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="N15C2F" level="4" n="1" type="chapter" type-free="capitulum">
                <p xml:id="N15D8B">
                  <s xml:id="N15DB3" xml:space="preserve">
                    <pb chead="Primi partis" file="0060" n="60"/>
                  aliquod mobile / hoc eſt aliquam reſiſentiam ali-
                    <lb/>
                  quãta velocitate ſubdupla virtus mouet ſubdu-
                    <lb/>
                  plam reſiſtentiam equali velocitate: hoc eſt. </s>
                  <s xml:id="N15DBF" xml:space="preserve">Si a-
                    <lb/>
                  liqua proportio maioris inequalitatis moueat
                    <lb/>
                  aliquam proportionē minoris inequalitatis ali-
                    <lb/>
                  qua velocitate: proportio equalis illi in minori-
                    <lb/>
                  bus terminis mouebit equali velocitate: quod la-
                    <lb/>
                  tius poſtea declarabitur.</s>
                </p>
              </div>
              <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
                  <lb/>
                et improbantur ſecunda et tertia opinio-
                  <lb/>
                nes. de cauſa velocitatis motuum.</head>
                <p xml:id="N15DD8">
                  <s xml:id="N15DD9" xml:space="preserve">SEcunda opinio ponit velocita­
                    <lb/>
                  tem motus ſequi proportionem exceſſus
                    <lb/>
                  potentie motoris ad potentiã rei mote.
                    <lb/>
                  </s>
                  <s xml:id="N15DE1" xml:space="preserve">Et vult dicere hec opinio /  velocitas in motibus
                    <lb/>
                  ſequitur proportionem exceſſus actiuitatis moto­
                    <lb/>
                  ris ad actiuitatem rei mote. </s>
                  <s xml:id="N15DE8" xml:space="preserve">Ita  ſi vnus motor
                    <lb/>
                  ita ſe habeat reſpectu ſui mobilis /  actiuitas eiꝰ
                    <lb/>
                  excedaṫ actiuitateꝫ mobilis per quatuor gradus /
                    <lb/>
                  et actiuitas alterius motoris excedat actiuitatem
                    <lb/>
                  ſui modilis per duos gradus:  tunc primus mo-
                    <lb/>
                  tor mouebit in duplo velocius ſecūdo. </s>
                  <s xml:id="N15DF5" xml:space="preserve">Et iſta opi-
                    <lb/>
                  nio videtur coincidere cum prima dempto /  vna
                    <lb/>
                  comparat actiuitatem ad reſiſtentiã: et altera acti-
                    <lb/>
                  uitatem ad actiuitatem.</s>
                </p>
                <note position="left" xml:id="N15DFE" xml:space="preserve">Obiicit̄̄
                  <lb/>
                ſecunde
                  <lb/>
                opinioni</note>
                <p xml:id="N15E06">
                  <s xml:id="N15E07" xml:space="preserve">Sed contra hanc opinionem arguit̄̄
                    <lb/>
                  ſic / quia ſi illa eſſet vera / ſequeretur /  aliquod mo-
                    <lb/>
                  uens ſucceſſiue moueret ſine reſiſtētia: īmo ita cito
                    <lb/>
                  cum reſiſtentia ſicut ſine reſiſtentia / ſed conſequēs
                    <lb/>
                  eſt falſum igitur, illud ex quo ſequitur: ſequela ꝓ-
                    <lb/>
                  batur et pono caſum /  ſit virtus: vt .8. agentis: et
                    <lb/>
                  virtus vt quatuor patientis in quo ſit reſiſtentia:
                    <lb/>
                  vt .2. / et ſit aliquod aliud paſſum in quo nulla ſit re­
                    <lb/>
                  ſiſtentia ſed dumtaxat actiuitas vt quatuor: quo
                    <lb/>
                  poſito arguitur ſic. </s>
                  <s xml:id="N15E1C" xml:space="preserve">Agens vt .8. eque velociter a-
                    <lb/>
                  git in vtrū iſtorum paſſorum: cum proportiones
                    <lb/>
                  actiuitatum ſint equales: et tamen in vno paſſo a-
                    <lb/>
                  git cum reſiſtentia: et in alio ſine reſiſtentia igitur
                    <lb/>
                  propoſitum.</s>
                </p>
                <p xml:id="N15E27">
                  <s xml:id="N15E28" xml:space="preserve">Tertia opinio eſt /  ponit velocitatē
                    <lb/>
                  in motu ſequi proportionem reſiſtentiarum inter
                    <lb/>
                  ſe: ita  ſi ſint duo agentia equalia: et moueãt du-
                    <lb/>
                  as reſiſtentias inequales: in quacun ꝓportione
                    <lb/>
                  vna reſiſtentia eſt minor alia in eadē proportione
                    <lb/>
                  velocius mouetur: vt ſi virtus vt octo moueat re-
                    <lb/>
                  ſiſtentiam: vt .4: et reſiſtentiam: vt .3. quia reſiſten-
                    <lb/>
                  tia: vt .3. eſt in ſexquitertio minor reſiſtentia: vt .4.
