Alvarus, Thomas, Liber de triplici motu, 1509

Table of contents

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                    <pb chead="Primi tractatus" file="0087" n="87"/>
                  b. tranſeundo d. partem non eſt proportio l. nec ma­
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                  ior: ergo latitudinis motus deperdite ab ipſa b. po­
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                  tentia tranſeundo .ef. partem in tempore g. adequa­
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                  te ad latitudinem motus deperditam ab a. potētia
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                  ſtante inuariata vel remittente potentiam ſuã tran­
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                  ſeundo d. partem in g. tempore adequate non eſt ꝓ­
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                  portio l. nec maior: ſed conſequens eſt falſuꝫ: igitur
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                  illud ex quo ſequitur. </s>
                  <s xml:id="N1879B" xml:space="preserve">Patet conſequentia: q2 om-
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                  nes poñe inuariate ſiue equales ſiue inequales ideꝫ
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                  medium etc. tranſeundo equalem latitudinem mo-
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                  tus deperdunt: et ſi aliqua potentia tranſeundo ali­
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                  quod medium inuariatum remittendo motum ſuuꝫ
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                  etc. remittat potentiam ſuam: ipſa maiorem latitu­
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                  dinem motus deperdit quam ſi ſtaret idem mediuꝫ
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                  inuariatum tranſeundo etc. / vt conſtat ex quarto ar­
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                  gumento ſexti capitis ſepius allegato. </s>
                  <s xml:id="N187AE" xml:space="preserve">Sed falſi­
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                  tas conſequentis ꝓbatur / quia ſi latitudinis deper­
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                  dite ab ipſa potentia b. tranſeundo .ef. partem ī g.
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                  tempore ad velocitatem deperditam ab a. poña trã­
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                  ſeundo d. partem in eodem g. tempore non eſt pro-
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                  portio l. nec maior: et a prīcipio motus ipſius b. ad
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                  motum ipſius a. eſt proportio l. / ſequitur /  facta ta­
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                  li variatione latitudinis motus ipſius b. ad latitu­
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                  dinem motus ipſius a. non eſt ꝓportio l. nec maior /
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                  quod eſt contra hypotheſim. </s>
                  <s xml:id="N187C3" xml:space="preserve">Conſequentia tamen
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                  patet ex primo et ſecundo correlariis quinte conclu­
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                  ſionis ſecundi capitis ſecunde partis: </s>
                  <s xml:id="N187CA" xml:space="preserve">Sed antece-
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                  dens eodem modo ꝓbabis omnino quo probatum
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                  eſt in quarta concluſione huius. </s>
                  <s xml:id="N187D1" xml:space="preserve">Iam probat̄̄ ſecun­
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                  da pars minoris videlicet /  per totum tēpus quo
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                  a. poña b. poñam ſequetur: continuo a. poña remit­
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                  tet potentiam ſuam. </s>
                  <s xml:id="N187DA" xml:space="preserve">quia ſi per aliquam partem il­
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                  lius temporis ſtat inuariata, aut intendit potentiã
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                  ſignetur illa pars temporis, et ſit g. in quo a. tranſe­
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                  at d. partem adequate, et b. in eodem g. tempore .ef.
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                  partem adequate pertranſeat: et manifeſtum ē /  ip­
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                  ſius .ef. partis ad ipſam d. partem eſt ꝓportio l. / vt
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                  patet intuenti hypotheſim. </s>
                  <s xml:id="N187E9" xml:space="preserve">Quo poſito arguo ſic /
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                  latitudinis motus deperdite ab ipſa b. poña tran­
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                  ſeūdo .ef. partem adequate ad latitudinē motus de­
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                  perditam ab eadem b. poña tranſeundo d. partem
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                  adequate eſt maior ꝓportio ꝙ̄ l. / igitur latitudinis
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                  motus deperdite ab ipſa poña b. tranſeundo .ef. ꝑ-
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                  tem in g. tempore adequate ad latitudinem motus
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                  deperditam ab ipſa poña a. ſtante inuariata vel in­
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                  tendente poñam ſuam tranſeundo adequate d. par­
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                  tem in eodem g. tempore eſt maior ꝓportio ꝙ̄ l. / ſed
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                  conſequens eſt falſum / igitur illud ex quo ſequitur.
