Alvarus, Thomas, Liber de triplici motu, 1509

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              <div xml:id="N19FD6" level="4" n="11" type="chapter" type-free="capitulum">
                <p xml:id="N1A28C">
                  <s xml:id="N1A29B" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0105" n="105"/>
                  prapartiente velocius: vel in aliqua proportione
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                  irrationali. </s>
                  <s xml:id="N1A2A5" xml:space="preserve">Et ſi queras in qua proportione ſupra­
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                  partiente vel irrationali.</s>
                </p>
                <note position="left" xml:id="N1A2AA" xml:space="preserve">calcu. ī 2.
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                capite de
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                medio nõ
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                reſiſtēte.</note>
                <p xml:id="N1A2B4">
                  <s xml:id="N1A2B5" xml:space="preserve">Reſpondeo et dico ſecundo / cum calcu­
                    <lb/>
                  latore in calce ſexte concluſionis ſecundi capitis de
                    <lb/>
                  medio non reſiſtente  id īquirere maiori egeret ſtu­
                    <lb/>
                  dio quaꝫ vtilitatem afferret.
                    <note position="left" xlink:href="note-0105-01a" xlink:label="note-0105-01" xml:id="N1A2D0" xml:space="preserve">hiero. 37.
                      <lb/>
                    d. c. nõne.</note>
                  </s>
                  <s xml:id="N1A2C3" xml:space="preserve">Et vt beato hieronimo
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                  placet noctibus diebuſ ad id excogitandum tor-
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                  queri at incomprehenſibili chaos immergi eſt in
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                  obſcuritate mentis ambulare.</s>
                </p>
                <p xml:id="N1A2D8">
                  <s xml:id="N1A2D9" xml:space="preserve">Secunda concluſio </s>
                  <s xml:id="N1A2DC" xml:space="preserve">Duabus poten-
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                  tiis aliquod medium vniformiter difforme ad non
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                  gradum terminatum tranſeundo vniformiter con­
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                  tinuo mouentibus per earum a non gradu poten-
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                  tie vniforme et continuum crementum: vna velociꝰ
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                  continuo ꝙ̄ altera creſcente in proportione maio-
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                  ri in ea proportione a qua altera continuo moue-
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                  tur: potentia que velocius continuo creſcit: velociꝰ
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                  continuo mouetur in ea proportione a qua moue-
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                  tur altera. </s>
                  <s xml:id="N1A2F1" xml:space="preserve">Probatur / ſit a. poña que c. medium vni­
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                  formiter difforme terminatum ad non graduꝫ trã­
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                  ſeundo vniformiter continuo mouetur ab f. ꝓpor-
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                  tione per ſue potentie a non gradu vniforme et con­
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                  tinuum crementum ſit .h. proportio maior f. ꝓpor­
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                  tione in ipſamet f. ꝓportiõe: et ſit b. poña que idem
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                  medium pertranſeundo vniformiter continuo mo-
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                  uetur creſcens continuo in h. ꝓportione velociꝰ: tūc
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                  dico /  b. poña continuo velocius mouetur ꝙ̄ a. po-
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                  tentia (velocius inquam in ꝓportione f.) </s>
                  <s xml:id="N1A306" xml:space="preserve">Quod ſic
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                  probatur / quia b. continuo mouetur velocius ipſa
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                  a. potentia in certa proportiõe (vt patet ex dictis) /
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                  et non continuo mouetur velocius in maiori ꝓpor-
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                  tione quaꝫ ſit f. nec in minori: igitur b. continuo mo­
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                  uetur in f. proportione velocius. </s>
                  <s xml:id="N1A313" xml:space="preserve">Conſequentia ē no­
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                  ta cum maiore: et probatur prima pars minoris vi­
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                  delicet /  b. non mouetur in maiori ꝓportione quã
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                  ſit f. velocius: quia ſi b. mouetur velocius ꝙ̄ a. ī ma­
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                  iori ꝓportione quam ſit f. / ſequitur /  reſiſtentie ip-
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                  ſius b. ad reſiſtentiam ipſius a. eſt maior proportio
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                  quam ſit f. </s>
                  <s xml:id="N1A322" xml:space="preserve">Patet conſequentia / quia c. medium eſt
                    <lb/>
                  vniformiter difforme ad non gradum terminatum
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                  et vltra reſiſtentie ipſius b. ad reſiſtentiaꝫ ipſius a.