                    <lb/>
                  ideo virtus vt .8. in ſexquitertio velocius mouebit
                    <lb/>
                  reſiſtentiam vt .3. ꝙ̄ reſiſtentiam vt .4.</s>
                </p>
                <p xml:id="N15E3D">
                  <s xml:id="N15E3E" xml:space="preserve">Sed contra iſtaꝫ opinionē arguitur
                    <lb/>
                  ſic. </s>
                  <s xml:id="N15E43" xml:space="preserve">Supponendo /  ſi aliqua virtus puta vt .8. / ſuf­
                    <lb/>
                  ficiat mouere aliquod mobile aliquanta velocita­
                    <lb/>
                  te /  eadē virtus ſufficit mouere aliquod aliud mo­
                    <lb/>
                  bile in duplo tardius, et aliquod in triplo, et aliqḋ
                    <lb/>
                  in quadruplo, et ſic in infinitum. </s>
                  <s xml:id="N15E4E" xml:space="preserve">Ita  ſi virtus vt
                    <lb/>
                  8. ſufficit mouere aliquod mobile in hora ꝑ leucã:
                    <lb/>
                  eadem virtus ſufficit mouere aliquod maius mo-
                    <lb/>
                  bile in hora per mediam leucam: et illamet virtus
                    <lb/>
                  ſufficit mouere aliquod maius in hora per tertiã
                    <lb/>
                  partem leuce: et aliquod aliud per quartaꝫ: et ſic in
                    <lb/>
                  infinitū. </s>
                  <s xml:id="N15E5D" xml:space="preserve">quo poſito ſic arguitur / ſi opinio eſſet ve-
                    <lb/>
                  ra ſequeretur /  mouens vt .8. poſſet mouere quã-
                    <lb/>
                  tumcun mobile: ſed conſequens eſt falſum: quia
                    <lb/>
                  tunc eſſet infinite actiuitatis: igitur illud ex quo
                    <lb/>
                  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
                    <lb/>
                  quate: quo poſito tale mouens poteſt mouere ali-
                    <lb/>
                  quod mobile in duplo tardius puta in hora per
                    <lb/>
                  mediam leucam, vt patet ex ſuppoſitione: et nõ ni­
                    <lb/>
                  ſi mobile vt .8. / vt patet ex opinione: quoniã ꝓpor-
                    <lb/>
                  tio velocitatem ſequitur ꝓportionem reſiſtentiaꝝ
                    <lb/>
                  ſed velocitas eſt ſubdupla: ergo reſiſtentia dupla
                    <lb/>
                  </s>
                  <s xml:id="N15E7B" xml:space="preserve">Itē aliquod mobile poteſt mouere illa virtus ſub-
                    <lb/>
                  tripla velocitate: vt patet ex ſuppoſitione: et non
                    <lb/>
                  niſi triple reſiſtentie / vt patet ex opinione: et ſic in
                    <lb/>
                  infinitum: igitur propoſitū. </s>
                  <s xml:id="N15E84" xml:space="preserve">Et hec ſola ratio ſuffi­
                    <lb/>
                  cienter hanc opinionem deſtruit et elidit.</s>
                </p>
              </div>
              <div xml:id="N15E89" level="4" n="3" type="chapter" type-free="capitulum">
                <head xml:id="N15E8E" xml:space="preserve">Capitulum tertium / in quo ponitur
                  <lb/>
                alia opinio et vera.</head>
                <p xml:id="N15E93">
                  <s xml:id="N15E94" xml:space="preserve">QUarta opinio et vera eſt que
                    <lb/>
                  nūc cõmuniter tenetur: et ponit velocita-
                    <lb/>
                  tem motus ſequi ꝓportionē ꝓportionū
                    <lb/>
                  hoc eſt proportionē geometricã: vt ſi aliqua virtꝰ
                    <lb/>
                  moueat aliquã reſiſtentiã a proportione dupla: et
                    <lb/>
                  vna alia moueat eandē reſiſtentiam vel vnã aliaꝫ
                    <lb/>
                  (in idem reddit) a proportione quadrupla: talis
                    <lb/>
                  virtus mouēs a proportione quadrupla in eadeꝫ
                    <lb/>
                  proportione velocius mouet in qua proportione
                    <lb/>
                  quadrupla proportio duplam excedit: et quia ex-
                    <lb/>
                  cedit quadrupla duplam in proportione dupla,
                    <lb/>
                  vt ptꝫ ex ſexto capite ſecunde partis: ideo quadru­
                    <lb/>
