Alvarus, Thomas, Liber de triplici motu, 1509

Table of contents

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            <div xml:id="N15C22" level="3" n="1" type="other" type-free="tractatus">
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                <pb chead="Primi partis" file="0059" n="59"/>
                <head xml:id="N15C38" xml:space="preserve">Capitulum primum / in quo ponitur
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                et improbatur vna opinio: de cauſa
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                velocitatis motus.</head>
                <p xml:id="N15C3F">
                  <s xml:id="N15C40" xml:space="preserve">QUoniã errores elimi-
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                  nãdi et extirpandi ſunt antea
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                  ̄ veritas inferatur: ideo pre-
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                  mittūtur et improbantur falſe
                    <lb/>
                  opiniones more communiter
                    <lb/>
                  hanc tractantium materiam.</s>
                </p>
                <p xml:id="N15C4D">
                  <s xml:id="N15C4E" xml:space="preserve">Prima opinio de velo­
                    <lb/>
                  citate motuum penes cauſam fuit aliquorum phi­
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                  loſophorū dicentium velocitatem in motu atten-
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                  di debere penes proportionem exceſſus potentia-
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                  rum ſupra ſuas reſiſtētias: ita  ſi exceſſus vnius
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                  potentie ſupra ſuam reſiſtentiaꝫ fuerit duplus ad
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                  exceſſum alterius potentie ſupra ſuam reſiſtentiã
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                  motus / ille erit duple velocitatis ad alium motuꝫ /
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                  vt ſi .6. moueant .3 / et .4. moueant .2. / hoc eſt actiui-
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                  tas vt .4. / quia exceſſus .6. ad .3. eſt ſexquialterus
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                  ad exceſſum .4. ad .2. in ſexquialtero velocius .6.
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                  mouebunt .3. ꝙ̄ .4.2. </s>
                  <s xml:id="N15C67" xml:space="preserve">Et ſic conſequenter dicas in
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                  aliis. </s>
                  <s xml:id="N15C6C" xml:space="preserve">Hanc opinionem fundant eius factores in
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                  verbo philoſophi primo celi et mundi capitulo de
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                  infinito. </s>
                  <s xml:id="N15C73" xml:space="preserve">inferentis velocitatem motuum penes ex­
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                  cellentiã exceſſus: et in verbo commentatoris quar­
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                  to phiſicorum cõmento .35. et .39. in quibus locis vi-
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                  detur huic opinioni ſatis applaudere.</s>
                </p>
                <note position="left" xml:id="N15C7C" xml:space="preserve">Contra
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                primam
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                opinio-
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                nē inſtat̄̄</note>
                <p xml:id="N15C86">
                  <s xml:id="N15C87" xml:space="preserve">Sed cõtra iſtam opinionē arguitur /
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                  qui ſi illa eſſet vera / ſequeretur /  motus proueni-
                    <lb/>
                  tes ab equalibus proportionibus eſſent inequa-
                    <lb/>
                  les: ſed conſequens eſt falſum / igitur illud ex quo
                    <lb/>
                  ſequitur. </s>
                  <s xml:id="N15C92" xml:space="preserve">Sequela probatur et volo /  potentia vt
                    <lb/>
                  8. moueat reſiſtentiam vt .4. et potentia vt .4. mo-
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                  reſiſtentiaꝫ vt .2. / quo poſito arguitur ſic. </s>
                  <s xml:id="N15C99" xml:space="preserve">Ille due
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                  proportiones potentiarum ad reſiſtentias ſunt
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                  equales cum vtra ſit dupla: et tamen vna illarū
                    <lb/>
                  puta .8. ad .4. velocius mouet ꝙ̄ altera igitur pro­
                    <lb/>
                  poſitum. </s>
                  <s xml:id="N15CA4" xml:space="preserve">Minor probatur / quia exceſſus eſt maior /
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                  igitur ſecundum opinionem velocitas eſt maior.