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                  eſt maior proportio ꝙ̄ ſit f. / ergo ipſius b. ad reſiſtē­
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                  tiam ipſius b. eſt minor ꝓportio ꝙ̄ ſit h.</s>
                </p>
                <p xml:id="N1A32D">
                  <s xml:id="N1A32E" xml:space="preserve">Patet hec conſequentia / quia ipſius a. ad reſiſten-
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                  tiam eiuſdem a. eſt proportio f. (ex hypotheſi) et re­
                    <lb/>
                  ſiſtentie ipſius b. ad reſiſtentiam ipſius a. eſt ma-
                    <lb/>
                  ior proportio quam ſit f. / ergo maior eſt reſiſten-
                    <lb/>
                  tia ipſius b. quam ipſa potentia a. </s>
                  <s xml:id="N1A339" xml:space="preserve">Patet conſeq̄n­
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                  tia / quia reſiſtentia ipſius b. habet maiorem ꝓpor-
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                  tionem ad vnum tertium puta ad reſiſtentiam ipſi-
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                  us a. quam a. potentia habeat ad idem tertium. </s>
                  <s xml:id="N1A342" xml:space="preserve">Et
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                  vltra maior eſt reſiſtentia ipſius b. quam ipſa a. po­
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                  tentia. </s>
                  <s xml:id="N1A349" xml:space="preserve">et b. habet h. proportionem ad a. potentiam /
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                  ergo b. habet minorem ꝓportionem quam h. ad re­
                    <lb/>
                  ſiſtentiam eiuſdem b. / et per conſequens b. mouetur
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                  continuo a minori proportione quam h. et h. ꝓpor­
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                  tio eſt in f. proportione maior quaꝫ ſit f. proportio
                    <lb/>
                  (vt patet ex hypotheſi) / ergo b. continuo mouetur in
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                  minori proportione velocius quam ſit f. proportio
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                  et ſic non mouetur in maiori proportione velocius
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                  a. quam ſit f. ꝓportio / quod fuit ꝓbandum. </s>
                  <s xml:id="N1A35C" xml:space="preserve">Sed iaꝫ
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                  probo ſecundam partem minoris videlicet /  b. nõ
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                  mouetur velocius ꝙ̄ a. in minori ꝓportione quam
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                  ſit f. quia ſi mouetur in minori ꝓportione quam ſit
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                  f. velocius / ſequitur /  continuo reſiſtentie ipſius b.
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                  ad reſiſtētiã ipſiꝰ a. ē minor ꝓportio quã ſit f. ex cor­
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                  relario ſuppoſitionis et vltra continuo reſiſtentie
                    <cb chead="Capitulum vndecimum"/>
                  ipſius b. ad reſiſtentiam ipſius a. eſt minor propor­
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                  tio quam ſit f. et b. ad a. habet proportionem h. / igi-
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                  tur b. habet ad reſiſtentiam ipſius b. maiorem pro­
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                  portionem quam ſit h. </s>
                  <s xml:id="N1A374" xml:space="preserve">Patet conſequentia / q2 reſi­
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                  ſtentia ipſius b. eſt minor quam a. potentia. </s>
                  <s xml:id="N1A379" xml:space="preserve">Sed 
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                  a. poña ſit maior ꝙ̄ reſiſtentia ipſius b. / patet / quia
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                  a. habet maiorem proportionem ad ſuam reſiſten-
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                  tiam quam reſiſtentia ipſius b. habeat ad eandē re­
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                  ſiſtentiam ipſius a. (cum a. ad ſuam reſiſtentiaꝫ ha­
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                  beat f. proportionem: reſiſtentia autem ipſius b. ad
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                  eandem reſiſtentiam per te minorem) / igitur ipſa a.
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                  potentia maior eſt quam reſiſtentia ipſius b. </s>
                  <s xml:id="N1A38A" xml:space="preserve">Pa-
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                  tet conſequentia per hanc maximam quod habet
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                  maiorem proportionem ad vnum tertium eſt maiꝰ
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                  </s>
                  <s xml:id="N1A392" xml:space="preserve">Et vltra ex illo conſequenti b. habet maiorem pro-
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                  portionem ad reſiſtentiaꝫ ipſius b. quam ſit h. et b.
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                  mouetur continuo ab illa proportione quam ſemel
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                  habet ad ſuam reſiſtentiam (quia continuo vnifor-
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                  miter) et h. proportio eſt in f. proportione maior ip­
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                  ſa f. proportione ex hypotheſi: igitur ꝓportio a q̈
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                  mouetur b. eſt maior ipſa proportione f. in maiori
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                  proportione ꝙ̄ ſit f. / et per conſequens b. non moue-
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                  tur in minori proportione velocius a. quam ſit f. / qḋ
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                  fuit probandum: et ſic patet minor: et per conſequēs
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                  tota concluſio.
