Alvarus, Thomas, Liber de triplici motu, 1509

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              <div xml:id="N1DD6A" level="4" n="3" type="chapter" type-free="capitulum">
                <pb chead="De motu locali quo ad effectum tempore difformi." file="0152" n="152"/>
                <p xml:id="N1ECB7">
                  <s xml:id="N1ECB8" xml:space="preserve">¶ Et confirmatur </s>
                  <s xml:id="N1ECBB" xml:space="preserve">Quia a. et b. in principio ſūt mo­
                    <lb/>
                  tus equales: et in toto tempore debent acquirere eq̈­
                    <lb/>
                  les latitudines: et in quolibet inſtanti intrinſeco eſt
                    <lb/>
                  plus acquiſitum ipſi a. quã b. illius latitudinis ac-
                    <lb/>
                  quirende. </s>
                  <s xml:id="N1ECC6" xml:space="preserve">igitur continuo a. motus eſt maior b. </s>
                  <s xml:id="N1ECC9" xml:space="preserve">Cõ­
                    <lb/>
                  ſequentia eſt ſatis manifeſta. </s>
                  <s xml:id="N1ECCE" xml:space="preserve">et minor patet / q2 con­
                    <lb/>
                  tinuo in quolibet inſtanti intrinſeco maior pars re­
                    <lb/>
                  ſtat acquirenda talis latitudinis ipſi b. quã ipſi a.
                    <lb/>
                  cum b. continuo velocius et velocius acquirat. </s>
                  <s xml:id="N1ECD7" xml:space="preserve">et a.
                    <lb/>
                  vniformiter:
                    <note position="left" xlink:href="note-0152-01a" xlink:label="note-0152-01" xml:id="N1ECEB" xml:space="preserve">54. ↄ̨clu.
                      <lb/>
                    cal. in c: ḋ
                      <lb/>
                    mo. lo.</note>
                  igitur in quolibet inſtanti intriuſeco
                    <lb/>
                  maior pars latitudinis eſt acquiſita ipſi a. quã ip-
                    <lb/>
                  ſi b. et hec eſt quinquageſima quarta concluſio cal-
                    <lb/>
                  culatoris in capitulo de motu locali.</s>
                </p>
                <p xml:id="N1ECF5">
                  <s xml:id="N1ECF6" xml:space="preserve">Tertia propoſitio </s>
                  <s xml:id="N1ECF9" xml:space="preserve">Omnis motus ve-
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                  lociꝰ et velociꝰ deꝑditꝰ quãtū ad tranſitioneꝫ ſpacii
                    <lb/>
                  inteuſiori gradui gradu medio correſpondet hoc ē
                    <lb/>
                  tale mobiie motum illo motu maius ſpacium in il-
                    <lb/>
                  lo tempore pertrãſit adequate quã ſi gradu medio
                    <lb/>
                  inter extrema illius motus continuo vniformiter
                    <lb/>
                  moueretur in illo tempore. </s>
                  <s xml:id="N1ED08" xml:space="preserve">Hec propoſitio proba-
                    <lb/>
                  ta eſt in ſecundo argumento prīcipali ante oppoſi­
                    <lb/>
                  tum in hoc capite.
                    <note position="left" xlink:href="note-0152-02a" xlink:label="note-0152-02" xml:id="N1EDC3" xml:space="preserve">.52. ↄ̨clu.
                      <lb/>
                    cal. in c. ḋ
                      <lb/>
                    mo. lo.</note>
                  </s>
                  <s xml:id="N1ED14" xml:space="preserve">Et hec eſt quinquageſima ſecun-
                    <lb/>
                  da ↄ̨cluſio calculatoris in predicto capitulo de mo­
                    <lb/>
                  tu locali
                    <note position="left" xlink:href="note-0152-03a" xlink:label="note-0152-03" xml:id="N1EDCD" xml:space="preserve">.1. correl.</note>
                  </s>
                  <s xml:id="N1ED20" xml:space="preserve">¶ Ex hac concluſione ſequitur /  ſi a. mobi­
                    <lb/>
                  le moueatur in hora incipiendo ab octauo vſ ad
                    <lb/>
                  quartum continuo vniformiter remittendo motum
                    <lb/>
                  ſuum, et b. mobile moueatur etiam in hora ab octa­
                    <lb/>
                  uo vſ ad quartum continuo velocius et velociꝰ re­
                    <lb/>
                  mittēdo motum ſuum et a. pertranſit .6. pedalia b.
