Alvarus, Thomas, Liber de triplici motu, 1509

Table of Notes

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                <p xml:id="N1A559">
                  <s xml:id="N1A5B1" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0107" n="107"/>
                  tio eſt maior f. proportione in minori proportione
                    <lb/>
                  quam ſit f. ex hypotheſi: igitur b. mouetur in mino-
                    <lb/>
                  ri proportione velocius a. quam ſit f. / quod fuit pro­
                    <lb/>
                  bandum. </s>
                  <s xml:id="N1A5C7" xml:space="preserve">Sed iam ꝓbatur minor videlicet /  b. nõ
                    <lb/>
                  mouetur velocius in maiori proportione quam ſit
                    <lb/>
                  f. / quod ſic ꝓbatur / quia ſi b. moueretur velocius a. ī
                    <lb/>
                  maiori proportione quam ſit f. ꝓportio a qua mo-
                    <lb/>
                  uetur a. / ſequitur /  continuo reſiſtentie ipſius b. ad
                    <lb/>
                  reſiſtentiam ipſius a. eſt maior proportio quam f.
                    <lb/>
                  et vltra reſiſtentie ipſius b. ad reſiſtentiaꝫ ipſius a.
                    <lb/>
                  eſt maior proportio quam f. et ipſius a. ad eandem
                    <lb/>
                  reſiſtentiaꝫ ipſius a. eſt f. proportio adequate ex hy­
                    <lb/>
                  potheſi. </s>
                  <s xml:id="N1A5DC" xml:space="preserve">igitur continuo reſiſtentia ipſius b. eſt ma­
                    <lb/>
                  ior a. poña. </s>
                  <s xml:id="N1A5E1" xml:space="preserve">Patet conſequentia / quia reſiſtentia ip­
                    <lb/>
                  ſius b. habet maiorem proportionem ad vnū terti­
                    <lb/>
                  um puta ad reſiſtentiam ipſius a. </s>
                  <s xml:id="N1A5E8" xml:space="preserve">Et vltra ex con-
                    <lb/>
                  ſequenti continuo reſiſtentia ipſius b. eſt maior a.
                    <lb/>
                  potentia. </s>
                  <s xml:id="N1A5EF" xml:space="preserve">et ipſius b. ad a. eſt proportio h. / igitur ip­
                    <lb/>
                  ſius b. ad reſiſtentiam eiuſdem b. eſt minor ꝓportio
                    <lb/>
                  quam h. et ab illa mouetur continuo b. / igitur b. con­
                    <lb/>
                  tinuo mouetur a minori proportione ꝙ̄ h. et h. pro-
                    <lb/>
                  portio eſt maior f. proportione a qua continuo mo­
                    <lb/>
                  uetur a. (in minori tamen ꝓportione quaꝫ ſit f.) / igi­
                    <lb/>
                  tur proportio a qua moueatur b. eſt maior quam f.