                    <note position="right" xlink:href="note-0105-02a" xlink:label="note-0105-02" xml:id="N1A426" xml:space="preserve">1. correl.</note>
                  </s>
                  <s xml:id="N1A3AE" xml:space="preserve">¶ Ex quo ſequitur primo /  ſi a. po-
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                  tentia continuo moueatur a proportione tripla etc.
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                  et b. a non gradu potentie idem medium tranſeun-
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                  do continuo creſcat velocius in proportione vicecu­
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                  pla ſeptupla qualis eſt .27. ad .1. / tunc ipſa b. poten-
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                  tia maior mouetur continuo in triplo velocius ip-
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                  ſa a. potentia minore. </s>
                  <s xml:id="N1A3BD" xml:space="preserve">Probatur / quia ꝓportio in
                    <lb/>
                  qua b. potentia maior velociꝰ creſcit a. potentia mi­
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                  nore eſt tripla ad proportionem a qua mouetur a.
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                  potentia minor: et a. potentia minor mouetur a tri­
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                  pla proportione: igitur b. potentia maior mouetur
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                  continuo in triplo velocius a. potentia minore / qḋ
                    <lb/>
                  eſt probandum </s>
                  <s xml:id="N1A3CC" xml:space="preserve">Patet conſequentia ex concluſio-
                    <lb/>
                  ne.
                    <note position="right" xlink:href="note-0105-03a" xlink:label="note-0105-03" xml:id="N1A42C" xml:space="preserve">2. correl.</note>
                  </s>
                  <s xml:id="N1A3D6" xml:space="preserve">¶ Sequitur ſecundo /  ſi a. potentia minor mo-
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                  ueatur a proportione quadrupla in caſu concluſio­
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                  nis: et b. poña maior creſcat continuo velocius in ꝓ­
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                  portione ducentecupla quingecupla ſextupla qua­
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                  lis eſt proportio .256. ad .1. / tunc b. potentia maior
                    <lb/>
                  mouebitur in quadruplo velocius adequate. </s>
                  <s xml:id="N1A3E3" xml:space="preserve">Pro-
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                  batur / quia ꝓportio in qua b. poña maior creſcit ve­
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                  locius a. potentia minore eſt quadrupla ad propor­
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                  tionem a qua mouetur a. poña minor: et ꝓportio a
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                  qua mouetur a. poña minor eſt quadrupla: ergo b.
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                  poña maior mouetur in quadruplo velocius b. po-
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                  tentia minore / quod eſt probandum. </s>
                  <s xml:id="N1A3F2" xml:space="preserve">Patet conſe-
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                  quentia ex hac concluſione. </s>
                  <s xml:id="N1A3F7" xml:space="preserve">Et ſic patet correlariuꝫ
                    <lb/>
                    <note position="right" xlink:href="note-0105-04a" xlink:label="note-0105-04" xml:id="N1A432" xml:space="preserve">3. correl.</note>
                  </s>
                  <s xml:id="N1A401" xml:space="preserve">¶ Sequitur tertio /  ſi a. potentia minor in caſu cõ­
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                  cluſionis moueatur continuo ab illa ꝓportione ir­
                    <lb/>
                  rationali que eſt ſexquialtera ad duplam que voce­
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                  tur h. et b. poña maior creſcat velocius continuo a.
                    <lb/>
                  potentia minore in proportione k. irrationali que
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                  ſe habeat ad proportionem h. in ipſa h. proportio­
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                  ne que eſt ſexquialtera ad duplam / tunc b. potentia
                    <lb/>
                  maior mouebitur velocius ipſa a. poña minore in ꝓ­
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                  portione h. que eſt ſexquialtera ad duplam. </s>
                  <s xml:id="N1A414" xml:space="preserve">Patet
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                  hoc correlarium facile ex concluſione et probatione
                    <lb/>
                  eius que vniuerſalis eſt. </s>
                  <s xml:id="N1A41B" xml:space="preserve">¶ Et ſic poteris inferre pro­
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                  prio labore quotcun velis ſimilia correlaria ſecū­
                    <lb/>
                  da parte huius operis intellecta.</s>
                </p>
                <p xml:id="N1A438">
                  <s xml:id="N1A439" xml:space="preserve">Tertia concluſio </s>
                  <s xml:id="N1A43C" xml:space="preserve">Duabus potentiis
                    <lb/>
                  aliquod medium vniformiter difforme ad nõ gra-
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                  dum terminatum tranſeundo vniformiter cõtinuo
                    <lb/>
                  mouentibus per earum a non gradu poñe vnifor-
                    <lb/>
                  me et continuum crementum, vna altera in maio- </s>
                </p>
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