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="N16983" level="4" n="6" type="chapter" type-free="capitulum">
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                  <s xml:id="N16F46" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0071" n="71"/>
                  quadrupla, valeat in tēpore finito pertranſiri a
                    <lb/>
                  potentia vt .4. vt dictū eſt: nichilominus ſi dimi-
                    <lb/>
                  nuatur talis reſiſtentia quo ad extenſionē ad ſub-
                    <lb/>
                  duplū vel ad ſubtriplū .etc̈. ita  efficiatur ſemipe­
                    <lb/>
                  dalis, vel vna tertia, vel quarta, vel quinta: et ſic
                    <lb/>
                  in infinitū: dūmodo partes reſiſtentie cõtinuo ma­
                    <lb/>
                  nent in eadē ꝓportione in qua ſe habebant antea
                    <lb/>
                  puta dupla: potentia vt .4. (intelligo ſemꝑ nõ va-
                    <lb/>
                  riata) in nullo tēpore finito valet talē reſiſtentiam
                    <lb/>
                  pertranſire. </s>
                  <s xml:id="N16F6A" xml:space="preserve">Patet facile ex primo correlario.</s>
                </p>
                <note position="left" xml:id="N16FA9" xml:space="preserve">7. correĺ.</note>
                <p xml:id="N16FAD">
                  <s xml:id="N16FAE" xml:space="preserve">¶ Sequitur ſeptimo /  quãuis potentia vt .4. non
                    <lb/>
                  ſufficit in tēpore finito pertranſire pedalē reſiſten­
                    <lb/>
                  tiam diuiſam in partes ꝓportionales ꝓportione
                    <lb/>
                  dupla: ad cuiꝰ primã habet ꝓportionē duplam et
                    <lb/>
                  ad ſecundã ſexquitertiã et ad tertiã ſexquiſeptimã
                    <lb/>
                  et ad quartã ſexquiquīdecimã et ſic in infinitum: vt
                    <lb/>
                  ponebatur in caſu argumenti: nichilominꝰ tamen
                    <lb/>
                  talis potentia ſufficit pertranſire in tēpore finito
                    <lb/>
                  reſiſtentiã pedalē diuiſam in partes ꝓportiõales
                    <lb/>
                  ꝓportione dupla ſimiliter: ad cuius primã habet
                    <lb/>
                  ꝓportionē duplã et ad tertiã ſexquialterã et ad ter­
                    <lb/>
                  tiã ſexquitertiã et ad quartã ſexquiquartã et ſic in
                    <lb/>
                  infinitū aſcendendo per ſpecies ꝓportiõis ſuper-
                    <lb/>
                  particularis nulla pretermiſſa. </s>
                  <s xml:id="N16FCB" xml:space="preserve">Prima pars hu-
                    <lb/>
                  ius correlarii probata eſt in argumento: et ſecūda
                    <lb/>
                  ꝓbatur: q2 talis potentia in aliquo tēpore finito
                    <lb/>
                  ſufficit pertãſire primã partē parē que eſt ſecūda
                    <lb/>
                  in ordine: et in minori quã ſit equalis ſufficit ꝑtrã-
                    <lb/>
                  ſire oēs ſequentes pares: et ſimiliter. </s>
                  <s xml:id="N16FD8" xml:space="preserve">in aliquo tē-
                    <lb/>
                  pore finito ſufficit pertranſire primã imparē: et in
                    <lb/>
                  minori tēpore quã in triplo ad illḋ ſufficit pertrã-
                    <lb/>
                  ſire oēs ſequentes impares: igitur oēs ſimul tam
                    <lb/>
                  pares quã impares ſufficit ꝑtranſire in tēpore fi-
                    <lb/>
                  nito. </s>
                  <s xml:id="N16FE5" xml:space="preserve">Cõſequētia patet ex ſe / et arguitur maior / qm̄
                    <lb/>
                  ſi illa potentia cõtinuo haberet ꝓportionē ſubdu­
                    <lb/>
