Alvarus, Thomas, Liber de triplici motu, 1509

Table of contents

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