Alvarus, Thomas, Liber de triplici motu, 1509

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                  <s xml:id="N1E081" xml:space="preserve">
                    <pb chead="De motu locali quo ad effectum tempore difformi." file="0144" n="144"/>
                  illud ex quo ſequitur. </s>
                  <s xml:id="N1E095" xml:space="preserve">Impoſſibilitas conſequētis
                    <lb/>
                  arguitur quoniam / ſi illi motus ſunt equales in prī­
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                  cipio: et manent equales in fine: et in toto tempore re­
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                  miſſionis illorum equales latitudines deperdunt
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                  adequate: ſequitur /  in toto illo tempore cathego­
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                  reumatice illi motus ſunt equales: et per conſequens
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                  non maius ſpacium in eodeꝫ tempore pertranſitur
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                  per vnum quam per reliquum: et per te eſt oppoſitū /
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                  igitur contradictio. </s>
                  <s xml:id="N1E0A8" xml:space="preserve">Sequela tamen probatur et ca­
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                  pio duos motus equales gratia exempli vt .8. puta
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                  a.b. / et volo /  a. vniformiter iu hora ſequenti deper­
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                  dat .4. gradus: ita  medietas illorum: .4. deperda­
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                  tur ī medietate illius tꝑis, et vna q̈rta in quarta ꝑte
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                  et quinta in quinta, et ſic confequenter: ita  cõtinuo
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                  in equali tempore ſit equalis deperditio .b. vero in
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                  hora illa deperdat .4. gradus ſucceſſiue non vnifor­
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                  miter ſed continuo velocius: ita  in qualibet par-
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                  te temporis ſequentis velocius quã in precedenti ſi­
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                  bi equali / quod facile poteſt fieri iſto modo: ſi dini-
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                  ſa illa hora per partes proportionales proportio­
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                  ne quadrupla, in prima illarum deperdat medie-
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                  tatem illius medietatis deperdēde, et ī ſecunda par­
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                  te proportionali proportiõe quadrupla ſubduplū
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                  et in tertia ſubquadruplum / et ſic in infinitum: et ma­
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                  nifeſtum eſt /  iam illo latitudo continuo deperdi-
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                  tur: continuo velocius et velocius / vt facile eſt intue­
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                  ri </s>
                  <s xml:id="N1E0CF" xml:space="preserve">Quo poſito ſic arguitur per motum b. / cõtinuo ꝑ
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                  totam horam pertranſibitur maius ſpacium quaꝫ
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                  per motum a. / et in fine et in principio ſunt equales,
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                  et in eodem tempore equalem latitudinem deperdēt
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                  adequate: igitur intentum. </s>
                  <s xml:id="N1E0DA" xml:space="preserve">Conſequentia patet cuꝫ
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                  minore: ſed arguitur maior videlicet /  continuo ꝑ
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                  motum b. tranſibitur maius ſpacium quam ꝑ mo-
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                  tum a. / quia continuo motus b. eſt maior et intenſior
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                  motu a. / igitur continuo per illum maius ſpacium
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                  pertranſibitur in eodem tempore </s>
                  <s xml:id="N1E0E7" xml:space="preserve">Conſequentia ſe
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                  manifeſtat et arguitur antecedens / quia b. motus in
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                  nullo inſtanti intrinſeco illius hore erit equalis a.
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                  nec miuor: ergo continuo maior. </s>
                  <s xml:id="N1E0F0" xml:space="preserve">Probatur antece­
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                  dens / quia ſi in aliquo inſtanti motus b. erit equa-
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                  lis aut minor ipſi a. ſignetur illud: et ſit c. inſtãs in-
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                  trinſecū / et arguitur ſic / in iſto inſtanti a. motus et b.