                  plam ad partē parem ſequentē ad illã ꝓportionē
                    <lb/>
                  quã habet ad partē parem īmediate precedētem:
                    <lb/>
                  ↄ̨tinuo ꝑtranſiret partē ſequentē parem in duplo
                    <lb/>
                  minori tēpore quã īmediate precedentē cū ipſa ſit
                    <lb/>
                  ſubquadrupla ad parē īmediate precedentem / et ꝑ
                    <lb/>
                  cõſequens ſi tranſiret primã parē in hora adequa­
                    <lb/>
                  te: ſecundã parē tranſiret in media hora: et ſequē-
                    <lb/>
                  tem parē in ſubduplo tēpore: et ſic oēs pares ꝓtrã­
                    <lb/>
                  ſiret in duabus horis / vt patet ex quīto capite pri­
                    <lb/>
                  me partis. </s>
                  <s xml:id="N16FFE" xml:space="preserve">modo ad quãlibet ſequentē parē habet
                    <lb/>
                  maiorē ꝓportionē quã ſubduplã ad ꝓportionem
                    <lb/>
                  quã habet ad partē parē īmediate precedentē: igi­
                    <lb/>
                  tur cõtinuo modo velocius mouebitur: et per con-
                    <lb/>
                  ſequens minus quã in equali tēpore ꝑtrãſibit oēs
                    <lb/>
                  pares ſequentes primã / quod fuit probandū. </s>
                  <s xml:id="N1700B" xml:space="preserve">Sed
                    <lb/>
                  iam ꝓbo iſtã minorē videlicet /  modo habet ad
                    <lb/>
                  quãlibet partē parē ſeq̄ntē maiorē ꝓportionē quã
                    <lb/>
                  ſubduplã ad ꝓportionē quã hꝫ ad partē parē īme­
                    <lb/>
                  diate p̄cedentē. </s>
                  <s xml:id="N17016" xml:space="preserve">Quod ſic ꝓbo / q2 ad primã parteꝫ
                    <lb/>
                  ꝓportionalē parē que eſt ſecunda hꝫ ꝓportionem
                    <lb/>
                  ſexquialterã: ad ſcḋam / q̄ eſt q̈rta hꝫ ꝓportioneꝫ
                    <lb/>
                  ſexquiquartã. </s>
                  <s xml:id="N1701F" xml:space="preserve">Modo ſexq̇quarta eſt maior quam
                    <lb/>
                  medietas ſexq̇altere. </s>
                  <s xml:id="N17024" xml:space="preserve">Itē ad tertiã partē parē que
                    <lb/>
                  eſt ſexta hꝫ ꝓportionē ſexq̇ſextã / vt ptꝫ ex caſu: mo­
                    <lb/>
                  do ſexq̇ſexta maior eſt quã medietas ſexquiq̈rte / et
                    <lb/>
                  ſic ↄ̨ñter / vt ptꝫ ex octauo correlario tertie ↄ̨cluſio­
                    <lb/>
                  nis q̈rti capitis ſcḋe partis. </s>
                  <s xml:id="N1702F" xml:space="preserve">Sed iã ꝓbo maiorem
                    <lb/>
                  prīcipalis argumēti videlicet /  in aliquo tꝑe fini­
                    <lb/>
                  to ſufficit ꝑtrãſire primã partē īparē: et in minori
                    <lb/>
                  quã triplo oēs īpares ſequētes. </s>
                  <s xml:id="N17038" xml:space="preserve">Qḋ ſic demõſtro /
                    <lb/>
                  q2 ſi ad quãlibet ſequētē īparē haberet ↄ̨tinuo ꝓ-
                    <lb/>
                  portionē ſubtriplã ad ꝓportionē quã haberet ad
                    <lb/>
                  īparē īmediate p̄cedentē / tūc ꝑtrãſiret oēs īpares
                    <lb/>
                  ſequētes primã in triplo tardius quã primã ade-
                    <cb chead="Capitulum ſextū."/>
                  quate: ita  ſi trãſiret primã īparem in vna hora
                    <lb/>
                  oēs īpares ſequētes primã in tribus horis adeq̈-
                    <lb/>
                  te ꝑtrãſiret: ſed modo cõtinuo mouetur a maiori
                    <lb/>
                  ꝓportione tranſeūdo aliquã partē imparē ſequē­