                    <lb/>
                  </s>
                  <s xml:id="N15CAA" xml:space="preserve">¶ Dices concedendo ſequelam: et negando falſi-
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                  tatem conſequentis.</s>
                </p>
                <p xml:id="N15CAF">
                  <s xml:id="N15CB0" xml:space="preserve">Sed contra / quia tunc ſequeretur 
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                  aliquam duo mobilia mouerentur ab equalibꝰ pro­
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                  portionibus: tamen vnum in duplo velocius mo-
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                  ueretur altero / ſed conſequens eſt falſum / ergo il-
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                  lud ex quo ſequitur. </s>
                  <s xml:id="N15CBB" xml:space="preserve">Sequela probatur retento ſu­
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                  periori caſu. </s>
                  <s xml:id="N15CC0" xml:space="preserve">Nam potentia vt .8. mouebit reſiſtē-
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                  tiam vt quatuor in duplo velocius ꝙ̄ potentia vt
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                  quatuor moueat reſiſtentiaꝫ vt .2. quoniã exceſſus
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                  eſt duplus / et tamen ille proportiões ſunt equales
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                  igitur propoſitum.
                    <note position="left" xlink:href="note-0059-01a" xlink:label="note-0059-01" xml:id="N15CDB" xml:space="preserve">Dicitur</note>
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                  <s xml:id="N15CD0" xml:space="preserve">¶ Dices concedendo qnod in-
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                  fertur: nec illud habes pro inconuenienti: īmo pro
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                  ſequela opinionis.</s>
                </p>
                <note position="left" xml:id="N15CE1" xml:space="preserve">Replica</note>
                <p xml:id="N15CE5">
                  <s xml:id="N15CE6" xml:space="preserve">Sed contra / quia tunc ſequeretur 
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                  ſi aliqua potentia moueret aliquam reſiſtentiam
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                  aliquali velocitate: medietas potentie non moue-
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                  ret medietatē reſiſtentie tanta velocitate cõſequēs
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                  eſt falſum: et contra philoſophum ſeptimo phiſi-
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                  corum expreſſe ponentem oppoſitum / igitur illud
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                  ex quo / ſequitur ſequela probatur et volo /  poten­
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                  tia vt .8. moueat reſiſtentiam vt quatuor: deinde
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                  medietas potentie vt octo puta .4. moueat medie-
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                  tatē reſiſtentie puta duo quo poſito arguo ſic / po­
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                  tentia vt octo in duplo plus excedit ſuam reſiſten­
                    <cb chead="Capitulum primū."/>
                  tiam ꝙ̄ medietas eius / que eſt vt quatuor excedat
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                  medietatem ſue reſiſtentie / que eſt vt .2. cum vna ex-
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                  cedat per quatuor et alia per .2. / igitur non tanta
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                  velocitate medietas potentie mouet medietatem
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                  reſiſtentie / quanta tota potentia mouet totam re-
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                  ſiſtentiam / quod fuit inferendum.</s>
                </p>
                <note position="right" xml:id="N15D0A" xml:space="preserve">Cõfirma­
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                tio.</note>
                <p xml:id="N15D10">
                  <s xml:id="N15D11" xml:space="preserve">¶ Et confirmatur / quia ſi opinio eſſet vera / ſeque-
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                  retur /  ſi duo equi traherent duas nauas diuiſim
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                  per vnã horam:  illi equi coniūcti traherent illas
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                  duas naues coniūctim in duplo velocius: ſed con­
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                  ſequens eſt contra experientiã / igitur illud ex quo
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                  ſequitur. </s>
                  <s xml:id="N15D1E" xml:space="preserve">Sequela ꝓbatur / quoniã ipſis coniūctis
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                  exceſſus eſſet duplus ad exceſſum vtriuſ diuiſim /
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                  igitur velocitas eſſet dupla: conſequentia patet ex
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                  opinione. </s>
                  <s xml:id="N15D27" xml:space="preserve">Sed antecedēs probatur / quia quando­
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                  cun ſunt due proportiones equales: ſi minores
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                  numeri vniantur et maiores ſimiliter / et fiat vna ꝓ­
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                  portio: exceſſus in tali proportiõe eſſet duplus ad
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                  exceſſum cuiuſlibet alterius. </s>
                  <s xml:id="N15D32" xml:space="preserve">Exemplum / vt capta