                    <lb/>
                  a qua mouetur a. in minori proportione quam f. / et
                    <lb/>
                  per conſequens b. mouetur continuo velocius a. in
                    <lb/>
                  minori ꝓportione quam ſit f. / quod fuit probandū:
                    <lb/>
                  </s>
                  <s xml:id="N1A605" xml:space="preserve">Patet tamen conſequentia / quia cum aliquid exce­
                    <lb/>
                  dit vnum tertium in aliqua proportione: </s>
                  <s xml:id="N1A60A" xml:space="preserve">omne mi­
                    <lb/>
                  nus maius tamen illo tertio excedit idem tertium ī
                    <lb/>
                  minori proportione. </s>
                  <s xml:id="N1A611" xml:space="preserve">ſed per te proportio a qua mo­
                    <lb/>
                  uetur b. potentia eſt maior quam ꝓportio f. et mi-
                    <lb/>
                  nor quam h. proportio: igitur. </s>
                  <s xml:id="N1A618" xml:space="preserve">Et ſic patet antece-
                    <lb/>
                  dens cum concluſione. </s>
                  <s xml:id="N1A61D" xml:space="preserve">¶ Has tres concluſiones pul­
                    <lb/>
                  chras diligenter nota </s>
                  <s xml:id="N1A622" xml:space="preserve">Poſſunt enim ex eis inferri
                    <lb/>
                  infinite concluſiones cum multis quas ponit calcu­
                    <lb/>
                  lator in ſecundo capite de medio non reſiſtente.</s>
                </p>
                <note position="left" xml:id="N1A629" xml:space="preserve">1. correl.</note>
                <p xml:id="N1A62D">
                  <s xml:id="N1A62E" xml:space="preserve">¶ Ex quo ſequitur primo /  ſi a. potentia minor mo­
                    <lb/>
                  ueatur ab aliqua proportiõe minore multiplici ra­
                    <lb/>
                  tionali in caſu concluſionis puta ab aliqua propor­
                    <lb/>
                  tione ſuperparticulari aut ſuprapartiente. </s>
                  <s xml:id="N1A637" xml:space="preserve">et b. po­
                    <lb/>
                  tentia maior creſcat velocius a. potentia minore in
                    <lb/>
                  alqua proportione multiplici: tunc b. potentia ma­
                    <lb/>
                  ior non mouebitur velocius b. poña minore in pro-
                    <lb/>
                  portione a qua mouetur a. potentia minor. </s>
                  <s xml:id="N1A642" xml:space="preserve">ſed in
                    <lb/>
                  maiore vel minore ſecundum tenorem tertie vel q̈r-
                    <lb/>
                  te concluſionis. </s>
                  <s xml:id="N1A649" xml:space="preserve">Patet hoc correlarium / quia vt pa­
                    <lb/>
                  tet ex ſuperioribus: nun̄ maior potentia mouetur
                    <lb/>
                  velocius minore mota a ꝓportione rationali in ea
                    <lb/>
                  ꝓportione a qua mouetur minor: niſi quando pro-
                    <lb/>
                  portio in qua maior velocius creſcit ſe habet ad ꝓ­
                    <lb/>
                  portionem a qua mouetur minor in ꝓportione ra-
                    <lb/>
                  tionali: ita  qualis eſt proportio a qua mouetur
                    <lb/>
                  minor talis debet eſſe proportio inter proportiõeꝫ
                    <lb/>
                  in qua maior velocius creſcit, et proportionē a qua
                    <lb/>
                  minor mouetur / vt patet: ſed nulla ꝓportio multi-
                    <lb/>
                  plex ſe habet ad proportionem minorem multipli-
                    <lb/>
                  ci rationalem in aliqua ꝓportione rationali: vt pa­
                    <lb/>
                  tet ex ſecunda et ſexta concluſionibus ſexti capitis
                    <lb/>
                  ſecunde partis / igitur correlarium verum.</s>
                </p>
                <note position="left" xml:id="N1A666" xml:space="preserve">2. correl.</note>
                <p xml:id="N1A66A">
                  <s xml:id="N1A66B" xml:space="preserve">¶ Sequitur ſecundo /  ſi a. potentia minor mouea­
                    <lb/>
                  tur ab aliqua ꝓportione multiplici: et b. potentia
                    <lb/>
                  maior creſcat velocius ipſa a. potentia in aliqua ꝓ­
                    <lb/>
                  portione multiplici ſuperparticulari: aut multipli­
                    <lb/>
                  ci ſuprapartiente. </s>
                  <s xml:id="N1A676" xml:space="preserve">tunc b. potentia maior nõ moue­
                    <lb/>
                  tur velocius a. minore in ꝓportione multiplici a q̈
                    <lb/>
                  mouetur a. potentia minor </s>
                  <s xml:id="N1A67D" xml:space="preserve">Probatur / quia ſi ſic iã
                    <lb/>
                  ꝓportio in qua creſcit b. maior potentia velocius
                    <lb/>
                  a. minore ſe haberet ad proportionem a qua moue­
                    <cb chead="Capitulum vndecimum"/>
                  tur a. potentia minor in eadem ꝓportione multipli­
                    <lb/>
                  ci a qua mouetur eadē a. poña minor / vt patet ex ſe­
                    <lb/>
                  cunda cõcluſione huius: ſed hoc eſt falſum / quia nul­
                    <lb/>
                  la multiplex eſt cõmenſurabilis ꝓportioni multipli­
                    <lb/>
                  ci ſuperparticulari, aut multiplici ſuprapartienti /
                    <lb/>
                  vt patet ex tertia cõcluſione ſecunde partis: igitur
                    <lb/>
                  illud ex quo ſequitur eſt falſum: et per conſequēs cor­
                    <lb/>
                  relarium verum.
