Alvarus, Thomas, Liber de triplici motu, 1509

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                <p xml:id="N1AA6F">
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                    <pb chead="De motu penes cauſã in medio vniformiṫ difformi īuariato." file="0110" n="110"/>
                  et reſiſtentie equales) equalem ꝓportionem habe-
                    <lb/>
                  rent: et cum cõtinuo mouentur vniformiter / vt dicit
                    <lb/>
                  concluſio quam impugnamus: ſequitur /  ſemper
                    <lb/>
                  antea habebant equalem ꝓportionem qualem ha­
                    <lb/>
                  bent in termino motus: et per cõſequens ſemꝑ equa­
                    <lb/>
                  liter mouebūtur: quod eſt contra ſolutionem.</s>
                </p>
                <p xml:id="N1AAB0">
                  <s xml:id="N1AAB1" xml:space="preserve">Reſpondeo negando ſequelam et ad
                    <lb/>
                  ꝓbationem dico /  quãuis ſemper in medio mino-
                    <lb/>
                  ri ceteris paribus qualificato conſimili reſiſtentia
                    <lb/>
                  vniformiter difformi, eadem vel cõſimilis potētia
                    <lb/>
                  tardius moueatur: nõ tamen tardius in ea ꝓporti-
                    <lb/>
                  one qua eſt minus: immo in minori tardius. </s>
                  <s xml:id="N1AABE" xml:space="preserve">Ita 
                    <lb/>
                  ſemper eadem potentia citius pertranſibit minus
                    <lb/>
                  medium quam maius: dummodo talia media ſint
                    <lb/>
                  qualificata eadem vel cõſimili qualitate vniformi-
                    <lb/>
                  ter difformi. </s>
                  <s xml:id="N1AAC9" xml:space="preserve">Quod ſic ptꝫ / quia a. potentia nõ põt
                    <lb/>
                  eque cito pertranſire mediū maius ſicut b. medium
                    <lb/>
                  minus: vt nuperrime ꝓbatum eſt, nec citius: q2 tūc
                    <lb/>
                  a minori ꝓportione moueretur a. quam b. et per cõ­
                    <lb/>
                  ſequens tardius quod eſt cõtra principalē ſolutio-
                    <lb/>
                  nē. </s>
                  <s xml:id="N1AAD6" xml:space="preserve">Sequela tamen ptꝫ / quia quando a. eſſet cum re­
                    <lb/>
                  ſiſtentia vt .8. potentia b. ei equalis eſſet cum mino­
                    <lb/>
                  ri reſiſtentia cum adhuc nõ eſſet in fine per te. </s>
                  <s xml:id="N1AADD" xml:space="preserve">Qua­
                    <lb/>
                  re cõcedendum eſt /  ſemper pertranſitur citius me­
                    <lb/>
                  dium minus quã maius in caſu poſito.</s>
                </p>
                <p xml:id="N1AAE4">
                  <s xml:id="N1AAE5" xml:space="preserve">Sed contra / quia tunc ſequeretur hec
                    <lb/>
                  concluſio /  infinite potentie darentur equales po­
                    <lb/>
                  tentie a. que inciperent ſimul moueri cum potentia
                    <lb/>
                  a. per media qualificata eadē vel conſimili qualita­
                    <lb/>
                  te vniformiter difformi: et in infinitum tardius con­
                    <lb/>
                  tinuo moueretur vnū illorum quam a. et tamen que­
                    <lb/>
                  libet aliarum potentiarum citius pertranſibit me­
                    <lb/>
                  dium ſuū ꝙ̄ a. / ſed conſequens videtur impoſſibile:
                    <lb/>
                  igitur illud ex quo ſequitur. </s>
                  <s xml:id="N1AAF8" xml:space="preserve">Sequela probatur et
                    <lb/>
                  pono caſum /  ſit vnū pedale / per quod extendatur
                    <lb/>
                  latitudo reſiſtentie vniformiter difformis a nõ gra­
                    <lb/>
                  du vſ ad octauū / vt dictum eſt ſupra: et ſit aliud in
                    <lb/>
                  duplo minus, et aliud in triplo, et aliud in quadru-
                    <lb/>
                  plo, et ſic in infinitum: et per quodlibet illorum extē­
                    <lb/>
                  datur eadem vel conſimilis latitudo reſiſtentie vni­
                    <lb/>
                  formiter difformis a nõ gradu vſ ad octauū: et in
                    <lb/>
                  aliquo inſtanti incipiat a. creſcēdo a nõ gradu po-
                    <lb/>
                  tentie moueri cõtinuo a ꝓportione dupla per me-
                    <lb/>
                  dium pedale: et in quolibet aliorum mediorum inci­
                    <lb/>
                  piat in eodem inſtanti etiam conſimilis potentia
                    <lb/>
                  conſimiliter oīno creſcens moueri a nõ gradu reſi-
                    <lb/>
                  ſtentie: ita  quelibet maneat cõtinuo equalis ipſi
                    <lb/>
                  a. </s>
