Alvarus, Thomas, Liber de triplici motu, 1509

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              <div xml:id="N1BD9F" level="4" n="15" type="chapter" type-free="capitulum">
                <p xml:id="N1C137">
                  <s xml:id="N1C161" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0125" n="125"/>
                  tremo intenſiori vnius et alia etiam vt .8. in extremo
                    <lb/>
                  intenſiori alterius: et moueantur ille potentie conti­
                    <lb/>
                  nuo verſus non gradum illarum latitudinum vna
                    <lb/>
                  illarum continuo quieſcente: et manente pedali: et
                    <lb/>
                  altera illarum continuo ſe cõdenſante ſubiecto eiꝰ
                    <lb/>
                  manente pedali: moueatur tamen punctus vt .4. in
                    <lb/>
                  latitudine que mouetur a minori ꝓportione ꝙ̄ ſit
                    <lb/>
                  proportio a qua potentia ſufficit moueri cum illo.
                    <lb/>
                  </s>
                  <s xml:id="N1C180" xml:space="preserve">Quo poſito ſic argumentor illa latitudo / que mo-
                    <lb/>
                  uetur continuo erit minor ꝙ̄ illa que quieſcit per to­
                    <lb/>
                  tum tempus motus: et tamen poña que mouetur in
                    <lb/>
                  illa tardius pertranſibit illam ꝙ̄ potentia que mo­
                    <lb/>
                  uetur in reſiſtentia maiori quieſcente: igitur. </s>
                  <s xml:id="N1C18B" xml:space="preserve">Ma-
                    <lb/>
                  ior eſt nota ex caſu: et minor probatur / quia continuo
                    <lb/>
                  poña que mouetur cū reſiſtentia ſe condenſante mo­
                    <lb/>
                  uetur tardius ꝙ̄ potentia que mouetur cum alia re­
                    <lb/>
                  ſiſtentia quieſcente: et tandē per continuum motum
                    <lb/>
                  deuenient ad non gradum illarum reſiſtentiarum /
                    <lb/>
                  vt ponitur in caſu: igitur citius poña que mouetur ī
                    <lb/>
                  reſiſtentia quieſcente deueniet ad non gradum illi-
                    <lb/>
                  us reſiſtentie in qua mouetur ꝙ̄ poña que mouet̄̄ cū
                    <lb/>
                  reſiſtentia ſe condenſante. </s>
                  <s xml:id="N1C1A0" xml:space="preserve">Conſequentia patet cuꝫ
                    <lb/>
                  minore: et maior probatur / quia illa potentia q̄ mo­
                    <lb/>
                  uet̄̄ cū reſiſtētia ſe ↄ̨denſãte in q̇libet pūcto medii pe­
                    <lb/>
                  dalis ꝑ qḋ extēdebat̄̄ illa reſiſtētia cū maiori reſiſtē­
                    <lb/>
                  tia mouetur quam alia potentia q̄ mouetur in reſi­
                    <lb/>
                  ſtentia quieſcente in conſimili puncto ſiue correſpõ­
                    <lb/>
                  dente: igitur illa poña que mouetur cum reſiſtentia
                    <lb/>
                  ſe condenſante continuo tardius mouetur quã alia
                    <lb/>
                  potentia que mouetur cum reſiſtentia quieſcente.</s>
                </p>
                <p xml:id="N1C1B3">
                  <s xml:id="N1C1B4" xml:space="preserve">Conſequentia patet et arguitur antecedens: q2 con­
                    <lb/>
                  tinuo in quolibet puncto illius medii pedalis ꝑ qḋ
                    <lb/>
                  a principio extendebatur reſiſtentia ſe condenſans
                    <lb/>
                  eſt maior et maior reſiſtentia quovſ in illo puncto
                    <lb/>
                  nõ ſit aliq̈ reſiſtentia: et in quolibet puncto medii pe­
                    <lb/>
                  dalis / per quod extenditur reſiſtentia quieſcēs ma-
                    <lb/>
                  net eadem reſiſtentia continuo: igitur potentia que
                    <lb/>
                  mouetur cum reſiſtentia ſe condenſante in quolib3
                    <lb/>
                  puncto medii pedalis / per quod extendebatur a prī­
                    <lb/>
                  cipio eadem reſiſtentia ſe condenſans cum maiori
                    <lb/>
                  reſiſtentia mouetur ꝙ̄ alia poña que mouetur cum
                    <lb/>
                  reſiſtentia quieſcente in conſimili puncto ſiue cor-
                    <lb/>
                  reſpondente: </s>
                  <s xml:id="N1C1CF" xml:space="preserve">Patet conſequētia / quia in prīcipio
                    <lb/>
                  in punctis correſpondentibus illorum mediorum ē
                    <lb/>
                  eadem reſiſtentia omnino / vt patet: et maior proba­
                    <lb/>
                  tur / quia ex caſu continuo puncta intenſiora illiꝰ re­
                    <lb/>
                  ſiſtentie ſe condenſantis mouentur verſus pūcta re­
                    <lb/>
                  miſſiora eiuſdem reſiſtentie: igitur continuo in quo­
                    <lb/>
                  libet puncto medii pedalis / per quod in prīcipio ex­
                    <lb/>
                  tendebatur latitudo ſe condenſans eſt maior et ma­
                    <lb/>
                  ior reſiſtentia: dummodo in illo puncto ſit aliqua
                    <lb/>
                  reſiſtentia.</s>
                </p>
                <p xml:id="N1C1E4">
                  <s xml:id="N1C1E5" xml:space="preserve">Reſpondeo concedendo quod infer-
                    <lb/>
                  tur et negando falſitatem conſequentis: et ad pro-
                    <lb/>
                  bationem concedo illud quod infertur / vt probat ar­
                    <lb/>
                  gumentum: </s>
                  <s xml:id="N1C1EE" xml:space="preserve">Nec illud eſt inconueniens ſignanter
                    <lb/>
                  quando vna illarum latitudinum reſiſtentiaruꝫ ſic /
                    <lb/>
                  condenſatur vt ponitur in caſu argumenti et altera
                    <lb/>
                  quieſcit.
