Alvarus, Thomas, Liber de triplici motu, 1509

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                    <pb chead="Primi tractatus" file="0094" n="94"/>
                  illa puncta mediãt ſeptem ſexdecime que ſunt prīa
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                  pars ꝓportionalis ꝓportione ſupraſeptipartiēte
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                  nonas / vt patet intelligenti quintum caput prime
                    <lb/>
                  partis: igitur. </s>
                  <s xml:id="N1927A" xml:space="preserve">Antecedens probatur / quia b. poña
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                  in inſtanti terminatiuo prime quarte temporis in
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                  quo adequate c. medium pertranſit habet ad pun-
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                  ctum in quo / tunc eſt ꝓportionem in ſexquitertio mi­
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                  norem ad ꝓportionem quam habet ad punctum in­
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                  itiatiuum: et in eodem inſtanti terminatiuo prime
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                  quarte illius temporis eſt in fine ſeptem ſexdecima­
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                  rum c. medii pertranſitaruꝫ ab ipſa b. poña: igitur
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                  inter punctum initiatiuum c. medii et punctum ad
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                  quod b. poña habet in ſexquitertio minorem ꝓpor­
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                  tionem quam ad punctum initiatiuum mediant ſe-
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                  ptem ſexdecime c. medii / quod fuit probandum. </s>
                  <s xml:id="N19293" xml:space="preserve">Cõ­
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                  ſequentia patet: et maior ꝓbat̄̄ / q2 in prīa quarta tē­
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                  poris in quo adequate b. poña c. medium pertran-
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                  ſit perdit eadem b. poña vnam quartam ꝓportiõis
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                  quam habet ad punctum initiatiuum c. medii: quia
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                  illa ꝓportio debet vniformiter continuo deperdi:
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                  igitur in inſtanti terminatiuo illius quarte habet
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                  tres quartas preciſe illius proportionis quam ha­
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                  bet ad punctum initiatiuum: et per conſequens pro­
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                  portionem in ſexquitertio minorem / quod fuit pro-
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                  bandum. </s>
                  <s xml:id="N192AA" xml:space="preserve">Nunc probo minorem videlicet /  in inſtã­
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                  ti terminatiuo prime quarte illius temporis eſt in
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                  fine ſeptem ſexdecimarum ab ea pertranſitaruꝫ etc.
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                  quia ſi b. poña in prima quarta illius temporis mo­
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                  ueret̄̄ adequate ita velociter ſicut in tota hora ca-
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                  thegorematice puta gradu medio totius motus,
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                  b. poña in illa quarta pertranſiret adequate vnam
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                  quartam c. medii que eſt quatuor decime ſexte / vt pa­
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                  tet ex ſecundo notato tertii capitis ſecundi tracta-
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                  tus: ſed modo mouetur b. poña in illa quarta in ꝓ-­
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                  portione ſupratripartiente q̈rtas velocius. </s>
                  <s xml:id="N192C1" xml:space="preserve">igitur
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                  modo pertranſit ī illa quarta ſeptem ſexdecimas.
                    <lb/>
                  </s>
                  <s xml:id="N192C7" xml:space="preserve">(quandoquidem ſeptem ſexdecimaruꝫ ad quatuor
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                  ſexdecimas eſt ꝓportio ſupratripartiens quartas) /
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                  et per conſequēs in fine illius prime quarte tempo­
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                  ris in quo c. medium pertranſit b. poña eſt in fine ſe­
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                  ptem ſexdecimarum ab ea pertranſitarum / qḋ fuit
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                  probandum. </s>
                  <s xml:id="N192D4" xml:space="preserve">Conſequentia patet cum maiore: et mi­
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                  nor probatur / quia gradus medius motꝰ quo b. po­
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                  tentia mouetur in illa quarta eſt in ꝓportione ſu-
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                  pratripartiente quartas maior quam gradus me-
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                  dius motus quo eadem b. potentia mouetur adeq̈-
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                  te in tempore in quo c. ſpacium ſiue medium pertrã­
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                  ſit: igitur b. poña in illa prima quarta mouetur ī ꝓ­
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                  portione ſupratripartiente quartas velocius quã
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                  in toto tempore quo c. mediuꝫ pertranſit / quod fuit
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                  probandum. </s>
                  <s xml:id="N192E9" xml:space="preserve">Antecedens probatur / quia motꝰ qui
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                  ꝓuenit a ꝓportione quam habet b. poña ad pūctuꝫ
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                  initiatiuum c. medii cum tribus quartis eiuſdem ꝓ­
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                  portionis ad motum prouenientem a proportione
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                  quam habet b. poña ad punctum initiatiuum c. me­
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                  dii tantummodo eſt proportio ſupratripartiens
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                  quartas / vt patet: quia inter illas ꝓportiones ē ꝓ-
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                  portio ſupratripartiens quartas: igitur medietas
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                  motus ꝓueniens a proportione quã habet b. poña
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                  ad punctum initiatiuum c. medii cum tribus quar-
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                  tis eiuſdem ꝓportionis adiunctis: eſt maior in pro­
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                  portione ſupratripartiente quartas quam medie-
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                  tas motus prouenientis a ꝓportione quam habet
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                  b. poña ad punctū initiatiuum c. medii tantūmodo /
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                  vt patet vndecima ſuppoſitione ſecundi capitis
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                  ſecunde partis. </s>
                  <s xml:id="N1930A" xml:space="preserve">ſed medietas motus prouenientis
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                  a ꝓportione quam habet b. poña ad punctum īitia­
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                  tiuum c. medii cum tribus eius quartis adiunctis ē
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                  gradus medius motus / quod b. poña mouetur in il­
                    <cb chead="Capitulum nonum"/>
                  la prima quarta: et medietas motus ꝓuenientis a
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                  ꝓportione quam habet b. potentia ad punctum in­
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                  itiatiuum c. medii tantummodo eſt gradus medius
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                  motus quo b. poña mouetur in tota hora adequa-
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                  te: igitur gradus medius motus quo mouetur b. po­
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                  tentia in illa prima quarta eſt maior in proportio­
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                  ne ſupratriꝑtiente quartas quam gradus medius
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                  motus quo mouetur eadem b. poña ī tempore ī quo
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                  c. medium pertranſit / quod fuit probandum. </s>
                  <s xml:id="N19326" xml:space="preserve">Conſe­
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                  quentia patet cum maiore: et probatur maior quo
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                  ad primam partem videlicet /  medietas motus ꝓ­
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                  uenientis a proportione quaꝫ habet b. poña ad pū­
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                  ctum initiatiuum c. medii cum tribus quartis eius
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                  coniunctis eſt gradus medius motus quo mouetur
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                  eadem poña b. in prima quarta: quia motus quo
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                  mouetur b. poña in prima quarta incipit a motu ꝓ­
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                  ueniente a proportione quam habet b. ad punctum
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                  initiatiuum c. medii. </s>
                  <s xml:id="N1933B" xml:space="preserve">et terminatur ad motum ꝓue-
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                  nientem a tribus quartis eiuſdem proportionis / vt
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                  patet intuenti: igitur medietas motus aggregati
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                  ex motu proueniente a proportione quam habet b.
