Alvarus, Thomas, Liber de triplici motu, 1509

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                    <pb chead="Tertii tractatus" file="0215" n="215"/>
                  volueris cõtinuo illud corpus augeretur ita veloci­
                    <lb/>
                  ter ſicut in prima parte proportionali: in ea ꝓpor-
                    <lb/>
                  tione qua aliqua pars eſt minor prima: in ea mi-
                    <lb/>
                  norem proportionē acquireret in illa quam in pri-
                    <lb/>
                  ma. </s>
                  <s xml:id="N253A8" xml:space="preserve">hec ſuppoſitio ex ſe conſtat. </s>
                  <s xml:id="N253AB" xml:space="preserve">¶ Secunda ſuppo-
                    <lb/>
                  ſitio. </s>
                  <s xml:id="N253B0" xml:space="preserve">Quando iſtud corpus augmentatur in hora
                    <lb/>
                  ſic diuiſa / vt ponitur in concluſione duas propor-
                    <lb/>
                  tiones equales acquirit in ſecunda parte ꝓportio­
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                  nali equales īquaꝫ illi quã acquireret ſi moueretur
                    <lb/>
                  equeuelociter in ea ſicut in prima quoniam moue-
                    <lb/>
                  tur in duplo velocius ꝙ̄ tunc: et in tertia tres equa-
                    <lb/>
                  les illi quã acquireret ſi moueretur eque velociter
                    <lb/>
                  ſicut in prima: et in quarta quatuor equales illi ̄
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                  acquireret ſi moueretur eque velociter ſicut ī prima
                    <lb/>
                  quia modo in quadruplo velocius mouetur ꝙ̄ tunc /
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                  et ſic in infinitum. </s>
                  <s xml:id="N253C7" xml:space="preserve">¶ Tertia ſuppoſitio ſequens ex
                    <lb/>
                  his duabus. </s>
                  <s xml:id="N253CC" xml:space="preserve">In caſu concluſionis proportio acqui­
                    <lb/>
                  ſita in prima parte ꝓportionali ſe habet ad vtrã
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                  illarū duarū acquiſitarū in ſcḋa in proportiõe di-
                    <lb/>
                  uiſionis: et vtra de hiis duabus acquiſitis in ſecū­
                    <lb/>
                  da ad quãlibet illarū triū acquiſitarū in tertia ſe-
                    <lb/>
                  habet etiam in eadem proportione diuiſiõis: et ſic
                    <lb/>
                  conſequēter. </s>
                  <s xml:id="N253DB" xml:space="preserve">Patet hec ex prīa ſuppoſitione. </s>
                  <s xml:id="N253DE" xml:space="preserve">¶ Ex
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                  quibus ſequitur /  ibi ſunt infiniti ordines infinito­
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                  rum continuo ſe habentium in proportiõe diuiſio-
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                  nis. </s>
                  <s xml:id="N253E7" xml:space="preserve">pro primi em̄ ordiuis prima parte capias pro­
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                  portionem acquiſitam in prima parte proportio-
                    <lb/>
                  nali: et pro ſecunda parte vnã acquiſitarū in ſcḋa
                    <lb/>
                  et pro tertia vnã acquiſitarū in tertia / et ſic in infi-
                    <lb/>
                  nitū. </s>
                  <s xml:id="N253F2" xml:space="preserve">Et ꝓ ſecundi ordinis prima parte capias al-
                    <lb/>
                  teram acquiſitam in ſecūda et vnam de acquiſitis
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                  in tertia pro ſecunda parte illius ſecundi ordinis:
                    <lb/>
                  et pro tertia parte vnã de acquiſitis in quarta: et
                    <lb/>
                  ſic in infinitū. </s>
                  <s xml:id="N253FD" xml:space="preserve">Et pro tertii ordinis prima parte ca­
                    <lb/>
                  pias vnam de acquiſitis in tertia que adhuc non
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                  eſt accepta: et pro ſecūda vnam de acquiſitis ī quar­
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                  ta / et ſic cõſequenter: ita  nulla maneat acquiſita
                    <lb/>
                  in aliqua parte proportiõali quin ſit aliqua pars
                    <lb/>
                  alicuius illorū ordinū: et manifeſtum eſt  ibi erūt
                    <lb/>
                  infiniti ordines continuo ſe habentes in proportio­
                    <lb/>
                  ne diuiſionis q2 ſemper partes eoꝝ ſe habent adin-
                    <lb/>
                  uicem continuo in proportione diuiſionis: et omni­
                    <lb/>
                  um illorum prime partes etiam ſe habent in ꝓpor­
                    <lb/>
                  tione diuiſionis: et ſecunde: et tertie: et quarte: et ſic
                    <lb/>
                  ſine fine: igitur illi ordines cõtinuo ſe habent in ꝓ-
                    <lb/>
                  portione diuiſionis. </s>
                  <s xml:id="N25418" xml:space="preserve">Iam hec ↄ̨ſequentia antea de­
                    <lb/>
                  ducta eſt: et per cõſequens aggregatum ex omnibꝰ
                    <lb/>
                  illis ordinibus ſe habet ad primū illorum in ea ꝓ-