                    <note position="left" xlink:href="note-0125-01a" xlink:label="note-0125-01" xml:id="N1C2D9" xml:space="preserve">1. correl.</note>
                  </s>
                  <s xml:id="N1C1FC" xml:space="preserve">¶ Ex quo ſequitur primo:  ſtat eandē po-
                    <lb/>
                  tentiam velocius moueri continuo tranſeundo ali-
                    <lb/>
                  quam reſiſtentiam minus extenſam quam tranſeū­
                    <lb/>
                  do eandem magis extenſam. </s>
                  <s xml:id="N1C205" xml:space="preserve">Probatur et capio /
                    <lb/>
                  duas latitudīes vniformiter difformes equales ex­
                    <lb/>
                  tenſiue et intenſiue omnino puta ab octauo vſ ad
                    <lb/>
                  quartum extenſas per duo pedalia exempli gratia /
                    <lb/>
                  et volo /  in eodem inſtanti ponatur vna potentia.
                    <lb/>
                  </s>
                  <s xml:id="N1C211" xml:space="preserve">vt .8. vel vt .10. (non eſt cura) in extremo remiſſiori
                    <cb chead="Capitulum quindecimum"/>
                  vnius: et alia ei equalis in extremo remiſſiori alte-
                    <lb/>
                  rius: et moueantur ille potentie continuo verſus ex­
                    <lb/>
                  tremum intenſius illarum latitudinum: vna illarū
                    <lb/>
                  continuo qnieſcente et manente pedali, et altera il-
                    <lb/>
                  larum continuo ſe condenſante (ſubiecto tñ eiꝰ ma­
                    <lb/>
                  nente pedali) verſus extremū ſui intēſius quieſcēs:
                    <lb/>
                  moueatur tamen punctat .4. in latitudine que con-
                    <lb/>
                  denſatur a minori proportione ꝙ̄ ſit ꝓportio a qua
                    <lb/>
                  potentia ſufficiat moueri cum illo. </s>
                  <s xml:id="N1C227" xml:space="preserve">Quo poſito ſic
                    <lb/>
                  argumentor illa latitudo / que mouetur cõtinuo erit
                    <lb/>
                  minor ꝙ̄ illa que quieſcit: et poña que mouetur cum
                    <lb/>
                  illa velocius mouetur illam reſiſtentiam tranſeun-
                    <lb/>
                  do quam potentia que mouetur in reſiſtentia ſibi
                    <lb/>
                  equali quieſcente: igitur correlarium verum. </s>
                  <s xml:id="N1C234" xml:space="preserve">Ma-
                    <lb/>
                  ior eſt nota ex caſu et minor probatur: quia potētia
                    <lb/>
                  que mouetur cum reſiſtentia ſe condenſante in quo­
                    <lb/>
                  libet puncto medii pedalis per qḋ in prīcipio extē­
                    <lb/>
                  debat illa reſiſtētia cū mīori reſiſtētia mouet̄̄ ꝙ̄ alia
                    <lb/>
                  poña q̄ mouetur in reſiſtetia q̇eſcente in cõſimili pū­
                    <lb/>
                  cto ſiue correſpondente: igitur illa potentia q̄ mo-
                    <lb/>
                  uetur cum reſiſtentia ſe condenſante velocius moue­
                    <lb/>
                  tur ꝙ̄ alia potentia que mouetur cum reſiſtentia q̇e­
                    <lb/>
                  ſcente. </s>
                  <s xml:id="N1C249" xml:space="preserve">Conſequentia patet / et arguitur antecedens /
                    <lb/>
                  quia continuo in quolibet puncto illius medii pe-
                    <lb/>
                  dalis / per quod in principio extendebatur reſiſten-
                    <lb/>
                  tia ſe condenſaus eſt minor et minor reſiſtentia: cum
                    <lb/>
                  ex caſu continuo puncta remiſſiora illius reſiſtētie
                    <lb/>
                  ſe condenſantis moueantur verſus puncta intenſio­
                    <lb/>
                  ra et extremum intenſius eiuſdem reſiſtentie: et ī quo­
                    <lb/>
                  libet puncto medii pedalis / per quod extenditur re­
                    <lb/>
                  ſiſtentia quieſcens manet eadem reſiſtentia vtpote
                    <lb/>
                  que erat in illo in principio: igitur poña que moue-
                    <lb/>