                    <lb/>
                  pertranſibit pluſ̄ ſex pedalia. </s>
                  <s xml:id="N1ED2F" xml:space="preserve">Probatur / q2 mo-
                    <lb/>
                  tus a. correſpondet gradui medio qui eſt ſextus. </s>
                  <s xml:id="N1ED34" xml:space="preserve">vt
                    <lb/>
                  patet ex prima propoſitione: motus vero b. correſ-
                    <lb/>
                  pondet gradui intenſiori medio / vt patet ex tertia ꝓ­
                    <lb/>
                  poſitione.
                    <note position="left" xlink:href="note-0152-04a" xlink:label="note-0152-04" xml:id="N1EDD3" xml:space="preserve">2. correl.</note>
                  </s>
                  <s xml:id="N1ED42" xml:space="preserve">¶ Sequitur ſecundo /  ſi a. incipiat mo-
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                  ueri ab octauo vſ ad quartum vniformiter et b. in
                    <lb/>
                  eodem tempore moueatur incipiendo a decimo ſex­
                    <lb/>
                  to vſ ad duodecimum perdendo latitudinem .4.
                    <lb/>
                  graduum velocius et velocius: tunc continuo b. mo-
                    <lb/>
                  uebitur pluſ̄ in duplo velocius a. et continuo per-
                    <lb/>
                  tranſibit pluſ̄ duplum ſpacium ad ſpacium in eo­
                    <lb/>
                  dem tempore pertranſitum ab a. </s>
                  <s xml:id="N1ED53" xml:space="preserve">Probatur / q2 qñ
                    <lb/>
                  a. et b. continue et vniformiter remitterentur perdē­
                    <lb/>
                  do .4. gradus continuo inter a. et b. ſſet maior ꝓpor­
                    <lb/>
                  tio quã dupla, īmo continuo maior et maior: qm̄ ꝑ
                    <lb/>
                  equalem remſſionem maioris et minoris: maiorē ꝓ­
                    <lb/>
                  portionem deperdit minus quã maius / vt patet ex
                    <lb/>
                  octaua ſuppoſitione quartis capitis ſecunde partis
                    <lb/>
                  et quando ſunt duo numeri ſe habentes in aliqua ꝓ­
                    <lb/>
                  portione, et continuo equaliter remittuntur: conti-
                    <lb/>
                  nuo ſe habent in maiori et maiori ꝓportione: igitur
                    <lb/>
                  ſequitur / ſi ille velocitates a. et b. que ſe habent in ꝓ­
                    <lb/>
                  portione dupla eque velociter remittantur cõtinuo
                    <lb/>
                  ſe habebunt in maiori ꝓportione quã dupla: et ſic
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                  b. coutinuo ſe haberet in maiori ꝓportione quã du­
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                  pla ad ipſum a. ſed modo continuo eſt minus deꝑ-
                    <lb/>
                  ditum ipſi b. quam ipſi a. cum cõtinuo reſtat ei plus
                    <lb/>
                  deperdendum / vt facile patet ex caſu / igitur per locū
                    <lb/>
                  a maiori continuo b. motus erit pluſ̄ in duplo ve­
                    <lb/>
                  locior ipſo a. motu. </s>
                  <s xml:id="N1ED7A" xml:space="preserve">Ex quo ſequitur alia pars cor-
                    <lb/>
                  relarii /  videlicet pluſ̄ duplum ſpacium pertran­
                    <lb/>
                  ſibit b. quam a. in eodē tempore.
