Alvarus, Thomas, Liber de triplici motu, 1509

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              <div xml:id="N1B67A" level="4" n="14" type="chapter" type-free="capitulum">
                <pb chead="De motu locali quo ad cauſam in medio non reſiſte." file="0118" n="118"/>
                <p xml:id="N1B6A9">
                  <s xml:id="N1B6AA" xml:space="preserve">Prima ſuppoſitio. </s>
                  <s xml:id="N1B6AD" xml:space="preserve">Latitudine reſiſtē­
                    <lb/>
                  tie vniformiter difformis ad nõ gradū terminate,
                    <lb/>
                  cõtinuo mouēte ſiue ꝓgrediente ꝑ mediū nõ reſiſtēs
                    <lb/>
                  ipſa cõtinuo vniformiter difformi manēte et nõ gra­
                    <lb/>
                  du eius cõtinuo quieſcēte: quodlibet eiꝰ punctū in-
                    <lb/>
                  trinſecū in ea ꝓportione cõtinuo quolibet altero re­
                    <lb/>
                  miſſiori velocius mouetur in qua eſt ipſo intenſius
                    <lb/>
                  </s>
                  <s xml:id="N1B6BD" xml:space="preserve">Probat̄̄: ſit a. latitudo reſiſtentie vniformiter dif-
                    <lb/>
                  formis ad nõ gradū terminate, q̄ cõtinuo vniformi­
                    <lb/>
                  ter difformis manēs ꝓgrediat̄̄ ſucceſſiue ꝑ mediuꝫ
                    <lb/>
                  nõ reſiſtēns nõ gradu eiꝰ quieſcēte eo modo quo ſu-
                    <lb/>
                  periꝰ declaratū eſt in tertia et quarta ſuppoſitioni­
                    <lb/>
                  bus p̄cedentis capitis: ſit b. punctꝰ intrinſecꝰ intē­
                    <lb/>
                  ſior c. vero etiã intrinſecꝰ et remiſſior inter q̄ puncta
                    <lb/>
                  ſit proportio f. </s>
                  <s xml:id="N1B6CE" xml:space="preserve">Tūc dico /  b. pūctus continuo in f.
                    <lb/>
                  ꝓportione velocius mouet̄̄ ipſo c. pūcto. </s>
                  <s xml:id="N1B6D3" xml:space="preserve">Quod ſic
                    <lb/>
                  oſtendēt̄̄: q2 intēſionis ipſiꝰ b. pūcti ad intēſioni c.
                    <lb/>
                  puncti cõtinuo eſt proportio f. ex hypotheſi: et con-
                    <lb/>
                  tinuo a. latitudo reſiſtentie manet vniformiter dif-
                    <lb/>
                  formis ad nõ gradū terminata: igitur cõtinuo di-
                    <lb/>
                  ſtantie quãtitate ipſius b. a nõ gradu ad diſtantiã
                    <lb/>
                  ipſius c. a non gradu eſt proportio f. </s>
                  <s xml:id="N1B6E2" xml:space="preserve">Patet conſe-
                    <lb/>
                  quentia ex diffinitione qualitatis vniformiter dif-
                    <lb/>
                  formis quarto tractatu: et continuo diſtantia ipſiꝰ
                    <lb/>
                  b. a nõ gradu et diſtantia ipſius c. a nõ gradu maio­
                    <lb/>
                  rantur per cõtinuū motū ipſius b. et ipſius c. / igitur
                    <lb/>
                  cõtinuo diſtantie acquiſite per motum ipſius b. ad
                    <lb/>
                  diſtantiã acquiſitã per motū ipſius c. eſt proportio
                    <lb/>
                  f. </s>
                  <s xml:id="N1B6F3" xml:space="preserve">Patet cõſequentia ex primo et ſecūdo correlario
                    <lb/>
                  quīte cõcluſionis ſecūdi capitis ſecūde partis: et ꝑ