                  <s xml:id="N1AB17" xml:space="preserve">Quo poſito patꝫ ſecunda pars illati videlicet / 
                    <lb/>
                  quelibet aliarum potentiarū ab a. citius pertran-
                    <lb/>
                  ſibit medium ſuū quam a. </s>
                  <s xml:id="N1AB1E" xml:space="preserve">Hoc em̄ dicit ſolutio pre­
                    <lb/>
                  cedentis replice. </s>
                  <s xml:id="N1AB23" xml:space="preserve">Et arguitur prima pars videlicet /
                    <lb/>
                   in infinitum tardius continuo mouetur aliqua il­
                    <lb/>
                  larum quam a. / quia citius a. preteribit punctū me-
                    <lb/>
                  diū illiꝰ pedalis per quod mouetur hoc eſt punctuꝫ
                    <lb/>
                  vt .4. quam aliqua aliarū potentiarū pertranſibit
                    <lb/>
                  ſuū mediū per quod ipſum mouetur: et in infinituꝫ
                    <lb/>
                  minus eſt aliquod illorū mediorū per quod mouet̄̄
                    <lb/>
                  aliqua illarū potentiarū, quam eſt medietas peda­
                    <lb/>
                  lis per quod mouetur a. / vt ptꝫ ex caſu: igitur in infi­
                    <lb/>
                  nitū tardius ꝙ̄ a. mouetur aliqua illaꝝ potentiarū /
                    <lb/>
                  quod fuit ꝓbandū. </s>
                  <s xml:id="N1AB3A" xml:space="preserve">Cõſequentia ptꝫ cum minore: et
                    <lb/>
                  arguitur maior: q2 nulla aliaruꝫ potentiarū eque
                    <lb/>
                  cito deueniet ad terminū ſui medii ſicut a. deueniet
                    <lb/>
                  ad punctum mediū pedalis per quod mouetur. </s>
                  <s xml:id="N1AB43" xml:space="preserve">nec
                    <lb/>
                  citius aliqua illarum deueniet ad terminū ſui me-
                    <lb/>
                  dii ꝙ̄ a. deueniet ad punctum medium pedalis per
                    <lb/>
                  quod mouetur: igitur citius a. preteribit punctum
                    <lb/>
                  medium quam aliqua aliarum deueniet ad finem
                    <cb chead="De motu penes cauſã in medio vniformiṫ difformi īuariato."/>
                  medii / per quod mouetur / quod fuit probandū. </s>
                  <s xml:id="N1AB51" xml:space="preserve">Cõ­
                    <lb/>
                  ſequentia patet et arguitur maior. </s>
                  <s xml:id="N1AB56" xml:space="preserve">quia ſi eque cito
                    <lb/>
                  aliqua illarum deueniret ad terminū ſui medii ſi-
                    <lb/>
                  cut a. deueniet ad punctum mediū: ſignetur illa et ſit
                    <lb/>
                  b. / et arguo ſic / cum primū a. eſt in puncto medio qui
                    <lb/>
                  eſt vt .4.b. eſt in puncto terminatiuo totius latitu-
                    <lb/>
                  dinis qui eſt vt .8. / et a. mouetur a proportiõe dupla /
                    <lb/>
                  vt ponitur: igitur qualis eſt proportio ipſius a. ad
                    <lb/>
                  reſiſtentiam ipſius a. talis eſt proportio reſiſtentie
                    <lb/>
                  ipſius b. ad reſiſtentiam ipſius a. / et per conſequens
                    <lb/>
                  reſiſtentia ipſius b. et ipſa potentia a. ſunt equales
                    <lb/>
                  cum habeant eadem proportionem ad vnū tertiuꝫ:
                    <lb/>
                  et a. et b. ſunt equales ex caſu: igitur reſiſtentia ipſiꝰ
                    <lb/>
                  b. et b. ſunt equales: ſic b. mouetur a proportione
                    <lb/>
                  equalitatis / quod eſt impoſſibile. </s>
                  <s xml:id="N1AB73" xml:space="preserve">Patet igitur / 
                    <lb/>
                  nulla illarum poteſt eque cito venire ad punctū ter­
                    <lb/>
                  minatiuū ſui medii, ſicut a. ad punctum medium pe­
                    <lb/>
                  dalis per quod mouetur. </s>
                  <s xml:id="N1AB7C" xml:space="preserve">Sed iam probo minorem
                    <lb/>
                  videlicet /  nulla illarum citius deueniet ad termi-
                    <lb/>
                  nū ſui medii quam a. deueniat ad punctum medium
                    <lb/>
                  ſui pedalis per quod mouetur: quia ſi ſic ſit illa b. /
                    <lb/>
                  et arguo ſic, b. potentia equalis ipſi a. eſt in puncto
                    <lb/>
                  terminatiuo ſui medii puta in puncto vt .8. et a. eſt
                    <lb/>
                  in minori puncto quam vt .4. et mouetur a. potentia
                    <lb/>
                  a proportione dupla: igitur maior eſt proportio re­
                    <lb/>
                  ſiſtentie ipſius b. ad reſiſtentiam ipſius a. ꝙ̄ ſit pro­
                    <lb/>
                  portio ipſius a. ad reſiſtentiam ipſius a. et a. et b.