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                  tem primã quã tūc ꝑtranſeūdo eandē q2 continuo
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                  a maiori quã ſubtripla / igitur modo in minori tē­
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                  pore quã triplo ꝑtranſibit oēs īpares ſequentes
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                  primã quam primã. </s>
                  <s xml:id="N17054" xml:space="preserve">Cõſequentia ptꝫ et maior ꝓ-
                    <lb/>
                  batur: q2 ſi tranſiret primã imparē in hora: et trã­
                    <lb/>
                  ſecūdo ſcḋam moueretur a ꝓportione ſubtripla
                    <lb/>
                  et ipſa eſſet equalis prime: tūc in triplo tēpore ꝑ-
                    <lb/>
                  tranſiret ipſam puta in tribꝰ horis: ſed modo il-
                    <lb/>
                  la ſecūda pars ꝓportionalis impar eſt ſubqua-
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                  drupla / ergo in ſubquadruplo tēpore modo ꝑtrã­
                    <lb/>
                  ſit eam: et per ↄ̨ñs in ſubſexquitertio tēpore ad tē­
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                  pus in quo ꝑtrãſit primã. </s>
                  <s xml:id="N17067" xml:space="preserve">Patet hec ↄ̨ña ex ſcḋo
                    <lb/>
                  correlario quarte cõcluſiõis quarti capitis pre-
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                  allegati. </s>
                  <s xml:id="N1706E" xml:space="preserve">Et ſic ꝓbabitur de quibuſcū aliis dua­
                    <lb/>
                  bus partibꝰ īparibꝰ: videlicet  cõtinuo ꝑtranſi­
                    <lb/>
                  bit quãlibet partē īparem ſequentē in ſexquiter-
                    <lb/>
                  tio tēpore minori quã īmediate precedentē: et ſic ſi
                    <lb/>
                  tranſit primã in hora oēs alias ꝑtranſit in tribꝰ
                    <lb/>
                  horis / vt ptꝫ intelligenti quintū caput prime par­
                    <lb/>
                  tis. </s>
                  <s xml:id="N1707D" xml:space="preserve">Sed reſtat ꝓbare minorem videlicet /  modo
                    <lb/>
                  cõtinuo pertranſit a maiori ꝓportione quãlibet
                    <lb/>
                  partē īparem ſequentem / quã tūc faceret eandem.
                    <lb/>
                  </s>
                  <s xml:id="N17085" xml:space="preserve">Quod ſic probo / qm̄ primã tranſit a ꝓportione
                    <lb/>
                  dupla / vt ptꝫ ex caſu: et ſecundã imparē que eſt ter-
                    <lb/>
                  tia a ꝓportiõe ſexquitertia. </s>
                  <s xml:id="N1708C" xml:space="preserve">Modo ſexquitertia
                    <lb/>
                  maior eſt quam ſubtripla duple: vt ptꝫ ex decimo
                    <lb/>
                  correlario tertie ↄ̨cluſiõis q̈rti capitis p̄allegati.
                    <lb/>
                  </s>
                  <s xml:id="N17094" xml:space="preserve">Itē tranſit tertiã imparē que eſt quinta in ordine
                    <lb/>
                  a ꝓportione ſexquiquinta. </s>
                  <s xml:id="N17099" xml:space="preserve">Modo ſexquiquinta
                    <lb/>
                  maior eſt quam ſubtripla īmo maior ꝙ̄ ſubdupla
                    <lb/>
                  ad ſexquitertiã / vt ptꝫ ex octauo correlario eiuſdē
                    <lb/>
                  cõcluſiõis / et ſic cõſequēter / vt facile ꝓbat dictum
                    <lb/>
                  correlariū / igitur cõtinuo ꝑtranſit a maiori ꝓpor­
                    <lb/>
                  tiõe quãlibet partē imparē quã tūc faceret eandē
                    <lb/>
                  </s>
                  <s xml:id="N170A7" xml:space="preserve">Et ſic ptꝫ correlariū.