                    <lb/>
                  cõſequens cõtinuo b. punctus in f. proportione ve-
                    <lb/>
                  locius mouetur c. puncto / quod fuit probandum. </s>
                  <s xml:id="N1B6FC" xml:space="preserve">Et
                    <lb/>
                  ſic patet ſuppoſitio.</s>
                </p>
                <p xml:id="N1B701">
                  <s xml:id="N1B702" xml:space="preserve">Secūda ſuppoſitio. </s>
                  <s xml:id="N1B705" xml:space="preserve">Latitudine reſi-
                    <lb/>
                  ſtentie vniformiter difformis vtrī ad gradū ter-
                    <lb/>
                  minate, cõtinuo mouēte ſiue ꝓgrediente pēr mediū
                    <lb/>
                  nõ reſiſtens, ipſa cõtinuo manente vniformiter dif-
                    <lb/>
                  formi et extremo eius remiſſiori quieſcente: quodli-
                    <lb/>
                  bet punctū eius intrinſecū in maiori ꝓportione cõ­
                    <lb/>
                  tinuo quolibet altero intrinſeco remiſſiori velociꝰ
                    <lb/>
                  mouetur quã ſit proportio in qua eſt ipſo intenſius
                    <lb/>
                  </s>
                  <s xml:id="N1B717" xml:space="preserve">Probatur: ſit a latitudo reſiſtētie vniformiter dif-
                    <lb/>
                  formis vtrin ad gradum terminate que cõtinuo
                    <lb/>
                  manens vniformiter difformis ꝓgrediatur ſucceſſi­
                    <lb/>
                  ue per medium nõ reſiſtens extremo remiſſiori eius
                    <lb/>
                  quieſcente / vt ſepe ſupra dictū eſt. </s>
                  <s xml:id="N1B722" xml:space="preserve">ſit b. punctus ex­
                    <lb/>
                  trinſecus intenſior .c. vero etiã intrinſecus et remiſ­
                    <lb/>
                  ſior, inter que puncta ſit ꝓportio f. </s>
                  <s xml:id="N1B729" xml:space="preserve">Tunc dico /  b.
                    <lb/>
                  punctus ↄ̨tinuo in maiore ꝓportione quã f. velociꝰ
                    <lb/>
                  continuo mouet̄̄ c. pūcto. </s>
                  <s xml:id="N1B730" xml:space="preserve">Qḋ ſic oñdit̄̄ / et capio / d. la­
                    <lb/>
                  titudinē reſiſtentie vniformiter difformis cõtinuo
                    <lb/>
                  eiuſdē extenſionis oīno cū a. incipientē in extremo
                    <lb/>
                  intenſiori ab eadē gradu cū a. terminatã tamen ad
                    <lb/>
                  nõ gradū: et ſit h. punctus qui tantū diſtat continuo
                    <lb/>
                  ab extremo remiſſiori d. latitudinis adequate quã­
                    <lb/>
                  tum b. diſtat ab extremo remiſſiori ipſius a. latitu-
                    <lb/>
                  dinis: et ſit k. pūctus remiſſior h (vt oportet) / qui cõ­
                    <lb/>
                  tinuo tantū diſtat adequate ab extremo remiſſiori
                    <lb/>
                  d. latitudinis quãtū c. diſtat ab extremo remiſſiori
                    <lb/>
                  ipſius a. </s>
                  <s xml:id="N1B747" xml:space="preserve">Et ſit l. ꝓportio h. puncti ad ipſum k. </s>
                  <s xml:id="N1B74A" xml:space="preserve">Et ar­
                    <lb/>
                  guo ſic / cõtinuo h. punctus in l. ꝓportione mouetur
                    <lb/>
                  velocius k. puncto / vt ptꝫ ex precedenti ſuppoſitiõe.
