Alvarus, Thomas, Liber de triplici motu, 1509

Table of contents

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                    <pb chead="Primi partis" file="0060" n="60"/>
                  aliquod mobile / hoc eſt aliquam reſiſentiam ali-
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                  quãta velocitate ſubdupla virtus mouet ſubdu-
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                  plam reſiſtentiam equali velocitate: hoc eſt. </s>
                  <s xml:id="N15DBF" xml:space="preserve">Si a-
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                  liqua proportio maioris inequalitatis moueat
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                  aliquam proportionē minoris inequalitatis ali-
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                  qua velocitate: proportio equalis illi in minori-
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                  bus terminis mouebit equali velocitate: quod la-
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                  tius poſtea declarabitur.</s>
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              <div xml:id="N15DCC" level="4" n="2" type="chapter" type-free="capitulum">
                <head xml:id="N15DD1" xml:space="preserve">Capitulum ſecundū / in quo recitantur
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                et improbantur ſecunda et tertia opinio-
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                nes. de cauſa velocitatis motuum.</head>
                <p xml:id="N15DD8">
                  <s xml:id="N15DD9" xml:space="preserve">SEcunda opinio ponit velocita­
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                  tem motus ſequi proportionem exceſſus
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                  potentie motoris ad potentiã rei mote.
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                  </s>
                  <s xml:id="N15DE1" xml:space="preserve">Et vult dicere hec opinio /  velocitas in motibus
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                  ſequitur proportionem exceſſus actiuitatis moto­
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                  ris ad actiuitatem rei mote. </s>
                  <s xml:id="N15DE8" xml:space="preserve">Ita  ſi vnus motor
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                  ita ſe habeat reſpectu ſui mobilis /  actiuitas eiꝰ
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                  excedaṫ actiuitateꝫ mobilis per quatuor gradus /
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                  et actiuitas alterius motoris excedat actiuitatem
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                  ſui modilis per duos gradus:  tunc primus mo-
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                  tor mouebit in duplo velocius ſecūdo. </s>
                  <s xml:id="N15DF5" xml:space="preserve">Et iſta opi-
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                  nio videtur coincidere cum prima dempto /  vna
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                  comparat actiuitatem ad reſiſtentiã: et altera acti-
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                  uitatem ad actiuitatem.</s>
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                <note position="left" xml:id="N15DFE" xml:space="preserve">Obiicit̄̄
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                ſecunde
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                opinioni</note>
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                  <s xml:id="N15E07" xml:space="preserve">Sed contra hanc opinionem arguit̄̄
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                  ſic / quia ſi illa eſſet vera / ſequeretur /  aliquod mo-
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                  uens ſucceſſiue moueret ſine reſiſtētia: īmo ita cito
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                  cum reſiſtentia ſicut ſine reſiſtentia / ſed conſequēs
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                  eſt falſum igitur, illud ex quo ſequitur: ſequela ꝓ-
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                  batur et pono caſum /  ſit virtus: vt .8. agentis: et
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                  virtus vt quatuor patientis in quo ſit reſiſtentia:
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                  vt .2. / et ſit aliquod aliud paſſum in quo nulla ſit re­
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                  ſiſtentia ſed dumtaxat actiuitas vt quatuor: quo
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                  poſito arguitur ſic. </s>
                  <s xml:id="N15E1C" xml:space="preserve">Agens vt .8. eque velociter a-
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                  git in vtrū iſtorum paſſorum: cum proportiones
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                  actiuitatum ſint equales: et tamen in vno paſſo a-
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                  git cum reſiſtentia: et in alio ſine reſiſtentia igitur
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                  propoſitum.</s>
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                <p xml:id="N15E27">
                  <s xml:id="N15E28" xml:space="preserve">Tertia opinio eſt /  ponit velocitatē
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                  in motu ſequi proportionem reſiſtentiarum inter
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                  ſe: ita  ſi ſint duo agentia equalia: et moueãt du-
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                  as reſiſtentias inequales: in quacun ꝓportione
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                  vna reſiſtentia eſt minor alia in eadē proportione
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                  velocius mouetur: vt ſi virtus vt octo moueat re-
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                  ſiſtentiam: vt .4: et reſiſtentiam: vt .3. quia reſiſten-
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                  tia: vt .3. eſt in ſexquitertio minor reſiſtentia: vt .4.