                    <note position="left" xlink:href="note-0152-05a" xlink:label="note-0152-05" xml:id="N1EDD9" xml:space="preserve">3. correl.</note>
                  </s>
                  <s xml:id="N1ED86" xml:space="preserve">¶ Sequitnr tertio /
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                   ſi tam. </s>
                  <s xml:id="N1ED8B" xml:space="preserve">quã b. remitterentur ad ſuum ſubduplum
                    <lb/>
                  in hora: ita  a. deperdat in hora continuo vnifor-
                    <lb/>
                  miter quatuor gradus et b. octo continuo velocius
                    <lb/>
                  et velocius: ſequitur /  b. pluſ̄ duplum ſpacium in
                    <lb/>
                  hora pertranſibit quã a. </s>
                  <s xml:id="N1ED96" xml:space="preserve">Probatur / quia ſi b. motꝰ
                    <lb/>
                  vniformiter remitteretur ꝑ totam illam horam ꝑ-
                    <lb/>
                  dendo vniformiter .8. gradus ſicut a. perdit vnifor­
                    <cb chead="De motu locali quo ad effectum tempore difformi."/>
                  miter quatuor: tunc motus eius correſpõderet gra­
                    <lb/>
                  dui medio duplo ad gradum medium motus a. / vt
                    <lb/>
                  patet / q2 gradus medius inter .16. et .8. eſt .12. et gra­
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                  dus medius inter .8. et .4. eſt vt .6: modo .12: ad .6. eſt
                    <lb/>
                  proportio dupla: ſed modo quando ſic velocius et
                    <lb/>
                  velocius et velocius remittitur ſua velocitas correſ­
                    <lb/>
                  pondet intenſiori gradui quã tunc: vt patet ex ter-
                    <lb/>
                  tia propoſitione: igit̄̄ in noſtro caſu b. motus ī illa
                    <lb/>
                  hora ꝑtranſibit pluſ̄ duplū ſpaciū ad ſpaciū ꝑtrã­
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                  ſitum ab a. in eodem tempore. </s>
                  <s xml:id="N1EDB2" xml:space="preserve">Quod tamen prima
                    <lb/>
                  fronte videtur mirabile quia in principio motꝰ b.
                    <lb/>
                  eſt duplus ad motum a. adequate et in toto tempo­
                    <lb/>
                  re perdit motum duplum ad motum quē perdit a.
                    <lb/>
                  tamen bene aſpicienti materiam proportionū ap-
                    <lb/>
                  parebit neceſſarium.</s>
                </p>
                <note position="right" xml:id="N1EDDF" xml:space="preserve">quītage-
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                ſimaquī­
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                ta calcu.</note>
                <p xml:id="N1EDE7">
                  <s xml:id="N1EDE8" xml:space="preserve">Quarta propoſitio </s>
                  <s xml:id="N1EDEB" xml:space="preserve">Omnis motꝰ tar-
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                  dius et tardius intenſius quantum ad pertranſitio­
                    <lb/>
                  nem ſpacii gradui intenſiori medio correſpondet.
                    <lb/>
                  </s>
                  <s xml:id="N1EDF3" xml:space="preserve">Probatur / quia ſi continuo vniformiter talis mo-
                    <lb/>
                  tus (qui ſit a) intenderetur: ipſe preciſe correſpõde-
                    <lb/>
                  ret gradui medio quantum ad pertranſitionē ſpa­
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                  cii / vt patet ex prima propoſitione: ſed modo in quo­
                    <lb/>
                  libet inſtanti intrinſeco temporis per quod a. mobi­
                    <lb/>
                  le mouetur: mouetur velocius quã tunc: ergo: veloci­
                    <lb/>
                  tas eius modo correſpondet gradui intenſiori me-
                    <lb/>
                  dio: quia intenſiori quã tunc. </s>
                  <s xml:id="N1EE04" xml:space="preserve">Conſequentia patet
                    <lb/>
                  et arguitur minor: et volo /  b. ſit motus in prīcipio
                    <lb/>
                  hore equalis ipſi a. qui in eadem hora vniformiter
                    <lb/>
                  continuo acquirit equalem latitudinem illi quã ac­
                    <lb/>
