Alvarus, Thomas, Liber de triplici motu, 1509

Table of Notes

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                  <s xml:id="N1A116" xml:space="preserve">
                    <pb chead="De motu penes cauſã in medio vniformiter difformi inuariato." file="0104" n="104"/>
                  quam in maiori proportione ꝙ̄ ſexquialtera in mi­
                    <lb/>
                  nori tamen velocius quam dupla. </s>
                  <s xml:id="N1A120" xml:space="preserve">Probatur et ſit
                    <lb/>
                  a. potentia / que continuo c. medium tranſeundo mo­
                    <lb/>
                  uetur a ꝓportione dupla per ſue potentie a nõ gra­
                    <lb/>
                  du vniforme et continuū crementum: ſit b. potētia
                    <lb/>
                  que idem c. medium tranſeundo creſcit a non gra-
                    <lb/>
                  du continuo in triplo velocius quam a. poña. </s>
                  <s xml:id="N1A12D" xml:space="preserve">tunc
                    <lb/>
                  dico /  b. poña mouetur continuo velocius ꝙ̄ a. po-
                    <lb/>
                  tentia in maiori ꝓportione ꝙ̄ ſexquialtera: et in mi­
                    <lb/>
                  nori quam dupla. </s>
                  <s xml:id="N1A136" xml:space="preserve">Quod ſic ꝓbatur / quia b. potētia
                    <lb/>
                  nõ mouetur in ſexquialtera ꝓportione velociꝰ ade-
                    <lb/>
                  quate: nec in minori. </s>
                  <s xml:id="N1A13D" xml:space="preserve">Similiter b. poña nõ mouetur
                    <lb/>
                  in dupla ꝓportione velocius: nec in maiori: igitur
                    <lb/>
                  b. potentia mouetur in maiori ꝓportione velocius
                    <lb/>
                  quam ſexquialtera: et in minori ꝙ̄ dupla: quod fuit
                    <lb/>
                  ꝓbandum. </s>
                  <s xml:id="N1A148" xml:space="preserve">Maior ꝓbatur / quia ſi b. mouetur in ſex­
                    <lb/>
                  quialtera ꝓportione velocius ꝙ̄ ipſa poña a. ade-
                    <lb/>
                  quate: ſequitur /  cõtinuo reſiſtentia ipſius b. eſt in
                    <lb/>
                  ſexquialtero maior reſiſtentia ipſius a. (quia c. me­
                    <lb/>
                  dium eſt vniformiter difforme ad non graduꝫ ter-
                    <lb/>
                  minatum) et vltra reſiſtentia ipſius b. eſt in ſexqui-
                    <lb/>
                  altero maior reſiſtentia ipſius a. et ipſius b. ad reſi­
                    <lb/>
                  ſtentiam ipſius a. eſt ꝓportio ſextupla (cum compo­
                    <lb/>
                  natur ex tripla que eſt ipſius b. ad potentiam a. et
                    <lb/>
                  ex dupla que eſt ipſius a. ad ſuam reſiſtentiam) / igi-
                    <lb/>
                  tur ipſius b. ad reſiſtentiam eiuſdem b. eſt propor-
                    <lb/>
                  tio quadrupla quia ſexquialterum ad ſubſextuplū
                    <lb/>
                  ad aliquod eſt ſubquadruplum ad illud et per cõſe-
                    <lb/>
                  quens b. mouetur a ꝓportione quadrupla: et ex hoc
                    <lb/>
                  in duplo velocius ꝙ̄ a. continuo mouens a ꝓportio­
                    <lb/>
                  ne dupla: et non in ſexquialtero velocius adequate /
                    <lb/>
                  quod fuit ꝓbandum. </s>
                  <s xml:id="N1A16B" xml:space="preserve">Sed  b. non moueatur in
                    <lb/>
                  minori ꝓportione velocius quam ſexquialtera pro­