                  pla proportio in duplo velocius mouet. </s>
                  <s xml:id="N15EAF" xml:space="preserve">Et ſi ali-
                    <lb/>
                  qua virtus moueat aliquam reſiſtentiã a propor-
                    <lb/>
                  tione ſexquialtera: et alia mouet eandem reſiſten-
                    <lb/>
                  tiam in proportione tripla: tunc virtus mouens a
                    <lb/>
                  proportione tripla velocius mouet virtute mouē-
                    <lb/>
                  proportione ſexquialtera in ea proportione qua
                    <lb/>
                  tripla ſexquialteram exuperat: et quia talis ꝓpor­
                    <lb/>
                  tio que eſt inter triplam et ſexquialteram eſt irra-
                    <lb/>
                  tionalis: vt ex ſexto et ſeptimo capitibꝰ ſecūde par­
                    <lb/>
                  tis facile monſtratur: ideo nec ſpaciū pertranſitū
                    <lb/>
                  a ꝓportione tripla excedit ſpaciū pertranſitum a
                    <lb/>
                  proportione ſexquialtera in proportione aliqua
                    <lb/>
                  multiplici, nec ſuperparticulari, nec ſupraparti-
                    <lb/>
                  ente, nec multiplici ſuperparticulari, nec multipli­
                    <lb/>
                  ci ſuprapartiente, quod poſtea magis elucidabit̄̄
                    <lb/>
                  </s>
                  <s xml:id="N15ECF" xml:space="preserve">Et pro fundamento et baſi huius opinionis pono
                    <lb/>
                  duas concluſiones.</s>
                </p>
                <p xml:id="N15ED4">
                  <s xml:id="N15ED5" xml:space="preserve">Prima concluſio / velocitas motꝰ nec
                    <lb/>
                  penes proportionem exceſſus potentiarū ad inui-
                    <lb/>
                  cem, nec penes proportionem actiuitatū ad inuicē /
                    <lb/>
                  nec reſiſtentiarum inter ſe attenditur. </s>
                  <s xml:id="N15EDE" xml:space="preserve">Probatur
                    <lb/>
                  hec concluſio ex hiis / que in ſuperioribus capitibꝰ
                    <lb/>
                  in impugnationibus triū opinionū dicta ſunt.</s>
                </p>
                <p xml:id="N15EE5">
                  <s xml:id="N15EE6" xml:space="preserve">Secunda concluſio. </s>
                  <s xml:id="N15EE9" xml:space="preserve">Uelocitas mo-
                    <lb/>
                  tuū ſequit̄̄ / et attendi hꝫ penes ꝓportionē propor-
                    <lb/>
                  tionū: ita  in quacū proportione vna ꝓportio
                    <lb/>
                  eſt maior aut mīor alia: ī eadē ꝓportiõe velocitas
                    <lb/>
                  maior aut minor euadet. </s>
                  <s xml:id="N15EF4" xml:space="preserve">Et ſi fuerat proportio ꝓ­
                    <lb/>
                  portionū rationalis: rationales velocitates erūt
                    <lb/>
                  et ſi irrationalis: cõmenſurari nõ poterunt veloci-
                    <lb/>
                  tates taliū motuū. </s>
                  <s xml:id="N15EFD" xml:space="preserve">Probatur hec concluſio ſic / de­
                    <lb/>
                  clarata per ſillogiſmum diuiſim eo ordine quo
                    <lb/>
                  eam paulus venetus inducit quoniã velocitas et
                    <lb/>
                  tarditas motus attendi habet penes ꝓportioneꝫ
                    <lb/>
                  exceſſiuū inter ſe, aut penes ꝓportionē actiuitatū
                    <lb/>
                  inter ſe, aut reſiſtentiarum, aut penes ꝓportiõe
                    <lb/>
                  ꝓportionū: ſed nõ penes .3. prima / vt ptꝫ ex ãterio-
                    <lb/>
                  ri cõcluſione. </s>
                  <s xml:id="N15F0E" xml:space="preserve">igitur penes quartum / quod fuit pro­
                    <lb/>
                  bandum. </s>
                  <s xml:id="N15F13" xml:space="preserve">Cõſequentia patet a ſufficienti diuiſiõe
                    <lb/>
                  </s>
                  <s xml:id="N15F17" xml:space="preserve">Nõ em̄ ymaginari valent aliqui alii modi ſaltem
                    <lb/>
                  um apparentia quibus attendi habet motuū ve-
                    <lb/>
                  ocitas et tarditas / igitur diuiſio ſufficiens.</s>
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