                  quirit a. adequate ipſo tamē a. tardius et tardius
                    <lb/>
                  continuo acquirente ita  ſicut ſunt equales in prī­
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                  cipio ita ſunt equales in fine. </s>
                  <s xml:id="N1EE13" xml:space="preserve">Quo poſito ſic argu-
                    <lb/>
                  mentor / continuo b. motus erit remiſſior ipſo a. mo­
                    <lb/>
                  tu et a. motus intenſior: igitur continue a. motꝰ erit
                    <lb/>
                  intenſior quã tunc quãdo continuo vniformiter in-
                    <lb/>
                  tenderetur ſicut b. quia b. et a: tunc ſemper eēnt eq̈-
                    <lb/>
                  les. </s>
                  <s xml:id="N1EE20" xml:space="preserve">Sed iam probo /  continuo a. motus erit inten­
                    <lb/>
                  ſior b. motu: quia ſi non detur aliqḋ inſtans in quo
                    <lb/>
                  non ſed in illo ſit equalis vel remiſſior ipſo b. et ſit
                    <lb/>
                  tale inſtans c. terminans vnam quartam gratia ar­
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                  gumenti vel quintam: vel ſextam non eſt cura. </s>
                  <s xml:id="N1EE2B" xml:space="preserve">Et ar­
                    <lb/>
                  guo ſic / in illo inſtanti a. motus et b. motus ſunt eq̈-
                    <lb/>
                  les per te: et in principio erant equales ex caſu et in
                    <lb/>
                  tota hora adequate equales latitudīes ſunt eis ac­
                    <lb/>
                  quiſite: et equales reſtant acquirende poſt illud in-
                    <lb/>
                  ſtans c. et quãtam latitudinem b. acquiſiuit in illa
                    <lb/>
                  quarta tantam acquiret in qualibet ſequenti ade-
                    <lb/>
                  quate: quia vniformiter intenditur et a. ex caſu in q̈­
                    <lb/>
                  libet quarta ſequenti minus acquirit ꝙ̄ in illa pre-
                    <lb/>
                  cedenti c. / vt patet ex caſu quoniã continuo tardius
                    <lb/>
                  et tardius acquiret illam latitudinem acquirendã /
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                  igitur in toto tempore ſequenti c. minorem latitudi­
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                  nem acquiret quã b. et antea acquiſiuerat equalem:
                    <lb/>
                  igitur in toto tempore adequate minorem latitudi­
                    <lb/>
                  nē acquiret a. quã b. / quod eſt contra caſum: </s>
                  <s xml:id="N1EE4A" xml:space="preserve">Et ſic
                    <lb/>
                  probabitur ꝑ locum a maiori /  in nullo inſtãti mo­
                    <lb/>
                  tus a. eſt remiſſior motu b. </s>
                  <s xml:id="N1EE51" xml:space="preserve">Et ſicut argutum eſt ſu-
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                  umndo quartam temporis argui poteſt ſumendo
                    <lb/>
                  quãcun partem aliquotam vel non aliquotam vĺ
                    <lb/>
                  quotcū: et ſic patet proportio. </s>
                  <s xml:id="N1EE5A" xml:space="preserve">Et hec eſt quinqua-
                    <lb/>
                  geſima quinta calculatoris</s>
                </p>
                <p xml:id="N1EE5F">
                  <s xml:id="N1EE60" xml:space="preserve">Quinta proportio </s>
                  <s xml:id="N1EE63" xml:space="preserve">Omnis motus tar­
                    <lb/>
                  dius et tardius deperditus: gradui remiſſiori me-
                    <lb/>
                  dio correſpondet. </s>
                  <s xml:id="N1EE6A" xml:space="preserve">Probatur hec propoſitio. </s>
                  <s xml:id="N1EE6D" xml:space="preserve">Sit
                    <lb/>
                  enim a. motus vt .8. qui in hora ſequenti adequate
                    <lb/>
                  perdat aliquaꝫ latitudinem in hora ita  maneat
                    <lb/>
                  in fine minor c. gradu et hoc cõtinuo vniformiter b.
                    <lb/>
                  vero ſit motus equalis ipſi a. et perdat in hora ade­ </s>
                </p>
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