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="N1BD9F" level="4" n="15" type="chapter" type-free="capitulum">
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                  cto per eandem lineam in eodem inſtanti: ergo con­
                    <lb/>
                  tinuo ſunt ſimul / quod fuit probandum </s>
                  <s xml:id="N1BE49" xml:space="preserve">Iam probo
                    <lb/>
                  ſecundam partem maioris / quia potentia que mo­
                    <lb/>
                  uetur cum reſiſtentia difformi non poteſt in caſu eē
                    <lb/>
                  citra punctū medium in medietate remiſſiori: nec vl­
                    <lb/>
                  tra mediū ī medietate intenſiori: et mouetur conti-
                    <lb/>
                  nuo cum latitudine: igitur continuo eſt in medio ta­
                    <lb/>
                  lis latitudinis. </s>
                  <s xml:id="N1BE58" xml:space="preserve">Conſequentia patet, et minor ꝓba-
                    <lb/>
                  tur / quia ſi aliquando poſſet in caſu eſſe citra pun-
                    <lb/>
                  ctum medium ī medietate remiſſiori capio inſtans ī
                    <lb/>
                  quo eſt in illa, et arguitur ſic / vel continuo potentia
                    <lb/>
                  illa a principio motus eſt citra punctum medium
                    <lb/>
                  īmedietate remiſſiori vel continuo vltra punctū me­
                    <lb/>
                  dium immediate intenſiori: vel aliquando citra pū­
                    <lb/>
                  ctum medium: et aliquando vltra: nullum iſtorum ē
                    <lb/>
                  dicendum: igitur: </s>
                  <s xml:id="N1BE6B" xml:space="preserve">Non primum quia tunc ſequere-
                    <lb/>
                  tur /  a principio motus talis poña mouetur conti­
                    <lb/>
                  nuo a proportione quadrupla cum tota illa medie­
                    <lb/>
                  tas ſit vniformis vt .2. et poña vt .8. et continuo po­
                    <lb/>
                  tentia eſt citra punctum medium per te: igitur (cum
                    <lb/>
                  poña et punctus medius ſuum motum inchoant ab
                    <lb/>
                  eodem puncto in eodem inſtanti) / ſequitur /  maior
                    <lb/>
                  velocitas prouenit a proportione dupla ꝙ̄ a qua-
                    <lb/>
                  drupla quod eſt tantum vel maius inconueniens ̄
                    <lb/>
                  illud quod inferre intendimus: </s>
                  <s xml:id="N1BE80" xml:space="preserve">Nec dicendum ē ſe-
                    <lb/>
                  cundum / quia tunc ſequeretur /  a principio motus
                    <lb/>
                  talis potentia cõtinuo mouetur a proportione ſex-
                    <lb/>
                  quitertia cum tota illa medietas ſit vniformis vt 6
                    <lb/>
                  et poña vt .8. et continuo poña eſt vltra punctū me-
                    <lb/>
                  dium per te: igitur (cuꝫ poña et punctus mediꝰ ſuum
                    <lb/>
                  motum inchoant ab eodem puncto in eodem inſtã-
                    <lb/>
                  ti et per eandeꝫ lineam) ſequitur /  maior velocitas
                    <lb/>
                  prouenit a proportione ſexquitertia ꝙ̄ a dupla qḋ
                    <lb/>
                  eque magnum inconueniens eſt ſicut illud quod in-
                    <lb/>
                  ferre intendimus: </s>
                  <s xml:id="N1BE97" xml:space="preserve">Sed  non ſit dicendum tertium
                    <lb/>
                  probatur / quia ſi aliquando eſt citra punctum medi­
                    <lb/>
                  um, et aliquando vltra capio inſtans in quo ē citra
                    <lb/>
                  punctum medium: et arguitur ſic / vel a principio mo­
                    <lb/>
                  tus ſemper fuit citra punctum medium in medieta­
                    <lb/>
                  te remiſſiori: vel aliquando vltra punctum medium
                    <lb/>
                  in medietate intenſiori: et deinde in medietate remiſ­
                    <lb/>
                  ſiori: </s>
                  <s xml:id="N1BEA8" xml:space="preserve">Non primum quia tunc ſequeretur /  cõtinuo
                    <lb/>
                  moueretur per totum illud tempus a proportione
                    <lb/>
                  quadrupla, et tamen moueretur tardius per te quã
                    <lb/>
                  punctus medius qui mouetur a ꝓportione dupla:
                    <lb/>
                  ſed hoc eſt impoſſibile, igitur illud ex quo ſequitur:
                    <lb/>
                  </s>
                  <s xml:id="N1BEB4" xml:space="preserve">Nec dicendum eſt ſecundum / quia ſi tranſit per pun­