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                  ideo virtus vt .8. in ſexquitertio velocius mouebit
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                  reſiſtentiam vt .3. ꝙ̄ reſiſtentiam vt .4.</s>
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                  <s xml:id="N15E3E" xml:space="preserve">Sed contra iſtaꝫ opinionē arguitur
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                  ſic. </s>
                  <s xml:id="N15E43" xml:space="preserve">Supponendo /  ſi aliqua virtus puta vt .8. / ſuf­
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                  ficiat mouere aliquod mobile aliquanta velocita­
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                  te /  eadē virtus ſufficit mouere aliquod aliud mo­
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                  bile in duplo tardius, et aliquod in triplo, et aliqḋ
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                  in quadruplo, et ſic in infinitum. </s>
                  <s xml:id="N15E4E" xml:space="preserve">Ita  ſi virtus vt
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                  8. ſufficit mouere aliquod mobile in hora ꝑ leucã:
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                  eadem virtus ſufficit mouere aliquod maius mo-
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                  bile in hora per mediam leucam: et illamet virtus
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                  ſufficit mouere aliquod maius in hora per tertiã
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                  partem leuce: et aliquod aliud per quartaꝫ: et ſic in
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                  infinitū. </s>
                  <s xml:id="N15E5D" xml:space="preserve">quo poſito ſic arguitur / ſi opinio eſſet ve-
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                  ra ſequeretur /  mouens vt .8. poſſet mouere quã-
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                  tumcun mobile: ſed conſequens eſt falſum: quia
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                  tunc eſſet infinite actiuitatis: igitur illud ex quo
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                  ſequitur. </s>
                  <s xml:id="N15E68" xml:space="preserve">Sequela probatur: et pono /  mouens vt
                    <cb chead="Capitulū ſcḋm  tertiū."/>
                  8. moueat reſiſtentiam vt .4. per leucã in hora ade­
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                  quate: quo poſito tale mouens poteſt mouere ali-
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                  quod mobile in duplo tardius puta in hora per
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                  mediam leucam, vt patet ex ſuppoſitione: et nõ ni­
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                  ſi mobile vt .8. / vt patet ex opinione: quoniã ꝓpor-
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                  tio velocitatem ſequitur ꝓportionem reſiſtentiaꝝ
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                  ſed velocitas eſt ſubdupla: ergo reſiſtentia dupla
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                  </s>
                  <s xml:id="N15E7B" xml:space="preserve">Itē aliquod mobile poteſt mouere illa virtus ſub-
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                  tripla velocitate: vt patet ex ſuppoſitione: et non
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                  niſi triple reſiſtentie / vt patet ex opinione: et ſic in
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                  infinitum: igitur propoſitū. </s>
                  <s xml:id="N15E84" xml:space="preserve">Et hec ſola ratio ſuffi­
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                  cienter hanc opinionem deſtruit et elidit.</s>
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                <head xml:id="N15E8E" xml:space="preserve">Capitulum tertium / in quo ponitur
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                alia opinio et vera.</head>
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                  <s xml:id="N15E94" xml:space="preserve">QUarta opinio et vera eſt que
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                  nūc cõmuniter tenetur: et ponit velocita-
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                  tem motus ſequi ꝓportionē ꝓportionū
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                  hoc eſt proportionē geometricã: vt ſi aliqua virtꝰ
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                  moueat aliquã reſiſtentiã a proportione dupla: et
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                  vna alia moueat eandē reſiſtentiam vel vnã aliaꝫ
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                  (in idem reddit) a proportione quadrupla: talis
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                  virtus mouēs a proportione quadrupla in eadeꝫ
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                  proportione velocius mouet in qua proportione
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                  quadrupla proportio duplam excedit: et quia ex-
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                  cedit quadrupla duplam in proportione dupla,
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                  vt ptꝫ ex ſexto capite ſecunde partis: ideo quadru­