                    <lb/>
                  batur: quia tunc reſiſtentia ipſius b. ad reſiſtentiaꝫ
                    <lb/>
                  ipſius a. eſſet minor proportio quam ſexquialtera:
                    <lb/>
                  vt patet ex correlario ſuppoſitionis huius et ipſiꝰ
                    <lb/>
                  b. ad reſiſtentiam ipſius a. eſt ꝓportio ſextupla (vt
                    <lb/>
                  ſupra argutum eſt) / ergo ipſius b. ad reſiſtentiaꝫ ip­
                    <lb/>
                  ſius b. eſſet maior ꝓporio quam quadrupla. </s>
                  <s xml:id="N1A17C" xml:space="preserve">Pa-
                    <lb/>
                  tet conſequentia per hoc /  quando aliquis nume-
                    <lb/>
                  rus eſt ſextuplus ad alterum talis numerus eſt ma­
                    <lb/>
                  ior quam quadruplus ad omnem numerum qui eſt
                    <lb/>
                  minor ſexquialtero ad ſuum ſubſextuplum (vt pa-
                    <lb/>
                  tet intelligenti quartum caput ſecunde partis) </s>
                  <s xml:id="N1A189" xml:space="preserve">Iaꝫ
                    <lb/>
                  ꝓbatur minor / quia ſi b. mouetur in duplo velocius
                    <lb/>
                  ̄ a. / ſequitur cum caſu /  reſiſtentia ipſius b. conti-
                    <lb/>
                  nuo eſt dupla ad reſiſtentiam ipſius a. / vt patet ex
                    <lb/>
                  correlario ſuppoſitionis (cum c. mediuꝫ terminetur
                    <lb/>
                  ad non gradum) et vltra reſiſtentia ipſius b. conti-
                    <lb/>
                  nuo eſt dupla ad reſiſtentiaꝫ ipſius a. et ipſius b. ad
                    <lb/>
                  reſiſtentiam ipſius a. eſt ꝓportio ſextupla (vt ꝓba-
                    <lb/>
                  tum eſt) / ergo ipſius b. ad reſiſtentiam eiuſdem b. eſt
                    <lb/>
                  ꝓportio tripla. </s>
                  <s xml:id="N1A19E" xml:space="preserve">Patet hec conſequentia per hoc / 
                    <lb/>
                  omne duplum ad ſubſextuplum alicuius numeri ē
                    <lb/>
                  ſubtriplum ad talem numerum (vt patet intelligen­
                    <lb/>
                  ti quartam concluſionem quarti capitis ſecunde ꝑ­
                    <lb/>
                  tis cum ſuis correlariis) / et per conſequens ſequitur /
                    <lb/>
                   b. mouetur a ꝓportione tripla que non eſt dupla
                    <lb/>
                  duple (vt patet intelligenti ſextum caput ſecunde ꝑ­
                    <lb/>
                  tis) / et ex hoc b. non mouetur in duplo velocius a. po­
                    <lb/>
                  tentia mota a ꝓportione dupla: quod fuit ꝓbandū
                    <lb/>
                  </s>
                  <s xml:id="N1A1B2" xml:space="preserve">Sed  non moueatur a maiori dupla: patet / q2 tūc
                    <lb/>
                  reſiſtentia ipſius b. eſſet maior quam dupla ad reſi­
                    <lb/>
                  ſtentiam ipſius a. et ſic ipſius b. ad reſiſtentiam ipſi­
                    <lb/>
                  us b. eſſet minor ꝓportio quam tripla (vt facile de­
                    <lb/>
                  ducitur ex dictis) / et per conſeqnens non mouetur a
                    <lb/>
                  maiori ꝓportione quam dupla cuꝫ nulla minor tri­
                    <lb/>
                  pla: nec ipſa tripla ſit dupla ad duplam. </s>
                  <s xml:id="N1A1C1" xml:space="preserve">Et ſic pa-
                    <lb/>
                  tet correlarium.