                    <lb/>
                  </s>
                  <s xml:id="N1B752" xml:space="preserve">Et cõtinuo in eadē l. ꝓportione b. punctus mouetur
                    <lb/>
                  velocius ipſo c. puncto (vt patꝫ intuenti caſum). </s>
                  <s xml:id="N1B757" xml:space="preserve">Et
                    <lb/>
                  intenſionis ipſius h. puncti ad intenſionem ipſius
                    <lb/>
                  k. puncti eſt maior ꝓportio quã intenſionis ipſius
                    <lb/>
                  b. ad intenſionem ipſius c. puncti que eſt f. ex hypo-
                    <cb chead="De motu locali quo ad cauſam in medio non reſiſte."/>
                  theſi: ergo k. ꝓportio eſt maior quã f. ꝓportio et k.
                    <lb/>
                  eſt ꝓportio a qua velocius mouetur b. quã c. et f. eſt
                    <lb/>
                  ꝓportio intenſionis ipſius b. puncti ad ipſum c. po­
                    <lb/>
                  tentiarū: ergo b. punctus cõtinuo in maiori ꝓpor-
                    <lb/>
                  tione quam f. velocius mouetur c. puncto: quod fuit
                    <lb/>
                  ꝓbandū. </s>
                  <s xml:id="N1B76D" xml:space="preserve">Cõſequentia ptꝫ cū maiore cū prima par­
                    <lb/>
                  te minoris. </s>
                  <s xml:id="N1B772" xml:space="preserve">Et ſecūda pars minoris ꝓbatur videli­
                    <lb/>
                  cet / ꝙ̄ intenſionis ipſius h. puncti ad intenſionē etc̈.
                    <lb/>
                  quia b. et c. ſunt pūcta intenſiora quã h. et k. / vt ↄ̨ſtat /
                    <lb/>
                  et b. minori exceſſu excedit c. quã h. ipſum k. (cum to­
                    <lb/>
                  tus exceſſus inter extrema d. latitudinis ſit maior
                    <lb/>
                  toto exceſſu inter extēa ipſiꝰ a. latitudīs: et ſic inter
                    <lb/>
                  extrema partiū equaliū ipſius d. eſt maior exceſſus
                    <lb/>
                  quã inter cõſimiles partes ipſius a) / ergo intenſio-
                    <lb/>
                  nis ipſius h. puncti ad intenſionē ipſius k. pūcti eſt
                    <lb/>
                  maior ꝓportio quã intenſionis ipſius b. puncti ad
                    <lb/>
                  intenſionē ipſius c. puncti que eſt f. / quod fuit infe-
                    <lb/>
                  rendum. </s>
                  <s xml:id="N1B78B" xml:space="preserve">Et ſic patet ſuppoſitio.</s>
                </p>
                <p xml:id="N1B78E">
                  <s xml:id="N1B78F" xml:space="preserve">Tertia ſuppoſitio. </s>
                  <s xml:id="N1B792" xml:space="preserve">Quandocun ali­
                    <lb/>
                  que potentie que continuo inequaliter mouetur in­
                    <lb/>
                  cipiūt in eodem inſtanti moueri / vt attingant eque
                    <lb/>
                  cito / et in eodem inſtanti duo mobilia precedētia ta­
                    <lb/>
                  les potentias que mobilia etiam continuo mouen-
                    <lb/>
                  tur recedendo ab ipſis potentiis: et in principio
                    <lb/>
                  motus diſtat potentia velocius mota a mobili / qḋ
                    <lb/>
                  ipſa inſequitur pluſ̄ reliqua tardius mota a ſuo
                    <lb/>
                  in ea ꝓportione qua velocius continuo mouetur:
                    <lb/>
                  oportet ſi eque cito debeat vtra potentia ſuū mo­
                    <lb/>
                  bile attingere:  in ꝓportione in qua potentia ve-
                    <lb/>
                  locior velociꝰ mouetur potentia tardiore in ea pro­
                    <lb/>
                  portione mobile quod debet attingi a potētia tar-