                    <note position="right" xlink:href="note-0107-01a" xlink:label="note-0107-01" xml:id="N1A6F0" xml:space="preserve">3. correl.</note>
                  </s>
                  <s xml:id="N1A69A" xml:space="preserve">¶ Sequitur tertio /  ſi a. poña mi­
                    <lb/>
                  nor moueatur ab aliqua ꝓportione non multipli-
                    <lb/>
                  ci rationali: et b. poña maior creſcat velocius mino­
                    <lb/>
                  re in proportione aliqua multiplici: tunc b. poten-
                    <lb/>
                  tia maior nõ mouetur velocius a. poña minore in ꝓ­
                    <lb/>
                  portione a qua mouetur a. poña minor. </s>
                  <s xml:id="N1A6A7" xml:space="preserve">Patet cor­
                    <lb/>
                  relarium / quia alias ſequeretur /  proportio non
                    <lb/>
                  multiplex in qua b. poña maior velocius creſcit a.
                    <lb/>
                  poña minore ſe haberet ad ꝓportionem non multi­
                    <lb/>
                  plicem rationalem a qua mouetur a. poña minor ī
                    <lb/>
                  eadem proportione non multiplici rationali a qua
                    <lb/>
                  mouetur a. potentia minor / vt patet ex ſecunda con­
                    <lb/>
                  cluſione huius: ſed conſequens eſt falſum / vt patet
                    <lb/>
                  ex quarta concluſione ſexti capitis ſecunde partis:
                    <lb/>
                  igitur illud ex quo ſequitur: et per conſequens cor-
                    <lb/>
                  relatium verum.
                    <note position="right" xlink:href="note-0107-02a" xlink:label="note-0107-02" xml:id="N1A6F6" xml:space="preserve">4. correl.</note>
                  </s>
                  <s xml:id="N1A6C3" xml:space="preserve">¶ Sequitur quarto /  ſi a. potētia
                    <lb/>
                  minor moueatur ab aliqua proportione ſuperpar­
                    <lb/>
                  ticulari: et poña b. maior creſcat velocius a. poten-
                    <lb/>
                  tia minore in aliqua ꝓportione ſuperparticulari:
                    <lb/>
                  tunc b. potentia maior nõ mouetur velocius a. potē­
                    <lb/>
                  tia minore in ea ꝓportione ſuperparticulari a qua
                    <lb/>
                  mouetur a. poña minor. </s>
                  <s xml:id="N1A6D2" xml:space="preserve">Probatur / quia alias ſe-
                    <lb/>
                  queretur ex ſecunda concluſione cum aliis  ꝓpor-
                    <lb/>
                  tio ſuperparticularis in qua b. poña maior velociꝰ
                    <lb/>
                  creſcit minore ſe haberet ad ꝓportionem ſuperpar­
                    <lb/>
                  ticularem a qua mouetur a. poña minor in eadem
                    <lb/>
                  ꝓportione ſuperparticulari a qua mouetur eadem
                    <lb/>
                  a. poña minor: ſed hoc eſt falſum. </s>
                  <s xml:id="N1A6E1" xml:space="preserve">quia nulla ꝓpor-
                    <lb/>
                  tio ſuperparticularis eſt cõmenſurabilis alicui ſu­
                    <lb/>
                  perparticulari / vt patet ex quinta concluſione ſexti
                    <lb/>
                  capitis ſecunde partis: igitur illud ex quo ſequitur /
                    <lb/>
                  et per conſequens correlarium verum.</s>
                </p>
                <note position="right" xml:id="N1A6FC" xml:space="preserve">5. correl.</note>
                <p xml:id="N1A700">
                  <s xml:id="N1A701" xml:space="preserve">¶ Sequitur quinto /  nūquam poña maior poteſt
                    <lb/>
                  moueri velocius minore in ꝓportione multiplici a
                    <lb/>
                  qua mouetur minor. </s>
                  <s xml:id="N1A708" xml:space="preserve">niſi ipſa maior creſcat conti-
                    <lb/>
                  nuo velocius minore in alia ꝓportione multiplici.
