Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N15C22" level="3" n="1" type="other" type-free="tractatus">
              <div xml:id="N16983" level="4" n="6" type="chapter" type-free="capitulum">
                <pb chead="Primi tractatus" file="0073" n="73"/>
                <note position="left" xml:id="N172EA" xml:space="preserve">argumē-
                  <lb/>
                tū calcu.</note>
                <p xml:id="N172F0">
                  <s xml:id="N172F1" xml:space="preserve">Quinto arguitur ſic </s>
                  <s xml:id="N172F4" xml:space="preserve">Si ille regule
                    <lb/>
                  eſſent vere: ſequeretur /  ſi aliqua reſiſtentia vni-
                    <lb/>
                  formiter ꝓportionabiliter creſceret reſpectu dua­
                    <lb/>
                  rum potentiarum equaliuꝫ potentium moueri cū
                    <lb/>
                  tali reſiſtentia: tales potentie vniformiter remit-
                    <lb/>
                  terent motus ſuos. </s>
                  <s xml:id="N17301" xml:space="preserve">ſed conſequens eſt falſum / igi-
                    <lb/>
                  tur illud ex quo ſequitur. </s>
                  <s xml:id="N17306" xml:space="preserve">Sequela eſt nota. </s>
                  <s xml:id="N17309" xml:space="preserve">et falſi­
                    <lb/>
                  tas conſequentis oſtenditur. </s>
                  <s xml:id="N1730E" xml:space="preserve">q2 ex illo ſequitur / 
                    <lb/>
                  alique due potentie equales ab eodem gradu ve-
                    <lb/>
                  locitatis incipiunt remittere motus ſuos ad non
                    <lb/>
                  gradum ſemper eque velociter remittendo. </s>
                  <s xml:id="N17317" xml:space="preserve">et nihi­
                    <lb/>
                  lominus non equaliter mouentur ſed conſequens
                    <lb/>
                  manifeſte implicat / igitur illud ex quo ſequitur.</s>
                </p>
                <p xml:id="N1731E">
                  <s xml:id="N1731F" xml:space="preserve">Sequela probatur et pono duas poteutias equa­
                    <lb/>
                  les / vt .8.a. videlicet et b. / et capio duo media equa-
                    <lb/>
                  lis reſiſtētie c. videlicet et d. reſiſtentie vt .4. et c. ſit
                    <lb/>
                  pedalis quãtitatis et d. ſemipedalis. </s>
                  <s xml:id="N17328" xml:space="preserve">et moueatur
                    <lb/>
                  a. potentia ſupra c. pedale: et b. ſupra d. ſemipeda­
                    <lb/>
                  le per horam. </s>
                  <s xml:id="N1732F" xml:space="preserve">et creſcat reſiſtentia vtriuſ eque ꝓ­
                    <lb/>
                  portionabiliter vniformiter per horam in qua d.
                    <lb/>
                  ſemipedale rarefiat vniformiter ſecundum partē
                    <lb/>
                  non pertranſitam: taliter  in fine hore ſit etiam
                    <lb/>
                  pedale ſicut c. / quo poſito arguitur ſic / a. et b. incipi­
                    <lb/>
                  unt remittere motus ſuos ab equali gradu veloci­
                    <lb/>
                  tatis propter eque proportionale crementum re-
                    <lb/>
                  ſiſtentie: et mouebuntur ſemper vniformiter: et ta-
                    <lb/>
                  men non mouebuntur eque velociter in illa hora.