                    <note position="left" xlink:href="note-0104-01a" xlink:label="note-0104-01" xml:id="N1A21F" xml:space="preserve">3. correl.</note>
                  </s>
                  <s xml:id="N1A1CB" xml:space="preserve">¶ Sequitur tertio /  duabus potē­
                    <cb chead="De motu penes cauſã in medio vniformiter difformi inuariato."/>
                  tiis aliquod medium vniformiter difforme ad non
                    <lb/>
                  gradum terminatum tranſeundo. </s>
                  <s xml:id="N1A1D3" xml:space="preserve">vniformiter cõ-
                    <lb/>
                  tinuo mouentibus per earuꝫ a non gradu poñe vni­
                    <lb/>
                  forme et continuum crementum: vna altera in du­
                    <lb/>
                  plo velocius continuo creſcente: et poña que tardiꝰ
                    <lb/>
                  creſcit continuo mouente a ꝓportione ſexquialte-
                    <lb/>
                  ra: poña que velocius continuo creſcit velocius cõ­
                    <lb/>
                  tinuo mouetur: in minori tamen ꝓportione quã du­
                    <lb/>
                  pla: et maiori quam ſexquialtera. </s>
                  <s xml:id="N1A1E4" xml:space="preserve">Probatur / et ſit
                    <lb/>
                  b. poña que in duplo velocius continuo creſcat po­
                    <lb/>
                  tentia a. continuo mouēte a ꝓportione ſexquialte­
                    <lb/>
                  ra c. medium terminatum ad non gradum pertran­
                    <lb/>
                  ſeundo </s>
                  <s xml:id="N1A1EF" xml:space="preserve">Quo poſito arguitur ſic / b. poña nõ moue-
                    <lb/>
                  tur in dupla ꝓportione velocius nec in maiori (vt
                    <lb/>
                  patet ex concluſione) / nec b. poña mouetur in ſexqui­
                    <lb/>
                  altera ꝓportione velocius adequate, nec in minori /
                    <lb/>
                  igitur b. potentia mouetur continuo in minori pro­
                    <lb/>
                  portione quam dupla velocius, et in maiori quam
                    <lb/>
                  ſexquialtera: quod fuit ꝓbandum. </s>
                  <s xml:id="N1A1FE" xml:space="preserve">Conſequentia
                    <lb/>
                  patet cum maiore et arguitur minor / quia ſi b. po-
                    <lb/>
                  tentia mouetur in ſexquialtera ꝓportione velociꝰ
                    <lb/>
                  quam a. / ſequitur /  reſiſtentia ipſius b. eſt ſexquial­
                    <lb/>
                  tera ad reſiſtentiam ipſius a. / vt patet ex correlario
                    <lb/>
                  ſuppoſitiõis (quia medium eſt terminatum ad non
                    <lb/>
                  gradum) / et vltra reſiſtentia ipſius b. eſt ſexquialte-
                    <lb/>
                  ra ad reſiſtentiam ipſius a. et ipſius b. ad reſiſten-
                    <lb/>
                  tiaꝫ ipſius a. eſt proportio tripla: ergo ipſius b. ad
                    <lb/>
                  reſiſtentiam ipſius b. eſt ꝓportio dupla / et per con-
                    <lb/>
                  ſequens b. mouetur a proportione dupla.</s>
                </p>
                <p xml:id="N1A225">
                  <s xml:id="N1A226" xml:space="preserve">Patet tamen cõſequentia per hoc /  omne tripluꝫ
                    <lb/>
                  ad aliquem numerum eſt duplum ad numerum ſex­
                    <lb/>
                  quialterum ad illum numerum ſubtriplum (vt con­
                    <lb/>
                  ſtat intelligenti quartum caput ſepius allegatum
                    <lb/>
                  et vltra b. mouetur a ꝓportione dupla, et dupla nõ
                    <lb/>
                  eſt ſexquialtera ad duplam: </s>
                  <s xml:id="N1A233" xml:space="preserve">Sed maior quaꝫ ſexqui­
                    <lb/>
                  altera: vt patet ex ſexto capite ſecunde partis: igi-
                    <lb/>
                  tur b. mouetur in maiori ꝓportione velocius quaꝫ
                    <lb/>
                  ſexquialtera / quod fuit ꝓbandum. </s>
                  <s xml:id="N1A23C" xml:space="preserve">Sed  b. nõ mo­
                    <lb/>
                  ueatur in minori ꝓportione quam ſexquialtera ve­
                    <lb/>
                  locius: ꝓbatur / quia tunc reſiſtentia ipſius b. eſt mi­
                    <lb/>
                  nor quam ſexquialtera ad reſiſtentiam ipſius a. / et
                    <lb/>
                  per conſequens ipſius b. ad reſiſtentiam ipſius b.
