Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N15C22" level="3" n="1" type="other" type-free="tractatus">
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                <pb chead="Primi tractatus" file="0117" n="117"/>
                <p xml:id="N1B52F">
                  <s xml:id="N1B530" xml:space="preserve">Probatur / et ſit illa b. potentia: et arguo ſic / b. potē­
                    <lb/>
                  tia nun̄ vniformiter mouetur / vt ptꝫ ex ſecūdo cor­
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                  relario prime concluſionis: nec continuo remittit
                    <lb/>
                  motū ſuū: nec aliquãdo intendit et īmediate poſtea
                    <lb/>
                  remittit: aut econtra: igitur b. potentia cõtinuo in-
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                  tendit motū ſuū / quod ruit ꝓbandū. </s>
                  <s xml:id="N1B53D" xml:space="preserve">Cõſequētia ptꝫ
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                  cū maiore, et ꝓbatur prima pars minoris / q2 ſi ſic
                    <lb/>
                  detur ꝓportio a qua incipit moueri b. potentia cõ-
                    <lb/>
                  tinuo remittendo motum ſuū que ſit f. quã habeat ad
                    <lb/>
                  a. punctū illius reſiſtentie a quo incipiendo moue-
                    <lb/>
                  ri continuo per te remittit motū ſuū et illud punctū
                    <lb/>
                  a. incipiat moueri a ꝓportione g. maiore f. / vt opor­
                    <lb/>
                  tet </s>
                  <s xml:id="N1B54E" xml:space="preserve">(Alias em̄ b. potentia nõ remitteret motum ſuū) / et
                    <lb/>
                  capio / tunc c. punctū intenſius a. puncto / quod inci-
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                  pit moueri ab h. ꝓportione maiore f. / a qua incipit
                    <lb/>
                  moueri b. potentia minori tamen g. proportione a
                    <lb/>
                  qua incipit moueri a. punctū: et arguo ſic / b. poten-
                    <lb/>
                  tia incipit remittere motum ſuū incipiendo moue-
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                  ri ab a. puncto ſucceſſiue: a. puncto et aliis punctis
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                  intenſioribus verſus potentiã mouentibus et ſequē­
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                  tibus eam: igitur per aliquod tempus b. potentia
                    <lb/>
                  precedit c. punctū: ſed cõſequens eſt falſum: igitur
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                  illud ex quo ſequitur. </s>
                  <s xml:id="N1B565" xml:space="preserve">Cõſequentia eſt nota, et falſi-
                    <lb/>
                  tas conſequentis arguitur, q2 b. potentia et c. pun-
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                  ctum incipiunt in eodē inſtanti moueri ab eodē pū-
                    <lb/>
                  cto etc̈. et ipſa b. potentia continuo mouetur a mino­
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                  ri ꝓportione quã punctū c: quia a minori f. cõtinuo
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                  cū remittat continuo motum ſuū per te: igitur per
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                  illud tempus continuo c. punctū precedit b. poten-
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                  tiam, et per cõſequens b. potentia nõ ꝑ illud tēpus
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                  precedit c. punctū / quod eſt oppoſitū conſequentis.
                    <lb/>
                  </s>
                  <s xml:id="N1B579" xml:space="preserve">Et ſic patet prima pars minoris. </s>
                  <s xml:id="N1B57C" xml:space="preserve">Sed ſecūda ꝓba­
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                  tur videlicet /  b. potentia nõ aliquãdo intendit, et
                    <lb/>
                  īmediate poſtea remittit, quia ſi ſic detur inſtans /
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                  in quo incipit remittere ante quod īmediate inten-
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                  debat motum ſuū in quo inſtanti b. potentia ſit in
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                  puncto a. / a quo incipit remittere motum ſuū per te
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                  continuo cū intenſiori puncto mouendo quã ſit a.