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                  proportiõe .4. ad .2. / et vna alia ſibi equali in eiſdē
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                  terminis puta .4. ad .2. / deinde vniendo minores
                    <lb/>
                  numeros puta binarium cum binario et maiores
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                  puta quaternarium cum quaternario: reſultabit
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                  proportio dupla .8. ad .4. / et ibi numerus maior ex­
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                  cedet minorem numerum duplo exceſſu ad exceſſū
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                  aliarum proportionum / vt patet ad ſenſum. </s>
                  <s xml:id="N15D43" xml:space="preserve">Aliud
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                  exemplum: capiantur due proportiones ſexquial­
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                  tere in eiſdem terminis: puta .6. ad .4. et .6. ad .4. / et
                    <lb/>
                  manifeſtum eſt /  exceſſus in talibus proportioni­
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                  bus eſt binarius. </s>
                  <s xml:id="N15D4E" xml:space="preserve">Et ſi vniantur numeri mino-
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                  res et maiores reſultabit proportio .12. ad .8. / que
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                  erit ſexquialtera: in qua maior numerꝰ excedit mi­
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                  norē quaternario: et per cõſequens duplo exceſſus
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                  ad aliū exceſſū et ſic infallibiliter īuenies in omni
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                  ſpecie proportiones cuiuſcun generis fuerit: vt
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                  patet abunde ex ſecūda parte in tertio correlario
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                  tertie concluſionis quarti capitis.</s>
                </p>
                <note position="right" xml:id="N15D5F" xml:space="preserve">Cõfirma­
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                tio ſcḋa.</note>
                <p xml:id="N15D65">
                  <s xml:id="N15D66" xml:space="preserve">¶ Confirmatur ſecundo / quoniam ſi poſitio eſſet
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                  vera: ſequeretur /  capta vna libra plumbi ele-
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                  uantis in rota mediam libram ex oppoſito per
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                  aliquod ſpacium in aliquo tempore:  due libre
                    <lb/>
                  eleuarent vnam libram ex oppoſito in duplo mi-
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                  nori tempore: et per conſequens in duplo velocius /
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                  ſed hoc eſt manifeſte falſum: et contra experientiã
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                  que ſatis facile haberi poteſt: igitur illud ex quo
                    <lb/>
                  ſequitur. </s>
                  <s xml:id="N15D79" xml:space="preserve">Sequela probatur / quia exceſſus eſſet du­
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                  plus ad priorem exceſſum: puta exceſſus quo due
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                  libre excedunt vnam libram / ad exceſſum quo vna
                    <lb/>
                  libra excedit mediam libram: vt in priori ↄ̨firma-
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                  tione probatum eſt. </s>
                  <s xml:id="N15D84" xml:space="preserve">¶ Et propter hoc relinquitur
                    <lb/>
                  hec opinio contraria experimento et rationi et ſen­
                    <lb/>
                  tentie paripatheticorum.</s>
                </p>
                <p xml:id="N15D8B">
                  <s xml:id="N15D8C" xml:space="preserve">Ad fulcimentum autem predicte opi­
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                  nionis que innititur auctoritatibus philoſophi
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                  et cõmentatoris. </s>
                  <s xml:id="N15D93" xml:space="preserve">Dicitur cõcedendo predictas au-
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                  ctoritates: et negando conſequentiam: et ratio eſt:
                    <lb/>
                  quia cum philoſophus aut cõmentator dicunt ve-
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                  locitatem motus ſequi exceſſum aut excellentiam
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                  potentie motoris ſupra ſuam reſiſtentiam: intelli­
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                  gitur per excellentiam ſiue exceſſum potentie mo-
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                  toris ſupra ſuam reſiſtentiam exceſſus vnius pro-
                    <lb/>
                  portionis ſupra alteram ita  ſit ſenſus: quanto
                    <lb/>
                  vna ꝓportio excedit alteram tanto velocitas mo-
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                  tus proueniens ab illa excedit velocitatem motus
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                  prouenientem ab alia. </s>
                  <s xml:id="N15DAA" xml:space="preserve">Et  iſta ſit intentio philo­
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                  ſophi patet ex regula / quam ponit in ſeptimo phi­
                    <lb/>
                  ſicorū ſuperius allegata que (vt latius poſtea di-
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                  citur) ſic intelligi debet. </s>
                  <s xml:id="N15DB3" xml:space="preserve">Si aliqua virtus moueat </s>
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