puncto
                    <lb/>
                  terminatiuo per continuam ſue potentie remiſſio-
                    <lb/>
                  nem / ſed hoc eſt falſum: igitur et concluſio. </s>
                  <s xml:id="N190C9" xml:space="preserve">Falſitas
                    <lb/>
                  conſequentis probatur / et capio a. poñam que habe­
                    <lb/>
                  at ad punctum initiatiuum c. medii quod inuaria-
                    <lb/>
                  tum b. poña inuariata pertranſit continuo vnifor-
                    <lb/>
                  miter remittēdo motum ſuum ad non gradum etc.
                    <lb/>
                  ꝓportionem in ſexquialtero maiorem quam b. ad
                    <lb/>
                  idem punctum: et arguo ſic / a. potentia tranſeūdo c.
                    <lb/>
                  medium non valet vniformiter continuo remittere
                    <lb/>
                  motum ſuum vſ ad non gradum in puncto termi­
                    <lb/>
                  natiuo c. medii in extremo intenſiori per continuaꝫ
                    <lb/>
                  ſue potentie remiſſionem: igitur non vbi potentia ī­
                    <lb/>
                  uariata aliquod medium tranſeundo inuariatum
                    <lb/>
                  etc. ad non gradum in puncto terminatiuo etc. om-
                    <lb/>
                  nis potentia maior idem medium tranſeundo ade­
                    <lb/>
                  quate, vniformiter continuo poteſt remittere motū
                    <lb/>
                  ſnum vſ ad non gradum in eodem puncto termi-
                    <lb/>
                  natiuo per continuam ſue potentie remiſſionem. </s>
                  <s xml:id="N190EC" xml:space="preserve">qḋ
                    <lb/>
                  eſt oppoſitum conſequentis. </s>
                  <s xml:id="N190F1" xml:space="preserve">Antecedens probatur /
                    <lb/>
                  quia ſi a. potentia tranſeundo c. medium valet re-
                    <lb/>
                  mittere motum ſuum vſ ad non gradum in pūcto
                    <lb/>
                  terminatiuo etc. per continuam ſue poñe remiſſio-
                    <lb/>
                  nem: maxime remitteret vniformiter continuo mo-
                    <lb/>
                  tum ſuum vſ ad non gradum in puncto termina-
                    <lb/>
                  tiuo etc. caſu quo b. poña inuariata inciperet moue­
                    <lb/>
                  ri a puncto initiatiuo ſecunde partis ꝓportionalis
                    <lb/>
                  c. medii diuiſi in partes ꝓportionales ꝓportione
                    <lb/>
                  ſexquialtera verſus extremum intenſius eiuſdem c.
                    <lb/>
                  medii: et a. potentia a puncto initiatiuo c. medii ver­
                    <lb/>
                  ſus extremum intenſius eiuſdem: taliter  cõtinuo
                    <lb/>
                  per ſui variationem in ſexquialtero velocius moue­
                    <lb/>
                  retur a. quam b. ſed hoc non: igitur </s>
                  <s xml:id="N1910E" xml:space="preserve">Maior ptꝫ / q2
                    <lb/>
                  tunc tam a. quam b. eque primum deuenirent ad pū­
                    <lb/>
                  ctum terminatiuum c. medii in quo vtra remitte-
                    <lb/>
                  ret motū ſuum ad non gradum: cū a. per caſum in </s>
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