                    <lb/>
                  </s>
                  <s xml:id="N1B58C" xml:space="preserve">Capio igitur / vnã partem illiꝰ reſiſteutie termina-
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                  tam ad a. punctū per quã b. potentia mouendo con­
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                  tinuo intendebat motum ſuū, et manifeſtū eſt /  ip-
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                  ſa potentia b. ſic continuo intendens motum ſuum
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                  per illam partem mouendo velocius mouetur cum
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                  quolibet puncto illius partis ꝙ̄ ille punctus moue­
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                  tur. </s>
                  <s xml:id="N1B59B" xml:space="preserve">Alias em̄ non continuo b. potentia intenderet
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                  motum ſuū illam partē tranſeundo. </s>
                  <s xml:id="N1B5A0" xml:space="preserve">Et ex alia par­
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                  te ipſa potentia b. per te continuo remittit motum
                    <lb/>
                  ſuū per illam reſiſtentiã vel aliquã eius partē mo-
                    <lb/>
                  uendo: igitur tunc ipſa potentia b. nõ continuo per
                    <lb/>
                  illam partē mouendo tardius mouetur cum quoli­
                    <lb/>
                  bet puncto illius partis quã ille punctus mouetur:
                    <lb/>
                  ſed cõſequens eſt falſum. </s>
                  <s xml:id="N1B5AF" xml:space="preserve">q2 antea quilibet punctus
                    <lb/>
                  illius partis tardius mouebatur quã potentia b.
                    <lb/>
                  ſufficit moueri cū illo: igitur etiam modo cū conti-
                    <lb/>
                  nuo quilibet punctus motum ſuum remittat. </s>
                  <s xml:id="N1B5B8" xml:space="preserve">Et ſic
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                  ptꝫ ſecunda pars minoris. </s>
                  <s xml:id="N1B5BD" xml:space="preserve">Sed iam tertia ꝓbatur
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                  videlicet /  b. potentia nõ aliquãdo remittit motū
                    <lb/>
                  ſuū, et immediate poſtea intendit, quia ſi ſic detur
                    <lb/>
                  inſtans in quo incipit intendere poſt̄ remittebat /
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                  et arguo ſic, quia tunc vel b. potentia continuo an-
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                  tea remittebat, vel aliquando intendebat et īmedia­
                    <lb/>
                  te remittebat (cum nun̄ poſſit vniformiter moueri
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                  ex ſecundo correlario prime concluſionis) non pri-
                    <lb/>
                  mū / vt ptꝫ ex prima parte minoris nec ſecundum / vt
                    <lb/>
                  patet ex ſecunda: igitur b. potentia nõ aliquãdo re­
                    <lb/>
                  mittit motum ſuum, et immediate poſtea intendit /
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                  quod fuit probandum. </s>
                  <s xml:id="N1B5D6" xml:space="preserve">Et ſic patet tertia pars mi-
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                  noris et ex hoc tota concluſio.
                    <note position="left" xlink:href="note-0117-01a" xlink:label="note-0117-01" xml:id="N1B627" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N1B5E0" xml:space="preserve">¶ Ex quo ſequitur
                    <cb chead="Capitulū quartūdecimū."/>
                  primo /  vbi in medio non reſiſtente eſt progreſſio
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                  ſiue extenſio latitudinis reſiſtentie vniformiter dif­
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                  formis in vtro extremo ad gradum terminate,
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                  quolibet eius puncto intrinſeco continuo remitten­
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                  te motum ſuum, quieſcente extremo intenſiori: et re­
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                  miſſiori velocius incipiente moueri quã mobile qḋ
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                  in tali reſiſtentia mouetur ſufficit mouere cum illo
                    <lb/>
                  et extremo remiſſiori remittente motum ſnū ad non
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                  gradum vel vſ ad motum prouenientē a propor-
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                  tione a qua incipit tale mobile moueri continuo in­
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                  tendēs motū ſuū īcluſiue, vel ad minorē: tandē mo-
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                  bile illud ad eodem puncto cum tali reſiſtentia in-
                    <lb/>
                  cipiens progredi deueniet ad extremum remiſſiſſi-
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                  mum eiuſdeꝫ latitudinis: dummodo ipſum mobile
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                  continuo / quo ad vſ reſiſtentiã inuenerit moueat̄̄.
                    <lb/>
                  </s>
                  <s xml:id="N1B603" xml:space="preserve">Probatur correlarium / quoniam ſi extremum re-
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                  miſſius illius reſiſtentie remittat motum ſuum ad
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                  non gradum, vel ad motum illum a quo incipit b.
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                  potentia in caſu concluſionis moueri intendendo
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                  motum ſuum, vel ad minorē ſequitur / cum b. poten-
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                  tia a motu a quo incipit moueri continuo intendit
                    <lb/>
                  motum ſuum  cum extremum remiſſius illius re-
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                  ſiſtentie remiſerit ſuum motum ad motum a quo b.
