Alvarus, Thomas, Liber de triplici motu, 1509

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                <p xml:id="N1E372">
                  <s xml:id="N1E373" xml:space="preserve">
                    <pb chead="De motu locali quo ad effectum tempore difformi." file="0146" n="146"/>
                  titulus queſtiõis falſus. </s>
                  <s xml:id="N1E383" xml:space="preserve">Arguitur añs: et pono ca-
                    <lb/>
                  ſum /  a. mobile in prima parte proportionali ꝓ-
                    <lb/>
                  portione dupla huius hore moueat̄̄ aliquantuluꝫ
                    <lb/>
                  velociter: et in ſecunda in ꝓportione ſexquialtera
                    <lb/>
                  velocius ꝙ̄ in prima et in tertia in ꝓportione ſexq̇­
                    <lb/>
                  quarta velocius quã in ſcḋa: et ſic conſequenter ꝓ-
                    <lb/>
                  cedendo per omnes ſpecies proportionis ſuꝑparti­
                    <lb/>
                  cularis: quo poſito talis motus eſt vniformiter dif­
                    <lb/>
                  formis: et non eſt dabilis eius intenſio: nec reductio
                    <lb/>
                  ad vniformitatem: igitur. </s>
                  <s xml:id="N1E398" xml:space="preserve">Arguitur minor / quia nõ
                    <lb/>
                  apparet cuius intenſionis ſit ille motus niſi fuerit
                    <lb/>
                  infinite: cum in infinitum velociter moueatur a. mo­
                    <lb/>
                  bile in aliqua parte proportionali temporis: igit̄̄
                    <lb/>
                  non repertiur eius certa intenſio.</s>
                </p>
                <note position="left" xml:id="N1E3A3" xml:space="preserve">dicitur.</note>
                <p xml:id="N1E3A7">
                  <s xml:id="N1E3A8" xml:space="preserve">¶ Dices et bene negando minorem: et quoniam ar-
                    <lb/>
                  gumentum nihil aliud petit niſi intenſionem talis
                    <lb/>
                  motus, et vniformitatem, et quomodo cognoſci de-
                    <lb/>
                  beat: et inueſtigari. </s>
                  <s xml:id="N1E3B1" xml:space="preserve">Ideo dico /  totalis illius mo-
                    <lb/>
                  tus velocitas correſpondet velocitati ſecunde par-
                    <lb/>
                  tīs ꝓportionalis: et ſic illud mobile a. in totali tem­
                    <lb/>
                  pore mouetur in ſexq̇altero velociꝰ quã in prīa ꝑte
                    <lb/>
                  proportionali temporis. </s>
                  <s xml:id="N1E3BC" xml:space="preserve">Quod ſic oſtenditur ſup­
                    <lb/>
                  poſito gratia argumenti /  in prīa parte ꝓportio-
                    <lb/>
                  nali moueatur vt duo: et  quelibet pars ſequēs al­
                    <lb/>
                  teram cum toto reſiduo ſequenti eã excedit īmedia-
                    <lb/>
                  te precedentem ſe per vnum ſemper equaliter (vt fa­
                    <lb/>
                  cile eſt intueri) illis ſuppoſitis ſic argumētor duo
                    <lb/>
                  gradus velocitatis qui ſunt per totam horam de-
                    <lb/>
                  nominant totuꝫ a. moueri vt duo in illa hora: et vnꝰ
                    <lb/>
                  gradus extenſus ſiue continuatus per totum reſi-
                    <lb/>
                  duum a prima parte ꝓportiõali / quod eſt ſubduplū
                    <lb/>
                  ad totum tempus denominat vt dimidium: quoniã
                    <lb/>
                  ſi eſſet per totum denominaret vt vnum: ergo ī ſub­
                    <lb/>
                  duplo denominat quia eſt in ſubduplo tēpore. </s>
                  <s xml:id="N1E3D7" xml:space="preserve">Itē
                    <lb/>
                  alter gradus qui eſt in toto reſiduo a. ſecunda par­
                    <lb/>
                  te proportionali denominat in ſubduplo minꝰ quã
                    <lb/>
                  ille qui eſt in toto reſiduo a prima: cum illa tempo-
                    <lb/>
                  ra ſe habeant in proportione ſubdupla: et ſic conſe­
                    <lb/>
                  quenter: igitur totalis denominatio omnium illo-
                    <lb/>
                  rum motuum demptis duobus gradibus extenſis
                    <lb/>
                  per totam horam componitur ex infinitis cõtinuo
                    <lb/>
                  ſe habentibus in proportione ſubdupla: ergo reſi-
                    <lb/>
                  duum a primo eſt equale primo </s>
                  <s xml:id="N1E3EC" xml:space="preserve">Patet conſequen-
                    <lb/>
                  tia ex correlario preallegato: et primum eſt vt dimi­
                    <lb/>
                  dium: ergo totus ille motus vt eſt vt vnū: et veloci-
                    <lb/>
                  tas proueniens a duobus gradibus per totam ho­
                    <lb/>
                  ram eſt vt duo: ergo totus motus adequatus illius
                    <lb/>
                  hore eſt vt tria: et velocitas prime partis id eſt quaꝫ
                    <lb/>
                  habet in prima parte ꝓportionali temporis eſt vt
                    <lb/>
                  duo: et trium ad duo eſt ꝓportio ſexquialtera: ergo
                    <lb/>
                  velocitas illius totalis motꝰ ſe habet in ꝓportiõe
                    <lb/>
                  ſexquialtera ad velocitatē quã habet in prima ꝑte
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                  ꝓportionali: et ſic ſe habet velocitas ſecunde par-
                    <lb/>
                  tis ꝓportionalis ad velocitatem prime / quod fuit
                    <lb/>
                  probandum.</s>
                </p>
                <p xml:id="N1E407">
                  <s xml:id="N1E408" xml:space="preserve">Sed contra mutando paululum ca-
                    <lb/>
                  ſum: volo /  a. in prima ꝓportionali hore ꝓportio­
                    <lb/>
                  ne dupla aliquantulū velociter moueat̄̄: et in ſecū-
                    <lb/>
                  da in ſexquialtero velociꝰ quã in prima: et in tertia
                    <lb/>
                  in ſexquitertio velocius quã in prima: et in quarta
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                  in ſexquiquarto velocius quã in prima: et ſic conſe-
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                  quenter procedēdo per oēs ſpecies ꝓportionis ſu-
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                  perparticularis ſemꝑ referēdo ad primã partem.