                    <lb/>
                  portione qua ſe habet tota hora diuiſa ad primaꝫ
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                  partem ꝓportionalem: et primus illorum ordinum
                    <lb/>
                  ſe habet etiam ad primã eius partem que eſt ꝓpor­
                    <lb/>
                  tio acquiſita in prima parte hore etiam in propor­
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                  tione diuiſionis: igitur aggregatū ex omnibus il-
                    <lb/>
                  lis ordinibus quod eſt proportio acquiſita in tota
                    <lb/>
                  hora ipſi corpori ſe habet ad proportionē acquiſi-
                    <lb/>
                  tam in prima parte ꝓportionali in proportiõe du­
                    <lb/>
                  pla ad proportionem in qua ſe habet tota hora ſic
                    <lb/>
                  diuiſa ad primam eius partem proportionalem.</s>
                </p>
                <p xml:id="N25433">
                  <s xml:id="N25434" xml:space="preserve">Patet conſequentia: quia ibi ſunt tres termini cõ­
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                  tinuo proportionabiles tali proportione quorum
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                  primus et maximus eſt aggregatum ex omnibꝰ il-
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                  lis ordininibus: et ſecūdus primus illorū ordinum: et
                    <lb/>
                  tertius proportio acquiſita ī prima parte propor-
                    <lb/>
                  tionali hore: igitur ibi eſt proportio dublicata / vt
                    <lb/>
                  patet intuenti. </s>
                  <s xml:id="N25443" xml:space="preserve">Multe alie concluſiones et correla-
                    <lb/>
                  ria ex hac imaginatione et induſtria horū ordinuꝫ
                    <lb/>
                  poſſunt inferri materiam ampliãdo que omnia fa­
                    <lb/>
                  cile inducūtur ex dictis.
                    <note position="left" xlink:href="note-0215-01a" xlink:label="note-0215-01" xml:id="N2550C" xml:space="preserve">Pḣs .1°.
                      <lb/>
                    ethi. et ce­
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                    li et mū. et
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                    elēchoꝝ et
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                    metha. 2.</note>
                  </s>
                  <s xml:id="N25451" xml:space="preserve">Prīcipiuꝫ em̄ pluſ̄ dimi-
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                  dium totius eſſe videtur ex primis Ethicorum. </s>
                  <s xml:id="N25456" xml:space="preserve">Et ce­
                    <cb chead="Capi. ſecundum"/>
                  li et mundi: et ex elenchorum et metaphiſices ſecun-
                    <lb/>
                  dis. </s>
                  <s xml:id="N2545E" xml:space="preserve">Quandoquidem hiis que circa materiam de
                    <lb/>
                  motu locali difformi quoad tēpus diligēter inſpe­
                    <lb/>
                  ctis facile proprio marte educentur cõcluſiones in
                    <lb/>
                  numere: quoniam omnes que ibi inducuntur mu-
                    <lb/>
                  tatis mutandis hic inferri valent.
                    <note position="right" xlink:href="note-0215-02a" xlink:label="note-0215-02" xml:id="N2551A" xml:space="preserve">Cõcluſio­
                      <lb/>
                    nes .2. po­
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                    ſitionis.</note>
                  </s>
                  <s xml:id="N2546E" xml:space="preserve">¶ Deinde ponē­
                    <lb/>
                  de ſunt alique cõcluſiones que ex poſitione ſecūda
                    <lb/>
                  naſcuntur. </s>
                  <s xml:id="N25475" xml:space="preserve">Prima concluſio: nullū quadratū cuiꝰ
                    <lb/>
                  omnia latera ſunt equalia ſiue ſuperficiale ſit ſine
                    <lb/>
                  ſolidum: poteſt vniformiter ad non quantum dimi-
                    <lb/>
                  nui: vtra eius dimenſione vniformiter ad nõ ̄tū
                    <lb/>
                  diminuta. </s>
                  <s xml:id="N25480" xml:space="preserve">Hec concluſio patet ex deductione octa-
                    <lb/>
                  ui argumenti. </s>
                  <s xml:id="N25485" xml:space="preserve">Et hanc cõcluſionem ſane intelligas
                    <lb/>
                  capiendo ly poteſt in ſenſu compoſito. </s>
                  <s xml:id="N2548A" xml:space="preserve">¶ Ex hac cõ­
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                  cluſiõe ſequitur /  ſi aliquod quadratuꝫ a non ̄to
                    <lb/>
                  incipit continuo vniformiter acquirere longitudi-
                    <lb/>
                  nem latitudinem et profunditatem: ip̄m infinite tar­
                    <lb/>
                  de incipit augeri. </s>
                  <s xml:id="N25495" xml:space="preserve">Probatur / quoniam incipit con­
                    <lb/>
                  tinuo acquirere proportionem octuplam in quali-
                    <lb/>
                  bet parte proportionali proportiõe dupla: igitur
                    <lb/>
                  incipit in infinitum tarde acquirere de quãtitate.