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                  </s>
                  <s xml:id="N18801" xml:space="preserve">Conſequentia cum falſitate conſequentis patet: et
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                  antecedens ꝓbatur videlicet /  latitudinis motus
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                  deperdite ab ipſa poña b. tranſeundo .ef. parteꝫ in
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                  g. tempore adequate ad latitudinem motus deper-
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                  ditam ab eadem poña b. tranſeundo d. partem ade­
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                  quate: eſt maior ꝓportio quam l. quia ipſius .ef. ꝑ-
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                  tis ad d. partem eſt ꝓportio l. et quamlibet partem
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                  exceſſus minorem d. parte ipſius .ef. partis b. poña
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                  tranſeundo continuo mouetur cum maiori reſiſten­
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                  tia quam tranſeundo quãlibet partem equalem ip­
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                  ſius d. partis: quoniaꝫ quelibet pars illius exceſſus
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                  plus diſtat a puncto initiatiuo c. medii quam que-
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                  libet pars ipſius d. partis diſtat ab eodem puncto
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                  (ſigno enim exceſſum verſus extremum intenſius) /
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                  igitur ex tertia ſuppoſitione huius. </s>
                  <s xml:id="N18820" xml:space="preserve">latitudinis de­
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                  perdite ab ipſa b. poña tranſeundo .ef. partem ī g.
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                  tempore adequate ad latitudinem motus deperdi­
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                  tam ab eadem b. poña tranſeundo d. partem ade­
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                  quate eſt maior ꝓportio quam l. / quod erat oſtendē­
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                  dum. </s>
                  <s xml:id="N1882D" xml:space="preserve">Patet igitur concluſio.</s>
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                  <s xml:id="N18831" xml:space="preserve">Septima concluſio / vbi aliqua poten­
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                  tia vniformiter continuo remittit motum ſuum ad
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                  non gradum aliquod medium inuariatum tranſe-
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                  undo: poña ei equalis valet continuo vniformiter
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                  remittere motum ſuum ad non gradum idem medi­
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                  um tranſeundo per ſui continuam remiſſionem.</s>
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                  <s xml:id="N18840" xml:space="preserve">Probatur / ſit b. poña que īuariata vniformiter cõ­
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                  tinuo remittit motum ſuum ad non gradum c. me-
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                  dium tranſeundo inuariatum: ſit a. poña ei equa­
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                  lis: et ponatur b. poña in puncto initiatiuo vltime
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                  quarte magis reſiſtentis ad quem habet proportio­
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                  nem ſubduplam ad illam quam habet ad punctum
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                  initiatiuum c. medii in extremo remiſſiori / et pona-
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                  tur poña a. ad punctum initiatiuū c. medii in extre-
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                  mo remiſſiori ad quam habet ꝓportioneꝫ in duplo
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                  maiorem ad ꝓportionem quam habet b. ad punctū
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                  in quo ponitur / vt conſtat: cum ſint equales: incipi-
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                  ant / igitur moueri ille due poñe in eodē īſtanti a pū­
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                  ctis in quibus ponuntur et moueatur a. continuo in
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                  duplo velocius b. / tunc dico /  a. continuo vniformi­
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                  formiter remittit motum ſuum ad non gradum: et
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                  hoc per ſue poñe continuam remiſſioneꝫ. </s>
                  <s xml:id="N18861" xml:space="preserve">Quod ſic
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                  ꝓbatur / quia a. continuo vniformiter remittit mo-
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                  tum ſuum / vt ſepius ꝓbatuꝫ eſt: et remittit ad nõ gra­
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                  dum: et continuo remittit potentiam ſuam: igitur ꝓ­
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                  poſitum. </s>