                    <lb/>
                  </s>
                  <s xml:id="N17343" xml:space="preserve">igitur propoſitum. </s>
                  <s xml:id="N17346" xml:space="preserve">Maior patet ex caſu et minor
                    <lb/>
                  probatur / quoniam a. pertranſibit c. pedale in ho­
                    <lb/>
                  ra et b. nõ pertranſibit d. / quod in fine preciſe erit
                    <lb/>
                  pedale nec aliquod tantum: igitur non equaliter
                    <lb/>
                  mouebuntur. </s>
                  <s xml:id="N17351" xml:space="preserve">Maior patet ex caſu et minor ꝓba-
                    <lb/>
                  tur / quoniam b. remittit motum ſuum ad non gra­
                    <lb/>
                  dum in illa hora / et d. ſpacium vniformiter rarefit
                    <lb/>
                  ſecundum partem non pertranſitam / ergo aliquã­
                    <lb/>
                  do in hora / aliqua pars non tranſita velocius mo­
                    <lb/>
                  uebitur quam ipſum b. / et per conſequens nūquã
                    <lb/>
                  ipſum b. perueniet ad illam partem. </s>
                  <s xml:id="N17360" xml:space="preserve">Patet hec cõ­
                    <lb/>
                  ſequentia </s>
                  <s xml:id="N17365" xml:space="preserve">Nam ſi aliquod mobile mouetur in ali­
                    <lb/>
                  quo medio: et pars aliqua ipſius medii antecedēs
                    <lb/>
                  mouetur velocius ipſo mobili: nun̄ illud mobile
                    <lb/>
                  perueniet ad illam partem / vt ſatis conſtat ſed ſic
                    <lb/>
                  fit in propoſito igitur.
                    <note position="left" xlink:href="note-0073-01a" xlink:label="note-0073-01" xml:id="N1742E" xml:space="preserve">1. ↄ̨firma­
                      <lb/>
                    tio.</note>
                  </s>
                  <s xml:id="N17375" xml:space="preserve">¶ Et confirmatur quoniaꝫ /
                    <lb/>
                  ſi illud conſequens eſſet verum ſequeretur in caſu
                    <lb/>
                  poſito /  b. pertrauſiret d. ante finem hore et tamē
                    <lb/>
                  non pertranſiret in hora ipſum d. / hoc manifeſte ī­
                    <lb/>
                  plicat igitur. </s>
                  <s xml:id="N17380" xml:space="preserve">Secunda pars huius conſequentis
                    <lb/>
                  deducta eſt. </s>
                  <s xml:id="N17385" xml:space="preserve">et prima probatur ſupponendo /  qñ
                    <lb/>
                  aliquid mouetur vniformiter difformiter vſ ad
                    <lb/>
                  non gradum in aliquo tempore: ſpaciū pertran-
                    <lb/>
                  ſitum in prima medietate illius temporis eſt tri-
                    <lb/>
                  plum ad ſpacium pertranſitum in ſecunda medie­
                    <lb/>
                  tate / vt poſtea in capite tertio ſecundi tractatꝰ oſtē­
                    <lb/>
                  detur. </s>
                  <s xml:id="N17394" xml:space="preserve">Suppono ſecundo /  d. ſemipedale in inſtã­
                    <lb/>
                  ti medio temporis motus erit tres quarte / vt patet
                    <lb/>
                  </s>
                  <s xml:id="N1739A" xml:space="preserve">Quoniam ipſum d. acquirit ſemipedalem quan-
                    <lb/>
                  titatem vniformiter in illa hora / igitur ī ṗma me-
                    <lb/>
                  dietate hore acq̇rit medietateꝫ ſemipedalis puta
                    <lb/>
                  vnam quartã adequate </s>
                  <s xml:id="N173A3" xml:space="preserve">Quo poſito ſic argumē-
                    <lb/>
                  tor motus ipſius b. eſt vniformiter difformis ad
                    <lb/>
                  uon gradum in illa hora / vt patet ex caſu et moue­
                    <lb/>
                  tur equaliter cum a. / ſed a. in prima medietate ho-
                    <lb/>
                  re pertranſit tres quartas pedalis / vt patet ex pri­
                    <lb/>
                  ma ſuppoſitione: igitur tunc b. pertranſit tres q̈r­
                    <lb/>
                  tas pedalis adeq̈te ipſius d. ſꝫ d. tūc adeq̈te ē quã­
                    <lb/>
                  titatis trium quartarum / vt patet ex ſecunda ſup-
                    <lb/>
                  poſitione: igitur tunc d. in medio hore eſt adequa­
                    <lb/>
                  te pertranſitum / quod fuit probandum.
