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="N19FD6" level="4" n="11" type="chapter" type-free="capitulum">
                <p xml:id="N1A719">
                  <s xml:id="N1A74F" xml:space="preserve">
                    <pb chead="De motu penes cauſã in medio vniformiṫ difformi īuariato." file="0108" n="108"/>
                  pars correlarii patet ex prima parte eiuſdem, et ex
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                  prima concluſione huius. </s>
                  <s xml:id="N1A759" xml:space="preserve">Et ſic patet correlarium.
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                  </s>
                  <s xml:id="N1A75D" xml:space="preserve">¶ Innumera poteris ſtudio ſe lector proprio labo-
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                  re his ſimilia inferre correlaria.</s>
                </p>
                <note position="left" xml:id="N1A762" xml:space="preserve">Octaua
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                cõcluſio
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                calcula.</note>
                <p xml:id="N1A76A">
                  <s xml:id="N1A76B" xml:space="preserve">Quinta cõcluſio. </s>
                  <s xml:id="N1A76E" xml:space="preserve">Duabus potentiis
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                  aliquod medium vniformiter difforme ad nõ gra-
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                  dum terminatum tranſeundo vniformiter cõtinuo
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                  mouentibus, vna altera velocius continuo creſcē­
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                  te in ea proportione que proportionem a qua mo-
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                  uetur altera per proportionem duplam excedit: po­
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                  tentia que velocius continuo creſcit velocius conti-
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                  nuo mouetur in proportione dupla ipſa potentia
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                  minore. </s>
                  <s xml:id="N1A781" xml:space="preserve">Probatur / ſit a. potentia que c. mediū .etc̈.
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                  tranſeundo continuo mouetur ab f. proportione ꝑ
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                  ſui a non gradu potentie continuū et vniforme cre-
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                  mentum: ſit h. proportio que f. proportionem ex-
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                  cedat per proportionem duplam, et ſit b. potentia
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                  que idem c. medium tranſeundo a nõ gradu poten-
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                  tie cõtinuo in h. proportione velocius creſcat quaꝫ
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                  a. potentia: tunc dico /  b. potentia continuo in du­
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                  plo velocius mouetur a. potētia minore. </s>
                  <s xml:id="N1A794" xml:space="preserve">Quod ſic
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                  probatur / quia b. mouetur velocius a. / vt conſtat, et
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                  non mouetur velocius in maiori proportione quã
                    <lb/>
                  dupla, nec in minori: igitur b. mouetur adequate ī
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                  duplo velocius: quod fuit probandū. </s>
                  <s xml:id="N1A79F" xml:space="preserve">Conſequen-
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                  tia ptꝫ cum maiore, et prima pars minoris proba-
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                  tur / quia ſi b. mouetur in maiori proportiõe quam
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                  dupla velocius ipſa potentia a. / ſequitur /  reſiſten­
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                  tie ipſius b. ad reſiſtentiã ipſius a. eſt maior quam
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                  dupla et proportio ipſius b. ad reſiſtentiam ipſius
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                  a. componitur adequate ex duplici f. et proportiõe
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                  dupla: igitur demendo a proportione ipſius b. ad
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                  reſiſtentiam ipſius a. proportionem que eſt reſiſten­
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                  tie ipſius b. ad reſiſtentiam ipſius a. non manet du­
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                  plex f. ſed minus. </s>
                  <s xml:id="N1A7B6" xml:space="preserve">Patet cõſequētia / quia per te pro­
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                  portio reſiſtentie ipſius b. ad reſiſtentiã ipſius a. eſt
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                  maior quam ſit proportio dupla: et vltra demendo
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                  a proportione ipſius b. ad reſiſtentiã ipſius a. pro-
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                  portionē que eſt reſiſtentie ipſius b. ad reſiſtentiaꝫ
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                  ipſius a. nõ manet duplex f. ſed minus, et demendo
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                  a proportione ipſius b. ad reſiſtentiã ipſius a. pro-
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                  portionem que eſt reſiſtentie ipſius b. ad reſiſtentiã
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                  ipſius a. non manet niſi proportio que eſt ipſius b.
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                  ad reſiſtentiam eiuſdem b. / igitur proportio que eſt
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                  ipſius b. ad reſiſtentiam eiuſdem b. nõ eſt duplex f.