                    <lb/>
                  cta intenſioris medietatis ad puncta medietatis re­
                    <lb/>
                  miſſioris / neceſſe eſt /  tranſeat per punctum mediū /
                    <lb/>
                  vt conſtat: et ſi venerit ad punctum medium nū̄ ab
                    <lb/>
                  eo diſcedet: igit̄̄ illa poña nū̄ eſt vltra pūctū medi­
                    <lb/>
                  um in medietate intenſiori et deinde in medietate re­
                    <lb/>
                  miſſiori. </s>
                  <s xml:id="N1BEC3" xml:space="preserve">Conſequentia patet cum maiore / et proba-
                    <lb/>
                  tur minor / quia ſi illa poña venerit ad punctū medi­
                    <lb/>
                  um: nullus punctus medietatis remiſſioris vn̄ po­
                    <lb/>
                  tentiam precedet / quia cum quolibet tali poña ſuffi­
                    <lb/>
                  cit mouere velocius quam ipſe mouetur, nec ip̄a po­
                    <lb/>
                  ctentia aliquem punctum intenſioris medietatis p̄-
                    <lb/>
                  cedet vn̄ (cuꝫ quodlibet tale velocius mouatur ̄
                    <lb/>
                  potentia ſufficit mouere cum illo) / igitur ſi talis po­
                    <lb/>
                  tentia venerit ad punctum medium nū̄ ab eo diſce­
                    <lb/>
                  det / quod fuit probandum.</s>
                </p>
                <p xml:id="N1BED8">
                  <s xml:id="N1BED9" xml:space="preserve">Reſpondeo ad argumentum negan-
                    <lb/>
                  do antecedens: et ad probationem nego ſequelam:
                    <lb/>
                  et ad probationem admiſſo caſu concedo maiorem /
                    <lb/>
                  et nego minorem, et ad probationem minoris con-
                    <lb/>
                  cedo /  nullus eſt ibi punctus ad quem adequate ta­
                    <lb/>
                  lis poña habet proportionem duplam, et cum infer­
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                  tur / ergo non poteſt continuo moueri a proportiõe
                    <lb/>
                  dupla negatur conſequentia / et ratio eſt / quoniã quã­
                    <lb/>
                  uis ad nullum punctum habeat ꝓportionem duplã
                    <lb/>
                  adequate habet tamē ad duo ſimul videlicet ad ex-
                    <lb/>
                  tremum prime medietatis et ad initium ſecunde.</s>
                </p>
                <p xml:id="N1BEF1">
                  <s xml:id="N1BEF2" xml:space="preserve">Sed contra / quia extremum prime
                    <lb/>
                  medietatis eſt vt .2. et principium ſecunde vt: 6. </s>
                  <s xml:id="N1BEF7" xml:space="preserve">Mo­
                    <lb/>
                  do duo et ſex ſunt octo, et poña eſt vt octo. </s>
                  <s xml:id="N1BEFC" xml:space="preserve">ergo ad
                    <lb/>
                  illa habet talis poña proportionem equalitatis et
                    <lb/>
                  non duplam: et per conſequens ſolutio nulla.</s>
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                <p xml:id="N1BF03">
                  <s xml:id="N1BF04" xml:space="preserve">Reſpondeo /  difficile eſt mihi ſoluere
                    <lb/>
                  argumentum et in eo diu cogitaui. </s>
                  <s xml:id="N1BF09" xml:space="preserve">Dico tamen ad
                    <lb/>
                  replicam negando conſequentiam. </s>
                  <s xml:id="N1BF0E" xml:space="preserve">Et ratio ē / quia
                    <lb/>
                  illa puncta vt .2. et vt .6. non faciunt reſiſtentiam vt
                    <lb/>
                  8. </s>
                  <s xml:id="N1BF15" xml:space="preserve">Imo dico /  illa duo puncta principium ſecunde
                    <lb/>
                  medietatis et finis prime ita ſe habent  in reſiſten­
                    <lb/>
                  do equiualent puncto reſiſtentie reſiſtentis vt .4.</s>
                </p>
                <note position="right" xml:id="N1BF1C" xml:space="preserve">regula</note>
                <p xml:id="N1BF20">
                  <s xml:id="N1BF21" xml:space="preserve">Unde pono talem regulam.</s>
                </p>
                <p xml:id="N1BF24">
                  <s xml:id="N1BF25" xml:space="preserve">Ubicun aliqua potentia mouetur
                    <lb/>
                  cum aliqua reſiſtentia difformi: et eſt in parte illius
                    <lb/>
                  reſiſtentie que tardius mouetur quam poña ſufficit
                    <lb/>
                  moueri cuꝫ illa adequate: et pars immediate ſeq̄ns
                    <lb/>
                  velocius mouetur quã potentia ſufficit mouere cum
