Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N20F21" level="3" n="3" type="other" type-free="tractatus">
              <div xml:id="N20F2E" level="4" n="1" type="chapter" type-free="capitulum">
                <pb chead="Tertii tractatus" file="0203" n="203"/>
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              <div xml:id="N24010" level="4" n="2" type="chapter" type-free="capitulum">
                <head xml:id="N24015" xml:space="preserve">Secundū capitulū huiꝰ tractatus / in quo ſolito
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                pro more diſputatiue inquirimus penes quid velo­
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                citas augmētationis attendi habeat.</head>
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                  <s xml:id="N2401D" xml:space="preserve">NUnc cõſequēter q̄ritur vtrū
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                  velocitas motus augmētatiõis penes ꝓ­
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                  portionalē acquiſitionē ̄titatis attēdi
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                  habeat: an penes abſolutã acq̇ſitione ̄titatis.</s>
                </p>
                <p xml:id="N24026">
                  <s xml:id="N24027" xml:space="preserve">Arguitur primo /  non penes propor­
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                  tionabilē acquiſitionē ̄titatis ita  non ſemꝑ illḋ
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                  quod in eodē tꝑe maiorem ꝓportionē acquirit ̄
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                  aliud velocius augmētetur ꝙ̄ aliud in eodē tēpore
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                  quia ſi ſic tūc ſequeretur /  a. et b. ſunt equalia: et a
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                  continuo velocius augmētabit̄̄ ꝙ̄ b. et tamen ſemꝑ
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                  a. manebit minus .b. / ſꝫ conſequēs eſt manifeſte fal-
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                  ſum: igitur illud ex quo ſequit̄̄. </s>
                  <s xml:id="N24038" xml:space="preserve">Sequela ꝓbat̄̄: et
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                  volo /  .a. et .b. ſint duo pedalia: et acquirat vnifor-
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                  miter .b. in hora vnū pedale: et nichil deperdat de
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                  qnantitate prehabita .a vero acquirat vnū pedale
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                  vniformiter ꝑ horã: et deꝑdat vnū ſemipedale ̄ti-
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                  tatis prehabite vniformiter in illa hora. </s>
                  <s xml:id="N24045" xml:space="preserve">quo poſi-
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                  to arguitur ſic / .a. et .b. ſunt modo equalia: et ſemꝑ .a
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                  poſt hoc manebit minꝰ .b. / vt cõſtat qm̄ ſi nichil de­
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                  perderet maneret equale: ſꝫ modo cõtinuo perdet.
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                  </s>
                  <s xml:id="N2404F" xml:space="preserve">ergo cõtinuo manet minus: et tamē .a. cõtinuo velo­
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                  cius augmētabitur ꝙ̄ .b. / igitur intentū. </s>
                  <s xml:id="N24054" xml:space="preserve">Probatur
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                  minor / q2 .a. cõtinuo erit minus .b. et cõtinuo equa-
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                  lem ̄titatē acquiret cū .b. / igit̄̄ .a. cõtinuo maiorem
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                  ꝓportionē acquiret ꝙ̄ .b. et penes acq̇ſitionē maio­
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                  ioris ꝓportiõis in eodē tēpore attēdit̄̄ maior veloci­
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                  tas augmētatõis: igit̄̄ .a. ↄ̨tinuo velociꝰ augmētabi­
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                  tur ꝙ̄ .b. / quod fuit ꝓbandū. </s>
                  <s xml:id="N24063" xml:space="preserve">Hec ↄ̨ſequētia patꝫ de
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                  ſe: et prior ex octaua ſuppoſitiõe quarti capitis ſe-
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                  cunde partis: et in aliis pleriſ locis libri arguta
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                  eſt.
                    <note position="left" xlink:href="note-0203-01a" xlink:label="note-0203-01" xml:id="N240AF" xml:space="preserve">Dicitur</note>
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                  <s xml:id="N24071" xml:space="preserve">¶ Dices et bene negando ſequelam: et ad ꝓbatio­
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                  nē admiſſo caſu ad bonū ſenſum poſſet em̄ negari /
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                  vt poſtea dicemus: reſpõdeo negando minorē vi-
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                  delicet /  .a. cõtinuo poſt hoc velocius augmentabi­
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                  tur ꝙ̄ .b. et ad ꝓbationē concedo /  .a. cõtinuo mane­
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                  bit minus et nego /  ↄ̨tinuo equalē quãtitatem acq̇­
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                  ret cū .b. ſicut de facto eſt negandū qm̄ ſi nichil de-
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                  perderet ſemꝑ acquireret equalē ̄titatē: ſꝫ modo
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                  cõtinuo deꝑdit: ergo cõtinuo acquirit minorē: quo­
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                  niã in tota hora nõ acquirit .a. niſi ſemipedale. </s>
                  <s xml:id="N24086" xml:space="preserve">Ma­
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                  nebit em̄ in fine pedale cū dimidio quoniã mãſiſſet
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                  bipedale niſi perdidiſſet dimidiū. </s>
                  <s xml:id="N2408D" xml:space="preserve">¶ Item in inſtã-
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                  ti medio hore acquiſiuit .a. vnã quartã pedalis .b.