                    <lb/>
                  </s>
                  <s xml:id="N2549F" xml:space="preserve">Patet conſequentia ex ſecunda confirmatione ſe-
                    <lb/>
                  cundi argumēti huius. </s>
                  <s xml:id="N254A4" xml:space="preserve">Probatur antecedēs / quia
                    <lb/>
                  in via dimunitionis quando continuo in qualibet
                    <lb/>
                  parte proportionali dupla proportione latitudo
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                  longitudo et profunditas perdunt proportionem
                    <lb/>
                  duplam: tunc totum quadratum perdit proportio­
                    <lb/>
                  nem octuplam: g̊ in via augmentationis econuerſo
                    <lb/>
                  augmentando in qualibet parte proportionali ꝓ-
                    <lb/>
                  portione dupla acquiret octuplam proportionem
                    <lb/>
                  illud quadratuꝫ: quod fuit probandū. </s>
                  <s xml:id="N254B7" xml:space="preserve">¶ Sequitur
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                  ſecundo:  ſi a non quanto aliquod quadratū in-
                    <lb/>
                  cipit vniformiter augeri: ſua latitudo et longitudo
                    <lb/>
                  incipiunt infinite velociter augeri. </s>
                  <s xml:id="N254C0" xml:space="preserve">Probatur / quia
                    <lb/>
                  longitudo et latitudo incipiunt acquirere in parte
                    <lb/>
                  proportionali pcoportione dupla minorem ꝓpor­
                    <lb/>
                  tionē dupla. </s>
                  <s xml:id="N254C9" xml:space="preserve">igitur longitudo et latitudo illiꝰ qua-
                    <lb/>
                  drati incipiunt in infinitū velociter augeri. </s>
                  <s xml:id="N254CE" xml:space="preserve">Patet
                    <lb/>
                  hec conſequentia ex ſecunda confirmatione prealle­
                    <lb/>
                  gata. </s>
                  <s xml:id="N254D5" xml:space="preserve">Probatur antecedēs / quoniã non augeutur
                    <lb/>
                  hee dimenſiones in proportione dupla: quia tunc
                    <lb/>
                  quadratum non vniformiter augeretur / vt patꝫ ex
                    <lb/>
                  priori correlario: nec in maiori dupla: q2 tunc etiã
                    <lb/>
                  quadratum in maiori quadrupla augeretur: et ſic
                    <lb/>
                  non augeretur vniformiter / vt cõſtat: igitur ille di-
                    <lb/>
                  menſiones in maiori proportiõe dupla augentur
                    <lb/>
                  in partibus proportionalibus temporis propor-
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                  tione dupla: quod fuit probanduꝫ. </s>
                  <s xml:id="N254E8" xml:space="preserve">¶ Sequitur ter­
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                  tio /  ſi aliquod quadratum incipit a non quanto
                    <lb/>
                  augeri: et in qualibet parte proportionali propor­
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                  tione dupla ipſius temporis acquirat proportio-
                    <lb/>
                  nem minorem dupla: ipſum incipit infinite veloci-
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                  ter augeri: et quelibet eius dimenſio incipit in infi-
                    <lb/>
                  nitum velociter augeri: et tamē incipit quelibet eiꝰ
                    <lb/>
                  dimenſio in infinitum velocius augeri ꝙ̄ ip̄m qua-
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                  dratum. </s>
                  <s xml:id="N254FB" xml:space="preserve">Patet hoc correlariuꝫ facile ex ſecunda cõ­
                    <lb/>
                  firmatiõe predicta: hoc addito  ſemper in tali ca-
                    <lb/>
                  ſu quadratum incipit maiorem proportionem ac-
                    <lb/>
                  quirere ꝙ̄ aliqua eius dimēſio / vt patet ex deductio­
                    <lb/>
                  ne octaui argumenti huius paucis facillimis ad-
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                  ditis.</s>
                </p>
                <p xml:id="N25524">
                  <s xml:id="N25525" xml:space="preserve">Secunda concluſio ſtat /  a. corpus
                    <lb/>
                  incipit in infinitum velociter augeri et infinite tar-
                    <lb/>
                  de: et vniformiter patet hec concluſio ex deductio-
                    <lb/>
                  ne replice octaui argumenti. </s>
                  <s xml:id="N2552E" xml:space="preserve">In hac materia poſ-
                    <lb/>
                  ſunt induci omnes ille concluſiones que indu-
                    <lb/>
                  cte et probate fuerunt tractatu ſecundo capite ter-
                    <lb/>
                  tio de motu locali difformi quoad tēpus. </s>
                  <s xml:id="N25537" xml:space="preserve">Uideas
                    <lb/>
                  ibi Cõcluſionibus expeditis et conſequenti ſecun- </s>
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