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                  poña ad punctum initiatiuum c. medii et ex motu ꝓ­
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                  ueniente ex tribus quartis eius eſt gradus medius
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                  inter illos. </s>
                  <s xml:id="N1934A" xml:space="preserve">Patet conſequentia ex primo correla-
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                  rio prime concluſionis ſecundi capitis ſecunde ꝑ-
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                  tis: et ꝑ conſequens medietas motus prouenientis
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                  a proportione quam habet b. poña ad punctum in­
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                  itiatiuum c. medii et tribus quartis eius adiunctis
                    <lb/>
                  eſt gradus medius motus quo mouetur b. poña ī il­
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                  la prima quarta / quod fuit probandum. </s>
                  <s xml:id="N19359" xml:space="preserve">Iam pro-
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                  bo ſecundã ꝑtem minoris videlicet /  medietas mo­
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                  tus ꝓuenientis a proportione quam habet b. poña
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                  ad punctum initiatiuum c. medii eſt gradus mediꝰ
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                  motus quo mouetur eadem b. poña in tempore in
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                  quo c. medium pertranſit adequate: quia cuiuſlib3
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                  motus vniformiter difformis ad non gradum ter-
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                  minati gradus medius eſt medietas motus remiſ-
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                  ſiſſimi qui non eſt in illo motu totali vnifomiṫ dif­
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                  formi / vt patet facile intelligenti tertium caput ſe-
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                  cundi tractatus: ſed motus proueniens a propor-
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                  tione quam habet b. poña ad punctum initiatiuum
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                  c. medii eſt remiſſiimus qui non eſt in illo motu to-
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                  tali quo mouetur adequate in tempore in quo c. me­
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                  dium pertranſit: igitur gradus medius motus quo
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                  mouetur in tempore. </s>
                  <s xml:id="N1937A" xml:space="preserve">in quo b. poña c. medium ꝑtrã-
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                  ſit eſt medietas motus prouenientis a proportio-
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                  ne quam habet b. poña ad punctum initiatiuum c.
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                  medii / quod fuit probandum. </s>
                  <s xml:id="N19383" xml:space="preserve">Conſimiliter omnino
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                  ꝓbabis in omnibus ſpeciebus ꝓportionum: videli­
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                  cet /  inter punctum initiatiuum c. medii et punctum
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                  intrinſecuꝫ ad quod b. poña habet in qua volueris
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                  ſpecie ꝓportionis proportionem minorem, mediat
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                  prima pars ꝓportionalis adequate c. medii diuiſi
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                  in partes proportionales ꝓportione dupla ad il-
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                  lam ſpeciem proportionis.</s>
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                <p xml:id="N19394">
                  <s xml:id="N19395" xml:space="preserve">¶ Hoc ſuppoſito probatur antecedens / quod aſſum­
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                  ptum eſt in replica. </s>
                  <s xml:id="N1939A" xml:space="preserve">et ſit b. poña que c. medium inua­
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                  riatum tranſeundo continuo vniformiter remittit
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                  motum ſuum ad non gradum in extremo intenſiori
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                  eiuſdem c. medii. </s>
                  <s xml:id="N193A3" xml:space="preserve">et ſit a. poña maior quecū volue-
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                  ris: cuius ꝓportio ad punctum initiatiuum c. medii
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                  in extremo remiſſiori ſit in f. proportione maior ꝓ-
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                  portione b. poñe ad idem punctum initiatiuuꝫ c. me­
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                  dii et ponatur b. potentia ad punctum intrinſecum
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                  c. medii ad quod habet proportionem in f. ꝓportio­
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                  ne minorem ꝓportione eiuſdem b. poñe ad punctuꝫ
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                  initiatiuum c. medii. </s>
                  <s xml:id="N193B4" xml:space="preserve">et manifeſtū ē /  proportio ip-
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                  ſius a. ad punctum initiatiuum c. medii eſt in dupli-
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                  ci f. ꝓportione maior proportione ipſius b. ad illḋ </s>
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