                    <lb/>
                  illi vel eque velociter: tunc talis reſiſtentia reſiſtit
                    <lb/>
                  ille poñe tantum adequate quantum reſiſteret vna
                    <lb/>
                  reſiſtentia ad quam haberet illa poña adequa-
                    <lb/>
                  te talem proportionem a quali mouetur illa reſiſtē­
                    <lb/>
                  ſtentia cui potentia continuo eſt proxima. </s>
                  <s xml:id="N1BF3A" xml:space="preserve">Et ideo /
                    <lb/>
                  tunc talis reſiſtentia equiualet alteri ad quam po-
                    <lb/>
                  tentia talem proportionem habet. </s>
                  <s xml:id="N1BF41" xml:space="preserve">Hac regula pre
                    <lb/>
                  ſuppoſita.</s>
                </p>
                <p xml:id="N1BF46">
                  <s xml:id="N1BF47" xml:space="preserve">Reſpondeo ad argumentum diſtīguē­
                    <lb/>
                  do minorem: aut  talis poña non poteſt in caſu cū
                    <lb/>
                  illis reſiſtentiis moueri cum eadē proportione quã
                    <lb/>
                  vtra illarum habeat formaliter ad aliquam illa­
                    <lb/>
                  rum reſiſtētiarum: et ſic conceditur: aut quã habeat
                    <lb/>
                  equiualenter: et ſic negatur.</s>
                </p>
                <p xml:id="N1BF54">
                  <s xml:id="N1BF55" xml:space="preserve">Sed cõtra q2 ſi hec ſolutio eſſet bona
                    <lb/>
                  ſequeretur /  eadem potentia nõ variata mouetur
                    <lb/>
                  eque velociter adequate cū reſiſtentia maiori ſicut
                    <lb/>
                  cū minori: ſed hoc videtur impoſſibile: igitur illud
                    <lb/>
                  ex quo ſequitur. </s>
                  <s xml:id="N1BF60" xml:space="preserve">Sequela ꝓbatur, et volo /  in caſu
                    <lb/>
                  argument</gap> tota ſecunda medietas illius reſiſtentie
                    <lb/>
                  perdat per totum vniformiter vnū gradum ita 
                    <lb/>
                  maneat vniformis vt .5. moueatur tamen eadē ve-
                    <lb/>
                  locitate qua antea mouebatur. </s>
                  <s xml:id="N1BF6B" xml:space="preserve">Quo poſito iã po-
                    <lb/>
                  tentia vt .8. cõtinuo erit in puncto medio illius reſi­
                    <lb/>
                  ſtentie qui mouetur eque velociter ſicut antea: ergo
                    <lb/>
                  talis potentia mouetur eque velociter adequate ſi-
                    <lb/>
                  cut antea et reſiſtentia ſua eſt minor quã antea: igit̄̄
                    <lb/>
                  aſſumptum verum.</s>
                </p>
                <p xml:id="N1BF78">
                  <s xml:id="N1BF79" xml:space="preserve">Reſpondeo concedendo / quod īfertur
                    <lb/>
                  dūmodo talis potentia nõ moueatur a proportiõe
                    <lb/>
                  quam formaliter habet ad talem reſiſtentiam, ſed
                    <lb/>
                  a proportione quam habet ad illam equiualenter
                    <lb/>
                    <note position="right" xlink:href="note-0123-01a" xlink:label="note-0123-01" xml:id="N1BFF8" xml:space="preserve">1. correl.</note>
                  </s>
                  <s xml:id="N1BF89" xml:space="preserve">¶ Ex quo ſequitur primo /  etiam ſi ſecunda me-
                    <lb/>
                  dietas in infinitum intederetur: et prima in infini-
                    <lb/>
                  tum remitteretur potentia tamen ſemper vniformi­
                    <lb/>
                  ter mouetur. </s>
                  <s xml:id="N1BF92" xml:space="preserve">Quod nihilomiuꝰ mirabile apparet.
                    <lb/>
                    <note position="right" xlink:href="note-0123-02a" xlink:label="note-0123-02" xml:id="N1BFFE" xml:space="preserve">.2correl.</note>
                  </s>
                  <s xml:id="N1BF9C" xml:space="preserve">¶ Sequitur ſecundo /  vbicuuq aliqua reſiſtentia
                    <lb/>
                  difformiter difformis cuius vtra medietas eſt et
                    <lb/>
                  manet vniformis incipit progredi a non quanto in
                    <lb/>
                  medio non reſiſtente: quolibet puncto eius intrinſe­
                    <lb/>
                  co continuo vniformiter mouente: omnis poña que
                    <lb/>
                  ſimul incipit moueri cum illa cõtinuo mouetur vni­
                    <lb/>
                  formiter. </s>
                  <s xml:id="N1BFAB" xml:space="preserve">Probatur / quia cū ea medietate cum qua </s>
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