                    <lb/>
                  </s>
                  <s xml:id="N1E41A" xml:space="preserve">Quo poſito arguitur ſic / talis motus eſt difformiṫ
                    <lb/>
                  difformis quo ad tempꝰ: et non valet ad vniformi-
                    <lb/>
                  tatē reduci, aut certa eius intēſio eiꝰ inueniri: igit̄̄
                    <lb/>
                  minor patet / q2 nõ apparet modus quo ille motus
                    <lb/>
                  poſſet ad vniformitatē reduci: et ſi aduerſariꝰ hoc
                    <lb/>
                  neget, det illum modū: et in dubie facile erit calcu-
                    <cb chead="De motu locali quo ad effectum tempore difformi."/>
                  latori philoſopho illum impugnare.
                    <note position="right" xlink:href="note-0146-01a" xlink:label="note-0146-01" xml:id="N1E4A8" xml:space="preserve">.1. confir.</note>
                  </s>
                  <s xml:id="N1E42F" xml:space="preserve">¶ Et confir-
                    <lb/>
                  matur / quia ſi aliquod mobile moueat̄̄ ī prima ꝑte
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                  ꝓportionali huiꝰ hore aliq̈ ꝓportiõe aliquantuluꝫ
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                  velociter: et in ſecūda in duplo velocius et in tertia
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                  in ſexquitertio velocius quã in prima et in quarta
                    <lb/>
                  in ſexquiquīto velocius quã in prima: et in quinta
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                  in ſexquioctauo velociꝰ: et inſequēti in ſexquiduo-
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                  decimo velociꝰ: et ſic in infinitū ꝓcedendo interſca­
                    <lb/>
                  lariter ꝑ ſpēs ꝓportionis ſuꝑparticularis ↄ̨tinuo
                    <lb/>
                  vna pĺes omittēdo: tūc taĺ motꝰ ē difformiṫ diffor­
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                  mis quo ad temdus: et nõ poteſt eius certa intenſio
                    <lb/>
                  dari. </s>
                  <s xml:id="N1E448" xml:space="preserve">igit̄̄. </s>
                  <s xml:id="N1E44B" xml:space="preserve">Et ſic poteſt etiam formari caſus vbi inṫ
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                  ſcalariter ꝓcedat̄̄ per eaſdē ſpecies ꝓportiõis ſuꝑ­
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                  particularis cõtinuo plures omittēdo duas dicen­
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                  do ī ſexquialtero, in ſexquiquīto: ī ſexquidecīo, in
                    <lb/>
                  ſexquidecimo ſeptimo. </s>
                  <s xml:id="N1E456" xml:space="preserve">Item ꝓcedendo per eaſdem
                    <lb/>
                  ſpecies cõtinuo dimittendo plures ꝑ tres vel q̈tuor
                    <lb/>
                  vel per .5. vel per .6. et ſic in īfinitū: et dabunt̄̄ motꝰ
                    <lb/>
                  difformes quo ad tēpus: et tamē ipſi non poſſūt ad
                    <lb/>
                  vniformitatē reduci: igitur:
                    <note position="right" xlink:href="note-0146-02a" xlink:label="note-0146-02" xml:id="N1E4AE" xml:space="preserve">2. confir.</note>
                  </s>
                  <s xml:id="N1E466" xml:space="preserve">¶ Cõfirmat̄̄ ſecundo et
                    <lb/>
                  pono caſum /  in prima parte ꝓportiõali aliquod
                    <lb/>
                  mobile moueat̄̄ aliquantulū velociter et in ſecūda
                    <lb/>
                  ī ſexquialtero velocius quã in prima: et in tertia in
                    <lb/>
                  ſuperbipartiēte tertias velocius quã in prima: et
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                  in quarta in ſexquitertio velocius ꝙ̄ in prima: et in
                    <lb/>
                  quinta in ſuꝑpartiente quartas velocius quam in
                    <lb/>
                  prima: et in ſexta in ſexquiquarto velocius ꝙ̄ in pri­
                    <lb/>
                  ma: et ſic cõſequenter ꝓcedēdo per oēs ſpecies pro­
                    <lb/>
                  portiõis ſuperparticularis interſerēdo ſpecies ꝓ­
                    <lb/>
                  portiõis ſuprapartientis: tūc tale mobile mouet̄̄