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                  ſed minus, et ab illa proportione continuo b. poten­
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                  tia mouetur: igitur continuo b. mouetur a propor-
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                  tione que nõ eſt duplex f. ſed minus: et a. potentia cõ­
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                  tinuo mouetur ab f. proportione: igitur b. potētia
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                  mouetur velocius a. in minori proportione quam
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                  dupla: et per conſequens nõ in maiori proportione
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                  quam dupla: quod fuit probandū. </s>
                  <s xml:id="N1A7DB" xml:space="preserve">Sed  propor-
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                  tio ipſius b. ad reſiſtentiam ipſius a. componitur
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                  adequate ex duplici f. et proportione dupla: patet /
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                  quia proportio ipſius b. ad reſiſtentiam ipſius a.
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                  cõponitur adequate ex proportione h. que eſt ipſiꝰ
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                  b. ad ipſum a. et ex proportiõe f. que eſt ipſius a. ad
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                  reſiſtentiam ipſius a. / vt conſtat. </s>
                  <s xml:id="N1A7EA" xml:space="preserve">et proportio h. eſt
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                  vnū f. et proportio dupla adequate / vt ptꝫ: q2 h. exce­
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                  dit f. per duplam proportionem adequate ex hypo­
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                  theſi: igitur proportio ipſius b. ad reſiſtentiam ip-
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                  ſius a. cõponitur adequate ex duplici f. et ex propor­
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                  tione dupla / quod fuit probandum. </s>
                  <s xml:id="N1A7F7" xml:space="preserve">Et ſic patet pri­
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                  ma pars minoris. </s>
                  <s xml:id="N1A7FC" xml:space="preserve">Iam probatur ſecunda pars mi­
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                  noris videlicet /  b. nõ mouetur velocius a. in mino­
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                  ri proportione quam dupla: quia ſi b. mouetur ve-
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                  locius a. in minori proportione quam dupla: ſequi­
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                  tur /  continuo reſiſtentie ipſius b. ad reſiſtentiam
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                  ipſius a. eſt minor preportio ꝙ̄ dupla proportio, et
                    <cb chead="De motu penes cauſã in medio vniformiṫ difformi īuariato."/>
                  vltra reſiſtentie ipſius b. ad reſiſtentiam ipſius a. cõ­
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                  tinuo eſt minor proportio ꝙ̄ dupla: et proportio ip­
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                  ſius b. ad reſiſtentiam ipſius a. cõponitur adequa-
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                  te ex duplici f. et ex proportione dupla / vt ſupra ar-
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                  gutum eſt: igitur demendo a proportione ipſius b.
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                  ad reſiſtentiam ipſius a. proportionem que eſt reſi­
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                  ſtentie ipſius b. ad reſiſtentiam ipſius a. manet ma­
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                  gis quam duplex f. </s>
                  <s xml:id="N1A81A" xml:space="preserve">Patet cõſequentia / quia per te
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                  proportio que eſt reſiſtentie ipſius b. ad reſiſtentiã
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                  ipſius a. eſt minor proportio quam dupla: et vltra
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                  demendo a proportione ipſius b. ad reſiſtentiã ip-
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                  ſius a. proportionem que eſt reſiſtentie ipſius b. ad
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                  reſiſtentiam ipſius a. manet magis quam duplex f.
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                  et demendo a proportione ipſius b. ad reſiſtentiam
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                  ipſius a. proportionem que eſt reſiſtentie ipſius b.
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                  ad reſiſtentiam ipſius a. manet proportio ipſius b.
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                  ad reſiſtentiam eiuſdem b. / igitur proportio b. ad re­
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                  ſiſtentiam eiuſdem b. eſt maior quam duplex f. et ab
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                  illa proportione b. potentia continuo mouetur: igi­
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                  tur b. continuo mouetur a maiori proportione quã
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                  dupla ad f. et a. potentia cõtinuo mouetur ab f. pro­
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                  portione: igitur b. continuo mouetur velocius a. in
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                  maiori proportione quam dupla: et per conſequēs
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                  non mouetur velocius in minori proportione quaꝫ
                    <lb/>
                  dupla / quod fuit probanduꝫ. </s>
                  <s xml:id="N1A83F" xml:space="preserve">Et ſic patet concluſio /
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                  que eſt octaua concluſio calculatoris in ſecundo ca­
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                  pite de medio non reſiſtente.