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                  pla proportio in duplo velocius mouet. </s>
                  <s xml:id="N15EAF" xml:space="preserve">Et ſi ali-
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                  qua virtus moueat aliquam reſiſtentiã a propor-
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                  tione ſexquialtera: et alia mouet eandem reſiſten-
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                  tiam in proportione tripla: tunc virtus mouens a
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                  proportione tripla velocius mouet virtute mouē-
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                  proportione ſexquialtera in ea proportione qua
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                  tripla ſexquialteram exuperat: et quia talis ꝓpor­
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                  tio que eſt inter triplam et ſexquialteram eſt irra-
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                  tionalis: vt ex ſexto et ſeptimo capitibꝰ ſecūde par­
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                  tis facile monſtratur: ideo nec ſpaciū pertranſitū
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                  a ꝓportione tripla excedit ſpaciū pertranſitum a
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                  proportione ſexquialtera in proportione aliqua
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                  multiplici, nec ſuperparticulari, nec ſupraparti-
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                  ente, nec multiplici ſuperparticulari, nec multipli­
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                  ci ſuprapartiente, quod poſtea magis elucidabit̄̄
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                  </s>
                  <s xml:id="N15ECF" xml:space="preserve">Et pro fundamento et baſi huius opinionis pono
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                  duas concluſiones.</s>
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                  <s xml:id="N15ED5" xml:space="preserve">Prima concluſio / velocitas motꝰ nec
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                  penes proportionem exceſſus potentiarū ad inui-
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                  cem, nec penes proportionem actiuitatū ad inuicē /
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                  nec reſiſtentiarum inter ſe attenditur. </s>
                  <s xml:id="N15EDE" xml:space="preserve">Probatur
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                  hec concluſio ex hiis / que in ſuperioribus capitibꝰ
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                  in impugnationibus triū opinionū dicta ſunt.</s>
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                <p xml:id="N15EE5">
                  <s xml:id="N15EE6" xml:space="preserve">Secunda concluſio. </s>
                  <s xml:id="N15EE9" xml:space="preserve">Uelocitas mo-
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                  tuū ſequit̄̄ / et attendi hꝫ penes ꝓportionē propor-
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                  tionū: ita  in quacū proportione vna ꝓportio
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                  eſt maior aut mīor alia: ī eadē ꝓportiõe velocitas
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                  maior aut minor euadet. </s>
                  <s xml:id="N15EF4" xml:space="preserve">Et ſi fuerat proportio ꝓ­
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                  portionū rationalis: rationales velocitates erūt
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                  et ſi irrationalis: cõmenſurari nõ poterunt veloci-
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                  tates taliū motuū. </s>
                  <s xml:id="N15EFD" xml:space="preserve">Probatur hec concluſio ſic / de­
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                  clarata per ſillogiſmum diuiſim eo ordine quo
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                  eam paulus venetus inducit quoniã velocitas et
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                  tarditas motus attendi habet penes ꝓportioneꝫ
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                  exceſſiuū inter ſe, aut penes ꝓportionē actiuitatū
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                  inter ſe, aut reſiſtentiarum, aut penes ꝓportiõe
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                  ꝓportionū: ſed nõ penes .3. prima / vt ptꝫ ex ãterio-
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                  ri cõcluſione. </s>
                  <s xml:id="N15F0E" xml:space="preserve">igitur penes quartum / quod fuit pro­
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                  bandum. </s>
                  <s xml:id="N15F13" xml:space="preserve">Cõſequentia patet a ſufficienti diuiſiõe
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                  </s>
                  <s xml:id="N15F17" xml:space="preserve">Nõ em̄ ymaginari valent aliqui alii modi ſaltem
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                  um apparentia quibus attendi habet motuū ve-
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                  ocitas et tarditas / igitur diuiſio ſufficiens.</s>
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