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                  ſunt equales: ergo ex caſu equalem perdiderunt la­
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                  titudinem: et equales reſtat deperdenda ipſi a. et ip­
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                  ſi b. et a. / continuo vniformiter deperdet illam deper­
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                  dendam ex caſu: et b. velocius quam antea deperde­
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                  bat. </s>
                  <s xml:id="N1E103" xml:space="preserve">et antea deperdebat equaliter cum a: ergo velo­
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                  cius deperdet modo totam latitudinem deperden-
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                  dam ꝙ̄ a. / et per conſequens citius tota latitudo de­
                    <lb/>
                  perdenda erit deperdita iꝑſi b. quam ipſi a. / quod ē
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                  cõtra caſum: </s>
                  <s xml:id="N1E10E" xml:space="preserve">Et per locum a maiori probabitur ſi-
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                  militer /  pro nullo inſtanti motus b. eſt minor mo-
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                  tu.
                    <note position="left" xlink:href="note-0144-01a" xlink:label="note-0144-01" xml:id="N1E140" xml:space="preserve">cõfirma-
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                    tio.</note>
                  </s>
                  <s xml:id="N1E11A" xml:space="preserve">¶ Et confirmatur ſuppoſito / quia vna pars pro­
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                  portionalis proportiõe quadrupla eſt due partes
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                  proportione dupla: et per conſequens due partes ꝓ­
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                  portionales ꝓportione quadrupla ſunt .4. propor­
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                  tione dupla: et ſic conſequenter procedendo per nu­
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                  meros pariṫ pares: quod poteſt patere intuenti q̇n­
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                  tum caput prīe partis </s>
                  <s xml:id="N1E129" xml:space="preserve">Quo ſuppoſito ſic argumē-
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                  tor ex caſu in fine prime partis proportionalis pro­
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                  portione quadrupla b. perdet primam partem pro­
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                  portionalem proportione dupla latitudinis deper­
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                  dende / et tunc a. deperdit duas partes proportiona­
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                  les proportione dupla latitudinis deperdende: q2
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                  tunc ſunt tranſacte due partes proportionales tē-
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                  poris proportione dupla / vt patet ex ſuppoſito: et
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                  a. motus remittitur vniformiter / vt patet ex caſu.</s>
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                <p xml:id="N1E148">
                  <s xml:id="N1E149" xml:space="preserve">In fine vero ſecunde partis proportionalis tempo­
                    <lb/>
                  ris proportione quadrupla b. deperdit duas par-
                    <cb chead="De motu locali quo ad effectum tempore difformi."/>
                  tes proportionales latitudinis deperdende ꝓpor-
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                  tione dupla: et a .4. qm̄ ille due partes ꝓportõe qua­
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                  drupla ſunt quatuor partes preportionales ꝓpor­
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                  tione dupla: igitur continuo maior latitudo eſt de­
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                  perdita a. quam ipſi b. vſ ad inſtans terminatiuū
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                  et ſic ſemper in quolibet inſtanti intrinſeco illiꝰ ho-
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                  re motus b. eſt velocior motu a. / quod fuit proban-
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                  dum.
                    <note position="right" xlink:href="note-0144-02a" xlink:label="note-0144-02" xml:id="N1E17E" xml:space="preserve">dicitur.</note>
                  </s>
                  <s xml:id="N1E164" xml:space="preserve">¶ Dices et bene ad argumentum concedendo /
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                  quod infertur vt bene probat argumentum, et negã­
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                  do falſitatem conſequentis: et cum aſtruitur illa fal­
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                  ſitas conſequentis negatur conſequenria </s>
                  <s xml:id="N1E16D" xml:space="preserve">Immo cõ­
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                  ceditur /  in principio illi motus ſunt equales, et in
                    <lb/>
                  fine equales, et equalem latitudinem adequate de-
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                  perdunt in eodem tempore et tamen in toto illo tem­
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                  pore vnus eſt intenſior altero / vt pulchre probat ar­
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                  gumentum.</s>
                </p>
                <p xml:id="N1E184">
                  <s xml:id="N1E185" xml:space="preserve">Sed contra ſi ſolutio veritati eſſet cõ­
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                  ſona talis ex ea duceretur concluſio:  videlicet ali­
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                  qui duo motus ſe habent modo in proportione du­
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                  pla et per idem tempus vniformiter et eque velociter
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                  remitterentur adequate: et tamen ſemper in illo tē-
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                  pore ſpacium pertranſitum a maiori erit pluſ̄ du­
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                  plū ad ſpaciū pertranſituꝫ a minori: ſꝫ cõſeq̄ns vr̄
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                  falſū: cū illo mõ ſe hñt ī ꝓportiõe dupla et ſꝑ equali­
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                  ter remittūtur. </s>
                  <s xml:id="N1E198" xml:space="preserve">apparet igitur /  cõtinuo manebūt
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                  ſe habētes in ꝓportione dupla: et ſic ſpaciū ꝑtran-
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                  ſitum a maiori nõ eſt pluſquam duplū ad ſpacium
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                  pertranſitū a minori: et ſic illud conſequens eſt fal­
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                  ſum: et per conſequēs illud ex quo ſequitur ꝓbatur
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                  tamē ſequela et pono caſum /  ſint .a. et .b. motus: et
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                  a. ſit duplus ad .b. / et remittantur continuo eque ve­
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                  lociter et vniformiter a. et b. perdendo equalē lati­
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                  tudinē omnino per totū tempus. </s>
                  <s xml:id="N1E1AB" xml:space="preserve">quo poſito ſic ar-
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                  gumentor in toto illo tēpore remiſſionis motus a.