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                  potentia incipit moueri, vel ad minorem, b. poten-
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                  tia in certa proportione continuo velocius moue-
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                  tur ꝙ̄ extremum remiſſius illius reſiſtentie cõtinuo
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                  illud extremum inſequendo, et per conſequens tan-
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                  dem in tempore finito illud extremū attinget / quod
                    <lb/>
                  fuit probandum. </s>
                  <s xml:id="N1B620" xml:space="preserve">Patet igitur correlarium.</s>
                </p>
                <note position="right" xml:id="N1B62D" xml:space="preserve">2. correĺ.</note>
                <p xml:id="N1B631">
                  <s xml:id="N1B632" xml:space="preserve">¶ Sequitur ſecundo /  illud idem dici poteſt de re-
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                  ſiſtentia difformi cuius nulla pars eſt vniformis,
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                  cuiuſ omnes partes īmediate ſecundum extenſio­
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                  nem ſunt immediate ſeundum intenſionem, vtrin
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                  ad gradum terminata / quod de reſiſtentia vnifor-
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                  miter difformi etc̈. dictum eſt in hac concluſione et
                    <lb/>
                  ſuo correlario. </s>
                  <s xml:id="N1B641" xml:space="preserve">Hoc patet ex probatione cõcluſiõis
                    <lb/>
                  et ſui correlarii.
                    <note position="right" xlink:href="note-0117-02a" xlink:label="note-0117-02" xml:id="N1B674" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N1B64B" xml:space="preserve">¶ Ex his omnibus concluſionibus
                    <lb/>
                  ſequitur tertio /  quãuis ita ſit vt in concluſiõibus
                    <lb/>
                  ponitur quando ſimul ab eodem puncto in eodem
                    <lb/>
                  inſtanti per eandem lineam potentia et talis latitu­
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                  do reſiſtentie incipiūt progredi ſiue moueri verſus
                    <lb/>
                  idem punctum: nõ tamen quando potentia incipe-
                    <lb/>
                  ret moueri quãdo illa latitudo iam mouetur. </s>
                  <s xml:id="N1B65A" xml:space="preserve">Tunc
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                  enim in caſu quarte concluſionis poſſet ipſa poten­
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                  tia intendere motum ſuum, et in caſu quinte conclu­
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                  ſionis remittere. </s>
                  <s xml:id="N1B663" xml:space="preserve">Patet hoc facile / quoniam poſſet
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                  pro aliquo inſtanti poni violenter in aliquo pūcto
                    <lb/>
                  quod velocius mouetur quã potentia ſufficiat mo-
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                  ueri cum illo, vel in puncto quod tardius mouetur
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                  quam potentia ſufficit adequate mouere cum illo
                    <lb/>
                  et ſic indifferenter intendet motum ſuū vel remittet</s>
                </p>
              </div>
              <div xml:id="N1B67A" level="4" n="14" type="chapter" type-free="capitulum">
                <head xml:id="N1B67F" xml:space="preserve">Quartumdecimum capitulum: in
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                quo ponuntur concluſiones de velo-
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                citate motus in medio non reſiſtente,
                  <lb/>
                in quo eſt progreſſio ſiue extenſio la-
                  <lb/>
                titudinis reſiſtentie nõ gradu aut ex­
                  <lb/>
                tremo remiſſiori quieſcente inſequē-
                  <lb/>
                do ordinem et modum calculatoris.</head>
                <p xml:id="N1B68E">
                  <s xml:id="N1B68F" xml:space="preserve">Expeditis concluſionibus de ve-
                    <lb/>
                  locitate motus in medio non reſiſtente in
                    <lb/>
                  quo eſt progreſſio latitudinis reſiſtentie
                    <lb/>
                  vniformiter difformis quieſcente extremo intenſio­
                    <lb/>
                  ri. </s>
                  <s xml:id="N1B69A" xml:space="preserve">Iam reſtat inducere concluſiones de eadem ma­
                    <lb/>
                  teria quieſcente non gradu aut extremo remiſſiori
                    <lb/>
                  </s>
                  <s xml:id="N1B6A0" xml:space="preserve">Quibus inducendis aliquas ſolito more ſuppoſi-
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                  tionis premittam.</s>
                </p>
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