                  tur cum reſiſtentia ſe condenſante in quolibet pun-
                    <lb/>
                  cto medii pedalis / per quod extendebatur in princi­
                    <lb/>
                  pio eadem reſiſtentia ſe condenſans cum minori re­
                    <lb/>
                  ſiſtentia mouetur quam alia potentia que moue-
                    <lb/>
                  tur cum reſiſtentia quieſcente in conſimili puncto ſi­
                    <lb/>
                  ue correſpondente. </s>
                  <s xml:id="N1C26A" xml:space="preserve">Conſequentia patet / quia in prī­
                    <lb/>
                  cipio in punctis correſpondentibus illoruꝫ medio­
                    <lb/>
                  rum eſt eadem reſiſtentia omnino. </s>
                  <s xml:id="N1C271" xml:space="preserve">Q, ſi volueris
                    <lb/>
                  demonſtrare ipſam poñam cum reſiſtentia ſe con-
                    <lb/>
                  denſate continuo velocius moueri: ideo modo pro­
                    <lb/>
                  bes quo probabitur ſequens correlarium. </s>
                  <s xml:id="N1C27A" xml:space="preserve">Patet
                    <lb/>
                  igitur correlarium.
                    <note position="right" xlink:href="note-0125-02a" xlink:label="note-0125-02" xml:id="N1C2DF" xml:space="preserve">.2correl.</note>
                  </s>
                  <s xml:id="N1C284" xml:space="preserve">¶ Sequit̄̄ ſecundo /  datis dua­
                    <lb/>
                  bus latitudinibus vniformiter difformibus equa-
                    <lb/>
                  libus intenſiue et inequalibꝰ extenſiue: et captis dua­
                    <lb/>
                  bus potentiis equalibus quarum vna incipit mo-
                    <lb/>
                  ueri per minus extenſam et altera per magis extēſã
                    <lb/>
                  ab extrēo remiſſiori: q̇eſcētibꝰ ↄ̨tinuo latitudinibꝰ:
                    <lb/>
                  potentiis non variatis: poña que mouetur cum re-
                    <lb/>
                  ſiſtentia minus extenſa tardius continuo mouetur
                    <lb/>
                  quam altera que mouebitur cum reſiſtentia magis
                    <lb/>
                  extenſa. </s>
                  <s xml:id="N1C299" xml:space="preserve">Probatur. </s>
                  <s xml:id="N1C29C" xml:space="preserve">Sit a. potentia que mouetur
                    <lb/>
                  cum reſiſtentia magis extenſa: et b. cum reſiſtentia
                    <lb/>
                  minus extenſa </s>
                  <s xml:id="N1C2A3" xml:space="preserve">Tunc dico /  b. continuo mouetur
                    <lb/>
                  tardius ip̄a a. potentia. </s>
                  <s xml:id="N1C2A8" xml:space="preserve">Quod ſic oſtenditur: quia
                    <lb/>
                  b. non continuo mouetur velocius ꝙ̄ a. </s>
                  <s xml:id="N1C2AD" xml:space="preserve">Nec per
                    <lb/>
                  aliquod tempus mouetur equeuelociter: </s>
                  <s xml:id="N1C2B2" xml:space="preserve">Nec ꝑ ali-
                    <lb/>
                  quod tempus mouetur velocius et immediate ante
                    <lb/>
                  mouetur per aliquod tempus tardius: </s>
                  <s xml:id="N1C2B9" xml:space="preserve">Nec ecõtra /
                    <lb/>
                  ergo continuo b. mouetur tardius ipſa potentia a. /
                    <lb/>
                  quod fuit probandum. </s>
                  <s xml:id="N1C2C0" xml:space="preserve">Conſequentia eſt nota. </s>
                  <s xml:id="N1C2C3" xml:space="preserve">Et
                    <lb/>
                  probatur maior: vcꝫ /  b. non continuo mouetur ve­
                    <lb/>
                  locius quam a. quia ſi continuo mouetur velocius
                    <lb/>
                  quam a. / ſequitur /  continuo b. eſt in puncto magis
                    <lb/>
                  diſtante a principio ſui medii ꝙ̄ a. </s>
                  <s xml:id="N1C2CE" xml:space="preserve">Et per conſeq̄ns
                    <lb/>
                  ſequitur /  continuo eſt in maiori reſiſtentia: et con­
                    <lb/>
                  tinuo mouetur tardius: quod eſt oppoſitum dati.</s>
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