                    <lb/>
                  </s>
                  <s xml:id="N1A70E" xml:space="preserve">Patet hoc correlarium / quia ſola multiplex eſt pro­
                    <lb/>
                  portioni multiplici cõmenſurabilis / vt patet ex ſex­
                    <lb/>
                  ta concluſione ſexti capitis ſecunde partis.</s>
                </p>
                <note position="right" xml:id="N1A715" xml:space="preserve">6. correl.</note>
                <p xml:id="N1A719">
                  <s xml:id="N1A71A" xml:space="preserve">¶ Sequitur ſexto /  ſi in caſu huius quarte conclu-
                    <lb/>
                  ſionis a. poña minor cõtinuo moueatur ab aliqua
                    <lb/>
                  proportione multiplici: et b. poña maior creſcat ve­
                    <lb/>
                  locius a potentia minore in aliqua ꝓportione mul­
                    <lb/>
                  tiplici ſuperparticulari vel multiplici ſuprapartiē­
                    <lb/>
                  te compoſita ex proportione multiplici a qua mo-
                    <lb/>
                  uetur minor: et aliqua ſuperparticulari, vel ſupra-
                    <lb/>
                  partiente (vt oportet): tunc illa b. potentia maior
                    <lb/>
                  mouetur velocius a. potentia minore in minori pro­
                    <lb/>
                  portione quam ſit proportio a qua mouetur a. po-
                    <lb/>
                  tentia minor: et etiam in minori ꝓportione quaꝫ ſit
                    <lb/>
                  ea in qua velocius creſcit a. poña minore. </s>
                  <s xml:id="N1A733" xml:space="preserve">Proba-
                    <lb/>
                  tur prima pars ex hac quarta concluſione / quia om­
                    <lb/>
                  nis ꝓportio multiplex ſuperparticularis, aut mul­
                    <lb/>
                  tiplex ſuprapartiens eſt minor quam multiplex ad
                    <lb/>
                  totum reſiduum eius dempta proportione ſupra-
                    <lb/>
                  partiente aut ſuperparticulari quam vltra illam
                    <lb/>
                  multiplicem continet / vt patet / quoniam ipſa nõ cõ-
                    <lb/>
                  tinet talem multiplicem niſi ſemel: ergo non exce-
                    <lb/>
                  dit illam in aliqua ꝓportione multiplici ſed in mi-
                    <lb/>
                  nori. </s>
                  <s xml:id="N1A748" xml:space="preserve">Et ſic ex concluſione ſequitur /  mouetur ī mi­
                    <lb/>
                  nori proportione velociꝰ ꝙ̄ ſit talis proportio mul­
                    <lb/>
                  tiplex a qua mouetur potentia minor. </s>
                  <s xml:id="N1A74F" xml:space="preserve">Sed ſecūda </s>
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