                    <lb/>
                  difformiter quo ad tempus: et tamē motꝰ illiꝰ vni­
                    <lb/>
                  formitas nõ poteſt venari: igit̄̄ titulꝰ q̄ſtiõis ē falſꝰ
                    <lb/>
                    <note position="right" xlink:href="note-0146-03a" xlink:label="note-0146-03" xml:id="N1E4B4" xml:space="preserve">.3. conur.</note>
                  </s>
                  <s xml:id="N1E488" xml:space="preserve">¶ Confirmatur tertio / et pono caſū /  a. mobile in
                    <lb/>
                  prima parte ꝓportiõali moueat̄̄ aliquãtulū: et in
                    <lb/>
                  ſecunda in duplo plus: et in tertia in ſexquialtero
                    <lb/>
                  plus quã in prima: et in quarta in ſuperbipartien­
                    <lb/>
                  te tercias plus quã in prima: et in quinta in duplo
                    <lb/>
                  ſexquialtero plus quã in prima: et in ſexta in duplo
                    <lb/>
                  ſuperbipartiēte tertias velocius quã ī prima et in
                    <lb/>
                  ſeptima in triplo velocius quã in prima: et ſic cõſe-
                    <lb/>
                  quenter capiēdo primoquin: et conſequen-
                    <lb/>
                  ter alias .5. et ſic in infinitū. </s>
                  <s xml:id="N1E49D" xml:space="preserve">Quo poſito illoꝝ motꝰ
                    <lb/>
                  eſt difformiter difformis: et tamē illius velocitas
                    <lb/>
                  non valet perſcrutari igitur.</s>
                </p>
                <p xml:id="N1E4BA">
                  <s xml:id="N1E4BB" xml:space="preserve">In oppoſitum tamen eſt vniuerſalis
                    <lb/>
                  opinio cõmuniter philoſophantiū / q̄ in hac parte
                    <lb/>
                  multū vigoris acroboris habet </s>
                  <s xml:id="N1E4C2" xml:space="preserve">Preterea ꝑ quēli­
                    <lb/>
                  bet talē motū difformem in totali tēpore adequate
                    <lb/>
                  ꝑtranſitur aliquod ſpaciū adequate: et tale ſpaciū
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                  in tali tēpore ab aliqua velocitate vniformi natum
                    <lb/>
                  eſt pertranſiri: igit̄̄ illa velocitas vniformis eſt tan­
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                  ta quanta eſt velocitas illius motꝰ difformis quo
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                  illud ſpaciū in eodē tempore pertrãſitur adequate
                    <lb/>
                  </s>
                  <s xml:id="N1E4D2" xml:space="preserve">Quod patet per diffinitionē motꝰ eque velocis: igi­
                    <lb/>
                  tur quilibet motꝰ difformis alicui vniformi corre-
                    <lb/>
                  ſpondet cui equiualet / quod fuit probandum.</s>
                </p>
                <p xml:id="N1E4D9">
                  <s xml:id="N1E4DA" xml:space="preserve">Pro deciſione huius queſtionis tria
                    <lb/>
                  faciemus. </s>
                  <s xml:id="N1E4DF" xml:space="preserve">Primo aliqua notabimꝰ, ſecundo non­
                    <lb/>
                  nullas cõcluſiones quibꝰ facilis erit ad queſitum
                    <lb/>
                  reſponſio eliciemus. </s>
                  <s xml:id="N1E4E6" xml:space="preserve">Proſtremo vero reſpondebi­
                    <lb/>
                  mus ad argumenta in oppoſitum.</s>
                </p>
                <p xml:id="N1E4EB">
                  <s xml:id="N1E4EC" xml:space="preserve">Pro primi expeditione repetētes quo­
                    <lb/>
                  dãmodo ea que ſuperius iam tacta ſunt dicamus /
                    <lb/>
                   duplex eſt motus difformis quod ad tempus puta
                    <lb/>
                  difformiter difformis et vniformiter difformis.</s>
                </p>
                <p xml:id="N1E4F5">
                  <s xml:id="N1E4F6" xml:space="preserve">Utriuſ membri definitio ſuperiꝰ data eſt. </s>
                  <s xml:id="N1E4F9" xml:space="preserve">Sꝫ mo­
                    <lb/>
                  tus vniformiter difformis quo ad tempꝰ adhuc du­ </s>
                </p>
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