                    <note position="left" xlink:href="note-0073-02a" xlink:label="note-0073-02" xml:id="N17436" xml:space="preserve">2. confir.</note>
                  </s>
                  <s xml:id="N173BD" xml:space="preserve">Confirma­
                    <lb/>
                  tur ſecundo / quia ſi illud conſequens eſſet verū ſe-
                    <cb chead="Capitulum ſextum"/>
                  queretur /  per motum vniformiter difformē ad
                    <lb/>
                  non gradum non pertranſiretur in triplo maius
                    <lb/>
                  ſpacium in prima medietate temporis quam in ſe­
                    <lb/>
                  cunda / ſed iſtud conſequens eſt falſum / vt inferiꝰ lo­
                    <lb/>
                  co preallegato oſtendetur / igitur illud ex quo ſe-
                    <lb/>
                  quitur. </s>
                  <s xml:id="N173CF" xml:space="preserve">Sequela probatur / quoniam in caſu
                    <lb/>
                  poſito in inſtanti medio temporis .b. non pertran­
                    <lb/>
                  ſit tres quartas: et illud eſt triplum ſpacium ad re­
                    <lb/>
                  ſiduum pedalis puta ad vnã quartam / igitur pro­
                    <lb/>
                  poſitum </s>
                  <s xml:id="N173DA" xml:space="preserve">Minor eſt nota et maior probatur / quo-
                    <lb/>
                  niam ex caſu b. ſpacium ſiue medium debet conti-
                    <lb/>
                  nue per horam vniformiter rarefieri ſecundum ꝑ-
                    <lb/>
                  tem non pertranſitam: ergo in ipſa hora in quoli­
                    <lb/>
                  bet inſtanti intrinſeco debet eſſe aliqua pars non
                    <lb/>
                  pertranſita: ſed ſi in medio inſtanti temporis b. ꝑ­
                    <lb/>
                  tranſiret tres quartas in illo inſtanti ipſum b. eſ­
                    <lb/>
                  ſet in termino illius ſpacii / et nulla pars tunc eſſet
                    <lb/>
                  non pertrãſita </s>
                  <s xml:id="N173ED" xml:space="preserve">(Erit enim d. ſpacium in inſtanti
                    <lb/>
                  medio adequate quantitatis trium quartarū pe­
                    <lb/>
                  dalis adequate / vt probatum eſt in anteriori con-
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                  firmatione) / igitur in tali inſtanti ille tres quarte
                    <lb/>
                  non ſunt adequate pertranſite / quod fuit proban­
                    <lb/>
                  dum. </s>
                  <s xml:id="N173FA" xml:space="preserve">Alias enim iam non rarefieret / tunc ſecū­
                    <lb/>
                  dum partem non pertranſitam.
                    <note position="right" xlink:href="note-0073-03a" xlink:label="note-0073-03" xml:id="N1743C" xml:space="preserve">3. confir.</note>
                  </s>
                  <s xml:id="N17404" xml:space="preserve">¶ Confirmat̄̄ ter­
                    <lb/>
                  tio / quia ſi illud conſequens eſſet veruꝫ ſequeretur
                    <lb/>
                  in caſu poſito /  cū motus vniformiter difformis
                    <lb/>
                  deueniret ad velocitatem equalem velocitati rare­
                    <lb/>
                  factionis (rarefactio enim motus localis eſt) nul-
                    <lb/>
                  lum penitus punctum talis ſpacii poſſet pertran-
                    <lb/>
                  ſire. </s>
                  <s xml:id="N17413" xml:space="preserve">quoniam poſt illud inſtans / quodlibet pūctuꝫ
                    <lb/>
                  precedens mobile mouebitur velocius ipſo mobi­
                    <lb/>
                  li quoniam tale punctum mouebitur vniformiter /
                    <lb/>
                  et b. continuo remittet motum ſuum. </s>
                  <s xml:id="N1741C" xml:space="preserve">ſed hoc ē fal-
                    <lb/>
                  ſum igitur illud ex quo ſequitur </s>
                  <s xml:id="N17421" xml:space="preserve">Falſitas conſeq̄n­
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                  tis oſtenditur / quoniam tunc ſequeretur /  b. ãtea
                    <lb/>
                  quam deueniret ad non gradum motus: ceſſaret
                    <lb/>
                  moueri ſuper dato ſpacio vel in dato ſpacio d.</s>
                </p>
                <p xml:id="N17442">
                  <s xml:id="N17443" xml:space="preserve">Item ſequeretur /  ipſum b. equalis potētie cū a.