                  <s xml:id="N1886C" xml:space="preserve">Probatur prima pars minoris / quoniaꝫ
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                  ſemper a. mouetur in duplo velocius quam b. ex hy­
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                  potheſi: igitur / quando b. potentia erit in termino
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                  c. medii a. potentia erit in termino duarum ṗmarū
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                  quartarum. </s>
                  <s xml:id="N18877" xml:space="preserve">Patet hec conſequentia adiecta hypo­
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                  theſi antecedenti: ſed cum b. remittit motum ſuum
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                  ad non gradum etiam a remittit motum ſuum ad
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                  non gradum: quia continuo motus illarum poten-
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                  tiarum ſe habent in proportione dupla: igitur cum
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                  vnus totaliter deperditur: etiam et alter: et ex conſe­
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                  quenti cuꝫ b. poña remittit motum ſuum ad nõ gra­
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                  dum in extremo intenſiori c. medii a. potentia remit­
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                  tit motum ſuum ad non gradum in fine duarū pri-
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                  marum quartarum. </s>
                  <s xml:id="N1888C" xml:space="preserve">Sed iam probo ſecundam par­
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                  tem minoris videlicet /  a. continuo remittit poten­
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                  tiam ſuam: quia ſi per aliquod tempus ſtaret aut ī­
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                  tenderet potentiam ſuam, ſignetur illud tempus et
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                  ſit g. in quo a. potentia tranſeat adequate .ef. par-
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                  tem, et in eodem g. tempore b. potentia pertran-
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                  ſeat d. partem adequate: et manifeſtum eſt /  .ef. ꝑ-
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                  tis ad d. partem eſt proportio dupla. / quo poſito ar­
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                  guitur ſic latitudinis motus deperdite ab ipſa po­
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                  tentia b. tranſeundo .ef. partem ad latitudinem de­
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                  perditam ab eadem poña b. tranſeundo d. partem
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                  in g. tempore adequate non eſt ꝓportio dupla: igi-
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                  tur latitudinis deperdite ab a. poña ſtante inuaria­
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                  ta vel intendente poñam ſuam tranſeundo .ef. par­
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                  tem adequate ī g. tempore ad latitudinem deper­
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                  ditam a b. poña tranſeundo d. partem in eodem g.
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                  tempore adequate non eſt ꝓportio dupla: ſed con-
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                  ſequens eſt falſum: igitur illud ex quo ſequitur. </s>
                  <s xml:id="N188B1" xml:space="preserve">Cõ­
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                  ſequentia patet cum falſitate conſequentis ex ſupe­
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                  rius dictis. </s>
                  <s xml:id="N188B8" xml:space="preserve">Iam probatur antecedens / quia .ef. par­
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                  tis ad d. partem eſt ꝓportio dupla et b. poña tran-
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                  ſeundo quamlibet parteꝫ exceſſus minorem d. quo
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                  exceſſu .ef. pars excedit d. partem mouetur cõtinuo
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                  cum maiori reſiſtentia quam tranſeundo quamli-
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                  bet partem equalem ipſius d. partis quia quelibet
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                  pars talis exceſſus īmo tota .ef. pars minus reſiſtit
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                  cum ſit ꝓpinquior extremo remiſſiori ipſius c. me-
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                  dii / vt patet ex ꝓbatione prioris partis: igitur lati­
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                  tudinis motus deperdite ab ipſa potentia b. tran­
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                  ſeundo .ef. partem adequate ad latitudinem deꝑ-
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                  ditam ab eadem poña tranſeundo d. partem ade-
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                  quate non eſt ꝓportio dupla. </s>
                  <s xml:id="N188D3" xml:space="preserve">Patet hec cõſeq̄ntia </s>
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