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                  vero vnã medietatē: et ſic in illa prīa medietate ma­
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                  iorē quãtitatē acquiſiuit .b. ꝙ̄ .a. cuius oppoſitum
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                  aſſumit argumētum.
                    <note position="left" xlink:href="note-0203-02a" xlink:label="note-0203-02" xml:id="N240B5" xml:space="preserve">Coutra
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                    ca'lcna.</note>
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                  <s xml:id="N2409D" xml:space="preserve">¶ Ex quo a ꝑte infertur cal-
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                  latorē male induxiſſe illud cõſequēs tan̄ ſequens
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                  ex opinione quam impugnamus: qm̄ illa cõcluſio
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                  nullo pacto ſequit̄̄ expoſitione. </s>
                  <s xml:id="N240A6" xml:space="preserve">Teneat̄̄ igit̄̄ poſi-
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                  tio vniuerſaliter.</s>
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                <p xml:id="N240BD">
                  <s xml:id="N240BE" xml:space="preserve">Sed contra hanc reſponſionē argui­
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                  tur ſic / quia ſi illa poſitio eſſet vniuerſaliter vera / ſe­
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                  queretur hec concluſio. </s>
                  <s xml:id="N240C5" xml:space="preserve"> ſi ſint duo ſiue equalia ſiue
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                  inequalia q̄ cõtinuo eque velociter diminuãtur per­
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                  dendo cõtinuo equales ꝓportiones eque cito veni-
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                  ent ad non quãtum: ſed ↄ̨ſequens eſt falſum: igitur
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                  illud ex quo ſequit̄̄: falſitas ↄ̨ſequētis ꝓbat̄̄: q2 ſtat
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                   aliqua duo in aliquo tepore eque velociter dimi­
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                  nuatur ꝑdendo in illo tꝑe p̄ciſe .4. duplas: igit̄̄ tūc
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                  ↄ̨tinuo eque velociter diminuētur: et tamē nõ eque
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                  cito deueniēt ad nõ ̄tū: et ꝑ ↄ̨ſequēs illḋ illatuꝫ eſt
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                  vna conditionalis q̄ eſt falſa: igitur illud cõſequēs
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                  eſt falſum. </s>
                  <s xml:id="N240DC" xml:space="preserve">¶ Dices et bñ /  de rigore illud ↄ̨ſequēs
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                  eſt falſum ̄uis ſub illa forma ponatur a calcula-
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                  tore: ſed oportet addere in antecedende illius con-
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                  ditionalis q̄ eque velociter diminuūtur vſ ad nõ
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                  quãtū: et tūc illa ↄ̨cluſio eſt ↄ̨cedenda ſecundū opi-
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                  nionē. </s>
                  <s xml:id="N240EA" xml:space="preserve">Quod ſic oſtēditur / quoniã ſi aliquod corpꝰ
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                  puta .a. in hora diminuat̄̄ ad nõ quãtū: illud corpꝰ
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                  infinitã latitudinē ꝓportionū deperdet: et .b. aliud
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                  corpus maius in tota illa hora eque velociter di-
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                  minuitur cū .a. / ergo ſequit̄̄ /  infinitã latitudinē ꝓ-
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                  portionis etiã deperdit .b. in illa hora: et vltra infi­
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                  nitã latitudinē ꝓportionis deperdit .b. in illa hora
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                  et nõ reſtituit̄̄ in inſtanti terminatiuo priſtine quã­
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                  titati vt volo: igit̄̄ in inſtãti termīatiuo hore .b. erit
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                  nõ ̄tum: et tunc .a. erit nõ ̄tum: igitur eq̄ cito .a. et .b.