                    <lb/>
                  non poſſet pertranſire equalem reſiſtentiam cū a. /
                    <lb/>
                  et hoc eſt impoſſibile igitur. </s>
                  <s xml:id="N1744A" xml:space="preserve">Sequela probat̄̄ / quo­
                    <lb/>
                  niam b. non poteſt pertranſire mediuꝫ d. poſtquã
                    <lb/>
                  deueniret ad equalitatem motus cum medio: et ta­
                    <lb/>
                  men medium d. eſt equalis reſiſtentie cuꝫ medio c /
                    <lb/>
                  quod pertranſit a. igitur propoſitum.</s>
                </p>
                <p xml:id="N17455">
                  <s xml:id="N17456" xml:space="preserve">Reſpondeo breuiter ad argumentuꝫ
                    <lb/>
                  cum duabus confirmationibus non admittendo
                    <lb/>
                  caſum. </s>
                  <s xml:id="N1745D" xml:space="preserve">Argumenta enim probant caſum implica­
                    <lb/>
                  re </s>
                  <s xml:id="N17462" xml:space="preserve">Probant enim /  b. nunquam deueniet ad ter-
                    <lb/>
                  minum ipſius d. / et confirmatio prima ꝓbat /  de­
                    <lb/>
                  ueniet ad terminum eius in medio īſtanti tempo-
                    <lb/>
                  ris: et ſic implicat /  rarefiat dūtaxat ſecundum ꝑ­
                    <lb/>
                  tem non pertranſitam cum ceteris particulis ca-
                    <lb/>
                  ſus. </s>
                  <s xml:id="N1746F" xml:space="preserve">¶ Pro ſolutione tertie confirmationis ſup-
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                  ponendem eſt /  rarefactio eſt motus localis.
                    <note position="right" xlink:href="note-0073-04a" xlink:label="note-0073-04" xml:id="N174FD" xml:space="preserve">duplex ē
                      <lb/>
                    mediuꝫ ꝑ
                      <lb/>
                    qḋ aliq̇d
                      <lb/>
                    mouetur</note>
                  </s>
                  <s xml:id="N17479" xml:space="preserve">Se­
                    <lb/>
                  cundo ſupponendum eſt /  duplex eſt medium per
                    <lb/>
                  quod aliquid mouetur quando ipſum mediū ra-
                    <lb/>
                  refit </s>
                  <s xml:id="N17482" xml:space="preserve">Quoddam enim eſt medium quod per motuꝫ
                    <lb/>
                  ſuum etiam mouet mobile in eo exiſtens. </s>
                  <s xml:id="N17487" xml:space="preserve">cuiuſmo­
                    <lb/>
                  di eſt nauis que mouet nautã ad motū ſui: ita  ſi
                    <lb/>
                  nauta moueatur verſus illam partem verſus quã
                    <lb/>
                  mouetur nauis duplici motu mouetur: et motu na­
                    <lb/>
                  uis et motu proprio. </s>
                  <s xml:id="N17492" xml:space="preserve">Ita etiam ſit de homine natã­
                    <lb/>
                  te in flumine qui ſi natet verſus fluctum illius flu­
                    <lb/>
                  minis duplici motu mouetur et motu proprio et
                    <lb/>
                  motu fluminis trahentis ipſum. </s>
                  <s xml:id="N1749B" xml:space="preserve">Aliud eſt mediuꝫ
                    <lb/>
                  ad cuius motum localem nõ mouetur mobile ī eo
                    <lb/>
                  exiſtens cuiuſmodi eſt aer. </s>
                  <s xml:id="N174A2" xml:space="preserve">Diuidit enim mobile
                    <lb/>
                  potius aerem quam trahetur ab aere. </s>
                  <s xml:id="N174A7" xml:space="preserve">¶ His poſi­
                    <lb/>
                  tis reſpondeo ad confirmationem diſtinguendo </s>
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