                    <lb/>
                  diore tardius moueatur quam mobile quod debet
                    <lb/>
                  attigi a potentia velociore. </s>
                  <s xml:id="N1B7B1" xml:space="preserve">Uolo dicere:  ſi ſortes
                    <lb/>
                  et plato incipiant in eodem inſtanti moueri perſe-
                    <lb/>
                  quendo ſuos equos fugientes: et ↄ̨tinuo ſortes mo­
                    <lb/>
                  ueatur in duplo velocius platone: et in inſtanti ini-
                    <lb/>
                  tiatiuo motus equus ſortis in duplo plus diſtet a
                    <lb/>
                  ſorte quã equꝰ platonis a platone: oportet /  equꝰ
                    <lb/>
                  platonis (cū plato tardiꝰ moueatur) in duplo tar-
                    <lb/>
                  dius moueatur ꝙ̄ equus ſortis: ſi vter ſuū equum
                    <lb/>
                  eque cito debeat attingere. </s>
                  <s xml:id="N1B7C4" xml:space="preserve">Probatur / ſit a. poten-
                    <lb/>
                  tia velocius continuo mota inſequens c. mobile cõ-
                    <lb/>
                  tinuo ab ea recedens: et b. potentia continuo tardiꝰ
                    <lb/>
                  mota inſequens d. mobile continuo ab ea recedens
                    <lb/>
                  diſtet in principio motus a. potētia plus in f. pro­
                    <lb/>
                  portiõe a c. quã b. ab ipſo d. et in eadem f. ꝓportiõe
                    <lb/>
                  a. potētia continuo velocius moueatur ipſa b. po-
                    <lb/>
                  tentia: et ſic moueantur continuo vt tandē in eodem
                    <lb/>
                  inſtanti quod ſit e. attingant ſua mobilia preceden­
                    <lb/>
                  tia. </s>
                  <s xml:id="N1B7D9" xml:space="preserve">Tunc dico /  oportet d. in f. ꝓportione cõtinuo
                    <lb/>
                  tardiꝰ moueri ipſo c. </s>
                  <s xml:id="N1B7DE" xml:space="preserve">Quod ſic oſtendit̄̄ / q2 cõtinuo
                    <lb/>
                  a. mouetur in f. ꝓportione velociꝰ ipſa b. potentia
                    <lb/>
                  inſequendo mobilia precedentia vſ ad inſtans e.
                    <lb/>
                  ex hypotheſi: igitur ſpacii pertranſiti ab a. poten-
                    <lb/>
                  tia vſ ad inſtans e. ad ſpaciū pertranſitū a b. po-
                    <lb/>
                  tentia vſ ad idem e. inſtans eſt ꝓportio f. / ptꝫ con-
                    <lb/>
                  ſequētia ex ſe: et vltra ſpacii ꝑtrãſiti ab a. potentia
                    <lb/>
                  vſ ad inſtãs e. ad ſpaciū ꝑtrãſitū a b. potētia vſ
                    <lb/>
                  ad idē inſtãs eſt f. ꝓportio: igr̄ demēdo ab illis ſpa­
                    <lb/>
                  ciis partes ſe ſi abētes in f. ꝓportione, puta ſpaciū
                    <lb/>
                  ꝑ qḋ a principio motꝰ a. diſtat a c. et ſpaciū ꝑ qḋ a
                    <lb/>
                  principio motus b. poña diſtat a d. q̄ ex hypotheſi
                    <lb/>
                  ſe hñt in f. ꝓportiõe reſidua ſpacia ſe hñt in f. ꝓpor­
                    <lb/>
                  tione: ptꝫ conſequentia ex ſeptimo correlario quar­
                    <lb/>
                  te concluſionis oceaui capitis ſecunde partis.</s>
                </p>
                <p xml:id="N1B7FD">
                  <s xml:id="N1B7FE" xml:space="preserve">Sed reſidua ſpacia puta reſiduum ſpacii maioris
                    <lb/>
                  pertranſiti ab a. et reſiduū ſpacii minoris pertran­
                    <lb/>
                  ſiti a b. potentia ſunt ſpacia pertranſita a c. mobi­ </s>
                </p>
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