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                  erit pluſquã duplus ad motum b. et modo a. ſe ha­
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                  bet ad b. in ꝓportione dupla: et continuo in illo tē-
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                  pore eque velociter remittentur .etc. / igitur cõcluſio
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                  vera. </s>
                  <s xml:id="N1E1B8" xml:space="preserve">Conſequentia patet cū minore / et arguit̄̄ ma­
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                  ior: et volo /  ſit c. equale ipſi a. in principio / et con-
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                  tinuo remittatur taliter /  coutinuo ſe habeat in ꝓ­
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                  portione dupla ad b. / et arguitur ſic. </s>
                  <s xml:id="N1E1C1" xml:space="preserve">continuo c. ꝑ-
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                  det maiorē latitudinē quã b. q2 continuo duplam /
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                  vt patet ex primo et ſecūdo correlariis quinte con-
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                  cluſionis ſecūdi capitis ſecūde partis / igitur conti­
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                  nuo maiorem quã a. cū a. et b. deperdant equales
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                  latitudines continuo / vt patet per caſum: et in prin­
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                  cipio a. et c. ſunt equalia: igitur continuo a. motus
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                  erit maior c. motu et c. continuo adequate eſt duplꝰ
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                  ad b. / ergo continuo a. erit maior motus quã duplꝰ
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                  ad b. / quod fuit ꝓbanduꝫ </s>
                  <s xml:id="N1E1D6" xml:space="preserve">Patet hec conſequentia
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                  per hanc maximam. </s>
                  <s xml:id="N1E1DB" xml:space="preserve">Quando duo inequalia ha-
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                  bent aliquas ꝓportiones ad vnū et idem tertium
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                  maiorem proportionem ad idem tertiū habet ma­
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                  ius illorū quam minus: vt ſatis conſtat.</s>
                </p>
                <p xml:id="N1E1E4">
                  <s xml:id="N1E1E5" xml:space="preserve">Tertio principaliter tangendo mate­
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                  riam principaliter intentam in hoc capite de com­
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                  menſuratione motus difformiter difformis cuius
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                  difformitas in infinitum procedit ſecundum nume­
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                  rum partium proportionalium: arguitur ſiic. </s>
                  <s xml:id="N1E1F0" xml:space="preserve">Si
                    <lb/>
                  motus difformiter difformis commēſurari habe-
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                  ret penes reductionem ad vniformitatē aut penes
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                  denominationē ſue intēſionis ſequeretur hec con-
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                  cluſio:  videlicet aliquis eſſet motꝰ difformis qui
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                  non poſſet ad vniformitatem reduci et cuius non
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                  poſſet dari certa intenſio: conſequens eſt falſū / igit̄̄
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                  illud ex quo ſequitur: </s>
                  <s xml:id="N1E201" xml:space="preserve">Falſitas conſequentis patet
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                  et arguitur ſequela et diuido horam in duas par-
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                  tes inequales quarum vtra ſe habet ad totã ho- </s>
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