                    <lb/>
                  ſunt equales: igitur maior eſt reſiſtentia b. quam b. /
                    <lb/>
                  et per conſequens b. mouetur a. proportione mino-
                    <lb/>
                  ris inequalitatis / quod eſt impoſſibile. </s>
                  <s xml:id="N1AB97" xml:space="preserve">Patet ta-
                    <lb/>
                  men conſequentia / quia pūcti vt .8. ad punctū quod­
                    <lb/>
                  libet minus puncto vt .4. eſt maior proportio quam
                    <lb/>
                  dupla: et ipſius a. ad reſiſtentiam eiuſdē que eſt mi-
                    <lb/>
                  nor puncto vt .4. eſt proportio dupla: igitur reſiſtē­
                    <lb/>
                  tia b. maiorem proportionem habet ad reſiſtentiã
                    <lb/>
                  ipſius a. quaꝫ a. habeat ad reſiſtentiam eiuſdem a. /
                    <lb/>
                  et per conſequens maior eſt reſiſtentia ipſius b. quã
                    <lb/>
                  a. potentia / quod fuit probandum. </s>
                  <s xml:id="N1ABAA" xml:space="preserve">Patet conſequē­
                    <lb/>
                  tia per hanc maximam: id quod habet maiorē pro­
                    <lb/>
                  portionem ad vnū tertium eſt maius. </s>
                  <s xml:id="N1ABB1" xml:space="preserve">Patet igitur
                    <lb/>
                  totum illatum.</s>
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                <p xml:id="N1ABB6">
                  <s xml:id="N1ABB7" xml:space="preserve">Reſpondeo / igitur concedendo quod
                    <lb/>
                  infertur vt demonſtrat argumentum.
                    <note position="right" xlink:href="note-0110-01a" xlink:label="note-0110-01" xml:id="N1AD20" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N1ABC1" xml:space="preserve">¶ Ex hoc ar-
                    <lb/>
                  gumento et ſolutionibus replicarū eiuſdem / ſequi-
                    <lb/>
                  tur primo:  vbicun ſunt infinite potentie vt po-
                    <lb/>
                  nitur in caſu vltime replice: neceſſe eſt /  potētia que
                    <lb/>
                  mouetur in maximo illorum mediorum pretereat
                    <lb/>
                  punctum ad quod punctum intenſiſſimū illius me-
                    <lb/>
                  dii habet ſimilem proportionem illi proportioni a
                    <lb/>
                  qua mouetur illa potentia, quam aliqua aliarum
                    <lb/>
                  potentiarum equalium deueniat ad extremum ſui
                    <lb/>
                  medii. </s>
                  <s xml:id="N1ABD6" xml:space="preserve">Uolo dicere /  ſi potentia in maxima illorū
                    <lb/>
                  mediorum (loquor ſemper incipientibus a nõ gra-
                    <lb/>
                  du) moueatur a proportione quadrupla: citius de-
                    <lb/>
                  ueniat ad punctum ad quem intenſiſſimus punctus
                    <lb/>
                  puta vt .8. (ſi medium terminetur ad illum) habeat
                    <lb/>
                  proportionem quadruplam, quam aliqua aliaruꝫ
                    <lb/>
                  potentiarum pertranſeat ſuum medium. </s>
                  <s xml:id="N1ABE5" xml:space="preserve">Ita  in
                    <lb/>
                  tali caſu oportet /  prius veniat ad punctum vt .2.
                    <lb/>
                  et pretereat illum. </s>
                  <s xml:id="N1ABEC" xml:space="preserve">Alias enim vel alia potentia mo­
                    <lb/>
                  ueretur a proportione equalitatis vĺ minoris ine-
                    <lb/>
                  qualitatis vt facile eſt inducere
                    <note position="right" xlink:href="note-0110-02a" xlink:label="note-0110-02" xml:id="N1AD26" xml:space="preserve">2. correĺ</note>
                  </s>
                  <s xml:id="N1ABF8" xml:space="preserve">¶ Sequitur ſecūdo /
                    <lb/>
                   ſi ſint duo media inequalia per que extēditur ea-
                    <lb/>
                  deꝫ latitudo reſiſtentie vniformiter difformis a nõ
                    <lb/>
                  gradu vſ ad octauū: et incipiant due potentie mo­
                    <lb/>
                  ueri per illa media a nõ gradu illiꝰ reſiſtentie: et con­
                    <lb/>
                  tinuo creſcãt ille potētie vniformiter īcipiēdo a nõ
                    <lb/>
                  g̈du potētie: illa tñ que mouet̄̄ in medio mīori in ea
                    <lb/>
                  ꝓportione velociꝰ creſcat altera q̄ mouet̄̄ in medio </s>
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