                    <note position="right" xlink:href="note-0071-01a" xlink:label="note-0071-01" xml:id="N170E7" xml:space="preserve">8. correĺ.</note>
                  </s>
                  <s xml:id="N170AF" xml:space="preserve">¶ Sequitur octauo /  hec cõ­
                    <lb/>
                  ſequētia nichil valet hoc mobile ſufficit ꝑtranſi-
                    <lb/>
                  re cū hac reſiſtentia quãlibet partē ꝓportionalē
                    <lb/>
                  huiꝰ pedalis: et quãlibet ſequentē in minori tēpo-
                    <lb/>
                  re quã īmediate precedentē: igitur ſufficit trãſire
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                  pedale cū hac reſiſtentia. </s>
                  <s xml:id="N170BC" xml:space="preserve">Et loquor in antecedēte
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                  de partibus ꝓportionalibꝰ ꝓportione dupla ſe-
                    <lb/>
                  cundū hanc diuiſionē. </s>
                  <s xml:id="N170C3" xml:space="preserve">Probatur correlariū / et vo­
                    <lb/>
                  lo /  aliquod pedale diuidatur ꝓportione dupla
                    <lb/>
                  et  aliqua potētia puta et .8. gr̄a exēpli ſufficiat
                    <lb/>
                  ꝑtranſire primã partē ꝓportionalē in hora: et ſe-
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                  cundã in media hora cū quarta. / et tertiã in media
                    <lb/>
                  hora cū octaua: et quartã in media hora cū decīa
                    <lb/>
                  ſexta: et ſic in īfinitū taliter /  quãlibet preter pri-
                    <lb/>
                  mã ꝑtranſiret in media hora cū aliquo tꝑe vltra:
                    <lb/>
                  qḋ tēpus vltra eſſet cõtinuo ſubduplū: quo poſito
                    <lb/>
                  iã ptꝫ totū correlariū. </s>
                  <s xml:id="N170D8" xml:space="preserve">Qm̄ manifeſtū eſt /  requi­
                    <lb/>
                  rerent̄̄ īfinite medie hore ad ꝑtrãſeundū illud pe-
                    <lb/>
                  dale: et tñ q̄libet pars ꝓportiõalis ſequēs in mi-
                    <lb/>
                  nori tꝑe ꝑtrãſit̄̄ quã īmediate p̄cedēs et quamlibet
                    <lb/>
                  ſufficit pertranſire / vt notum eſt: igitur.</s>
                </p>
                <p xml:id="N170ED">
                  <s xml:id="N170EE" xml:space="preserve">Tertio contra omnes concluſiones
                    <lb/>
                  ſimul arguitur ſic: ille vel maior pars illarum
                    <lb/>
                  ſupponit vnū falſū / ergo ſūt falſe. </s>
                  <s xml:id="N170F5" xml:space="preserve">Arguit̄̄ añs / q2
                    <lb/>
                  ſupponūt aliquã reſiſtentiã poſſe vniformiter ſuc­
                    <lb/>
                  ceſſiue diminui ab aliq̈ ponã: ſed hoc nõ eſt poſſi-
                    <lb/>
                  bile igit̄̄. </s>
                  <s xml:id="N170FE" xml:space="preserve">Minor ꝓbat̄̄ / q2 det̄̄ potētia vt .8. q̄ vni-
                    <lb/>
                  formiter corrūpat et remittat reſiſtentiã vt .4. per
                    <lb/>
                  vnã horã / et arguitur ſic: iſta potentia vt .8. remit-
                    <lb/>
                  tit vniformiter in hora reſiſtentiam vt .4. / ergo in
                    <lb/>
                  medietate hore remittit medietatē reſiſtentie: et </s>
                </p>
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