                    <note position="right" xlink:href="note-0108-01a" xlink:label="note-0108-01" xml:id="N1A8B9" xml:space="preserve">1. correl.</note>
                  </s>
                  <s xml:id="N1A84B" xml:space="preserve">¶ Ex quo ſequitur pri-
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                  mo /  ſi in caſu cõcluſionis a. potentia cõtinuo mo-
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                  ueatur a proportione ſexquialtera: et b. potētia ma­
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                  ior creſcat in triplo velocius continuo ipſa a. potē-
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                  tia minore: ipſa potentia b. mouetur cõtinuo in du-
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                  plo velocius a. potētia minore. </s>
                  <s xml:id="N1A858" xml:space="preserve">Probatur / quia tri­
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                  pla excedit ſexquialteram per duplam / vt patet ex
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                  quarta concluſione quarti capitis ſecunde partis /
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                  igitur ex hac concluſione ſequitur /  ſi a. potentia
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                  minor moueatur a proportione ſexquialtera, et b.
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                  potentia maior creſcat in triplo velocius  b. potē­
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                  tia maior mouetur cõtinuo in duplo velocius a. po­
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                  tentia minore / quod fuit probandum.
                    <note position="right" xlink:href="note-0108-02a" xlink:label="note-0108-02" xml:id="N1A8BF" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N1A86E" xml:space="preserve">¶ Sequitur
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                  ſecundo /  ſi a. potentia minor moueatur a. propor­
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                  tione dupla, et b. potentia maior creſcat in quadru­
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                  plo velocius continuo: ipſa potentia b. mouetur cõ­
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                  tinuo in duplo velocius a. potentia minore. </s>
                  <s xml:id="N1A879" xml:space="preserve">Patet /
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                  quia quadrupla excedit duplam per duplam / vt ptꝫ
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                  ex quarta concluſione preallegata igitur
                    <note position="right" xlink:href="note-0108-03a" xlink:label="note-0108-03" xml:id="N1A8C5" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N1A885" xml:space="preserve">¶ Sequit̄̄
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                  tertio /  ſi a. potētia minor moueatur a proportiõe
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                  quadrupla et b. potentia maior creſcat in octuplo
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                  velocius: tunc b. potentia maior mouetur continuo
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                  in duplo velocius. </s>
                  <s xml:id="N1A890" xml:space="preserve">Patet / quia octupla quadruplã
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                  per duplam excedit / vt patet ex quarta concluſione
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                  preallegata.
                    <note position="right" xlink:href="note-0108-04a" xlink:label="note-0108-04" xml:id="N1A8CB" xml:space="preserve">4. correĺ.</note>
                  </s>
                  <s xml:id="N1A89C" xml:space="preserve">¶ Sequitur quarto /  ſi a. potentia
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                  minor moueatur cõtinuo a proportione ſexquiter-
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                  tia et b. potentia maior continuo creſcat in propor­
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                  tione dupla ſuprabipartiēte tertias velociꝰ b. potē­
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                  tia maior mouetur cõtinuo in duplo velocius. </s>
                  <s xml:id="N1A8A7" xml:space="preserve">Ptꝫ /
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                  quia dupla ſuprabipartiens tertias ſexquitertiaꝫ
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                  per duplam excedit / vt patet ex quarta concluſione
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                  preallegata. </s>
                  <s xml:id="N1A8B0" xml:space="preserve">Et iſto modo infinita talia correlaria
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                  poteris inferre,</s>
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              <div xml:id="N1A8D1" level="4" n="12" type="chapter" type-free="capitulum">
                <head xml:id="N1A8D6" xml:space="preserve">Capitulum duodecimum: aliqui-
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                bus predictarum concluſionum pre-
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                cedentium capitum obiiciens.</head>
                <p xml:id="N1A8DD">
                  <s xml:id="N1A8DE" xml:space="preserve">HIs concluſionibus velocitatē
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                  motus in medio vniformiter difformi in-
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                  uariato declarantibus (vt potuimus) ali-
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                  qua ex parte expeditis: nunc opere precium eſt lima
                    <lb/>
                  diſputationis ea que dicta ſunt polire at limare.</s>
                </p>
                <p xml:id="N1A8E9">
                  <s xml:id="N1A8EA" xml:space="preserve">Et ideo ſecūde concluſioni decimi ca- </s>
                </p>
              </div>
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