                    <lb/>
                  eſt maior ꝓportio quam dupla: vt patet per hanc
                    <lb/>
                  maximam. </s>
                  <s xml:id="N1A24B" xml:space="preserve">Omnis numerus triplus ad alterum eſt
                    <lb/>
                  maior quam duplus ad omnem numerum minorē
                    <lb/>
                  numero ſexquialtero ad illum ſubtriplum (vt pa-
                    <lb/>
                  tet intuenti) / et ſi b. mouetur a maiori ꝓportiõe quã
                    <lb/>
                  dupla: conſequens eſt /  b. mouetur in maiori pro-
                    <lb/>
                  portione quam ſexquialtera velocius ipſa a. poña
                    <lb/>
                  mouente continuo a ꝓportione ſexquialtera (ſiqui­
                    <lb/>
                  dem dupla, et omnis maior ea, maior eſt quam ſex-
                    <lb/>
                  quialtera ad ſexquialteram) </s>
                  <s xml:id="N1A25E" xml:space="preserve">Componitur em̄ du-
                    <lb/>
                  pla ex ſexquialtera, et ſexquitertia: et ſexquitertia
                    <lb/>
                  maior eſt quam medietas ſexquialtere: vt patet ex
                    <lb/>
                  nono correlario tertie concluſionis quarti capitis
                    <lb/>
                  ſecunde partis. </s>
                  <s xml:id="N1A269" xml:space="preserve">¶ Infinita ſimilia correlaria intel­
                    <lb/>
                  ligens primam et ſecundam partem huius operis
                    <lb/>
                  ex his / que dicta ſunt / et ſtatim dicent̄̄ propria indu­
                    <lb/>
                  ſtria poterit inferre.
                    <note position="right" xlink:href="note-0104-02a" xlink:label="note-0104-02" xml:id="N1A284" xml:space="preserve">Nota q̄-
                      <lb/>
                    ſtionem.</note>
                  </s>
                  <s xml:id="N1A277" xml:space="preserve">¶ Et ſi queras / ex quo b. moue-
                    <lb/>
                  tur in minori ꝓportione quam dupla velocius a. et
                    <lb/>
                  in maiori quaꝫ ſexquialtera in qua ꝓportione ade­
                    <lb/>
                  quate b. mouetur velocius quam a.</s>
                </p>
                <p xml:id="N1A28C">
                  <s xml:id="N1A28D" xml:space="preserve">Reſpõdeo  dico primo /  in nulla ſu-
                    <lb/>
                  perparticulari (vt patet) / q2 nulla ſuperparticula-
                    <lb/>
                  ris eſt maior proportione ſexquialtera, nec in ali-
                    <lb/>
                  qua multiplici ſuperparticulari, nec multiplici ſu­
                    <lb/>
                  prapartiente: quia nulla talis eſt minor dupla (vt
                    <lb/>
                  conſtat intelligenti ſextum caput ſecunde partis)
                    <lb/>
                  </s>
                  <s xml:id="N1A29B" xml:space="preserve">Reſtat igitur / vt moueatur in aliqua ꝓportione ſu- </s>
                </p>
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