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                  deuenient ad nõ ̄tū in tali caſu: qḋ fuit ꝓbandum
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                  </s>
                  <s xml:id="N24102" xml:space="preserve">Sꝫ tã probo hanc cõſequētiã .b. inifinitã latitudinē
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                  ꝓportiõis deꝑdit ī hora et ñ reſtituit̄̄ in inſtanti ter­
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                  minatiuo priſtine ̄titati: ergo in illo inſtanti non
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                  quãtū manet </s>
                  <s xml:id="N2410B" xml:space="preserve">Quia ſi in illo inſtãti maneret alicuiꝰ
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                  quãtitatis: ſit illa quãtitas vna milleſima exempli
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                  gratia: et tã ſequit̄̄ /  in illa hora nõ deꝑdit niſi mil­
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                  lecuplã ꝓportionē: et per ↄ̨ſequēs nõ infinitã / quod
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                  eſt oppoſitū ↄ̨ſequētis. </s>
                  <s xml:id="N24116" xml:space="preserve">Et iſto modo ꝓbat̄̄ hec ↄ̨ſe-
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                  quētia prius facta deuenit .a. ad nõ ̄tum / ergo infi­
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                  nitam ꝓportionē deperdit: quia ſi ſolū finita puta
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                  millecuplã iam illud in fine maneret vt vna milleſi­
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                  ma et ſic non maneret nõ quãtum.</s>
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                  <s xml:id="N24122" xml:space="preserve">Sed contra hoc arguitur ſic / quia ſi
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                  hoc eſſet verū ſeq̇retur eodē mõ /  ſi in aliqua duo
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                  ſiue equalia ſiue inequalia in certa ꝓportione cõti­
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                  nuo inequaliter diminuãtur vſ ad non quãtum ta­
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                  lia eque cito deueniunt ad nõ quãtū: ſed conſequēs
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                  videtur falſum: igitur illud ex quo ſequitur. </s>
                  <s xml:id="N2412F" xml:space="preserve">Seq̄la
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                  ꝓbatur et volo /  ſint .a. et .b. pedale: et ꝑdat .a. in
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                  qualibet parte ꝓportionali ꝓportionē quadruplã
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                  b. vero ſemꝑ in duplo minorē proportionē in qua­
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                  libet parte ꝓportionali puta ꝓportionē duplam.
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                  </s>
                  <s xml:id="N2413B" xml:space="preserve">Et arguitur ſic / cū primū .a. ꝑdiderit infinitas ꝓpor­
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                  tiones quadruplas ip̄m deuenerit ad non quantū:
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                  et tunc .b. ꝑdidit īfinitas duplas / vt patet ex caſu: er­
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                  go tunc .b. deuenit ad nõ quãtū. </s>
                  <s xml:id="N24144" xml:space="preserve">Nõ em̄ poteſt infini­
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                  tas duplas perdere quī infinitã latitudinē ꝓportio­
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                  nis deperdat: et ꝑ conſequens eque cito .a et .b. de-
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                  uenient ad nõ quãtū: quod fuit probandū. </s>
                  <s xml:id="N2414D" xml:space="preserve">Et iſto
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                  modo probabis de q̇buſcū aliis corporibus ſiue
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                  equalibus ſiue inequalibus: dūmodo vnum altero
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                  in certa ꝓportione continuo velocius diminuatur
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                  ad non quantum.</s>
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                  <s xml:id="N24159" xml:space="preserve">Secūdo prīcipaliter ad idem arguit̄̄
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                  ſic. </s>
                  <s xml:id="N2415E" xml:space="preserve">Si velocitas augmētatiõis attenderet̄̄ penes ꝓ­
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                  portionalē acquiſitionē quãtitatis: ſequeretur hec
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                  concluſio /  ſi aliquid inciperet ſucceſſiue augeri
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                  a non quãto: ipſum infinite velociter inciperet au-
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                  geri: ſꝫ conſequens eſt falſum: igitur illud ex quo ſe­
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                  quitur. </s>
                  <s xml:id="N2416B" xml:space="preserve">Falſitas cõſequēs arguit̄̄ ſic: q2 tunc ſeq̇re­
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                  tur /  quodlibet tale infinite velociter inciperet ac-
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                  quirere de quãtitate: ſꝫ ↄ̨ſequens eſt falſum: igitur
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                  illud ex quo ſequitur. </s>
                  <s xml:id="N24174" xml:space="preserve">Sed tã probo ſequelam / quia
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                  ſi .a. incipit augeri a nõ quãto poſt inſtans inceptio­
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                  nis talis augmentationis ipſum eſt aliquãtum: et
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                  ante illud inſtans fuit in duplo minus: et in triplo
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                  et in quadruplo et ſic infinitum: ergo inter illud in­
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                  ſtans et īſtans initiatiuū illud acquiſiuit infinitam
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                  proportionem: et per cõſequēs ſequit̄̄ /  ipſum infi-
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                  nite velociter incipit augeri. </s>
                  <s xml:id="N24185" xml:space="preserve">patet conſequentia ex­
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                  poſitione.
                    <note position="right" xlink:href="note-0203-03a" xlink:label="note-0203-03" xml:id="N241A8" xml:space="preserve">Dictur.</note>
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                  <s xml:id="N2418F" xml:space="preserve">¶ Dices et bene concedendo cõcluſioneꝫ
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                  illatam / vt bene ꝓbat argumentū / et negando falſi­
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                  tatem conſequentis: et ad probationē nego iſtam
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                  conſequentiã infinite velociter incipit augeri: ergo
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                  infinite velociter incipit a. acquirerere de quãtitate / </s>
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