Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N1C8AF" level="3" n="2" type="other" type-free="tractatus">
              <div xml:id="N1DD6A" level="4" n="3" type="chapter" type-free="capitulum">
                <p xml:id="N1F995">
                  <s xml:id="N1FA53" xml:space="preserve">
                    <pb chead="Secundi tractatus" file="0161" n="161"/>
                  mīore velocitate quã in ſecūda / et ſic cõſequēter: tūc
                    <lb/>
                  ſpaciū ꝑtranſitū in totali hora ſe habet ad ſpaciū
                    <lb/>
                  ꝑtranſitū in prima parte ꝓportionali in ꝓportiõe
                    <lb/>
                  ſuꝑtripartiente quartas, qualis eſt .7. ad .4. </s>
                  <s xml:id="N1FA6B" xml:space="preserve">Pro-
                    <lb/>
                  batur / q2 ſpaciū ꝑtranſitū in prima parte ꝓporti-
                    <lb/>
                  onali ſe habet ad ſpaciū ꝑtranſitū in ſecunda in ꝓ­
                    <lb/>
                  portiõe dupla ſexquitertia, et in eadē ꝓportione ſe
                    <lb/>
                  habet ſpaciū ꝑtranſitū in ſeeunda ad ſpaciū ꝑtrã­
                    <lb/>
                  ſitum in tertia, et ſic cõſequenter: igitur totale ſpa-
                    <lb/>
                  ciū ſe habet ad ſpaciū ꝑtranſitū in prima parte ꝓ­
                    <lb/>
                  portiõali in ꝓportione ſupratripartiēte quartas
                    <lb/>
                  </s>
                  <s xml:id="N1FA7D" xml:space="preserve">Patet hec cõſequentia ex priori cõcluſione: hoc ad­
                    <lb/>
                  dito /  quodlibet corpus diuiſū per partes ꝓpor-
                    <lb/>
                  tionales ꝓportiõe dupla ſexquitertia ſe habet ad
                    <lb/>
                  primã partē ꝓportionalē in ꝓportione ſuꝑtripar­
                    <lb/>
                  tiente quartas: vt facile eſt intueri ex prima parte
                    <lb/>
                  huiꝰ operis. </s>
                  <s xml:id="N1FA8A" xml:space="preserve">Probat̄̄ tamen antecedens. </s>
                  <s xml:id="N1FA8D" xml:space="preserve">Quia ꝓ-
                    <lb/>
                  portio prime partis tēporis ad ſecundã eſt ſuꝑbi-
                    <lb/>
                  partiens tertias, et velocitatis prime partis ad ve­
                    <lb/>
                  locitatē ſecunde eſt ꝓportio ſuꝑbipartiens quītas /
                    <lb/>
                  igitur totius ſpacii ꝑtranſiti in prima parte ꝓpor­
                    <lb/>
                  tionali que eſt maius tēpus ad ſpaciū ꝑtranſitū in
                    <lb/>
                  ſecunda parte ꝓportionali eſt ꝓportio dupla ſex-
                    <lb/>
                  q̇tertia: et ſic ꝓbabis de ſpaciis ꝑtranſitis in aliis
                    <lb/>
                  partibꝰ quibuſcū īmediatis. </s>
                  <s xml:id="N1FAA0" xml:space="preserve">Cõſequentia ꝓbat̄̄ /
                    <lb/>
                  ꝑ tertiã ꝓpoſitionē ſecūdi notabilis huiꝰ q̄ſtionis
                    <lb/>
                  hoc addito /  proportio dupla ſexq̇tertia cõponit̄̄
                    <lb/>
                  adequate ex ꝓportione ſuꝑbipartiente tertias, et
                    <lb/>
                  ſuꝑbipartiente quintas: vt ptꝫ in his terminis .7.
                    <lb/>
                  .5.3. / et ſic ptꝫ correlariū
                    <note position="left" xlink:href="note-0161-01a" xlink:label="note-0161-01" xml:id="N1FB16" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N1FAB2" xml:space="preserve">¶ Sequitur ſecundo /  diui­
                    <lb/>
                  ſa hora ꝑ partes ꝓportionales ꝓportione dupla
                    <lb/>
                  mobili cõtinuo in duplo tardius mouente in parte
                    <lb/>
                  ſequēti minori quã in parte maiori īmediate prece­
                    <lb/>
                  denti illã: ſpaciū ꝑtranſitū in totali hora ſe habet
                    <lb/>
                  ad ſpaciū ꝑtranſitū in prima parte proportionali
                    <lb/>
                  hore in ꝓportione ſexquitertia. </s>
                  <s xml:id="N1FAC1" xml:space="preserve">Probatio / q2 pro­
                    <lb/>
                  portio cõpoſita ex ꝓportione tēporis maioris ad
                    <lb/>
                  tēpus minꝰ dupla, et velocitatis temporis maioris
                    <lb/>
                  ad velocitatē tēporis minoris ſimiliter dupla eſt
                    <lb/>
                  quadrupla, vt ſatis ↄ̨ſtat: et quodlibet totū diuiſū
                    <lb/>
                  ꝑ partes ꝓportionales ꝓportione quadrupla ſe
                    <lb/>
                  habet ad primã partē ꝓportionalē in proportione
                    <lb/>
                  ſexquitertia, vt ptꝫ ex prima parte: igr̄ totale ſpa-
                    <lb/>
                  ciū ꝑtranſitū in illa hora in caſu correlarii ſe ha-
                    <lb/>
                  bet ad ſpaciū ꝑtranſitū in prima parte ꝓportiõali
                    <lb/>
                  in ꝓportione ſexquitertia / quod fuit ꝓbandū. </s>
                  <s xml:id="N1FAD8" xml:space="preserve">Cõ-
                    <lb/>
                  ſequentia ptꝫ ex cõcluſione octaua </s>
                  <s xml:id="N1FADD" xml:space="preserve">¶ Sequit̄̄ tertio­
                    <lb/>
                   / diuiſa hora in partes ꝓportionales ꝓportione
                    <lb/>
                  tripla, mobili cõtinuo in quadruplo tardiꝰ mo-
                    <lb/>
                  uēte in parte ſequenti minori ꝙ̄ in īmediate p̄ceden­
                    <lb/>
                  ti eã: ſpaciū ꝑtranſitū in totali hora ſe habebit ad
                    <lb/>
                  ſpaciū ꝑtranſitū in prima parte ꝓportionali in ꝓ­
                    <lb/>
                  portione ſexquivndecima: pertranſito pedali in
                    <lb/>
                  prima: duodecim vndecimas pedalis ī totali hora
                    <lb/>
                  abſoluet. </s>
                  <s xml:id="N1FAF0" xml:space="preserve">Probatur / q2 ꝓportio cõpoſita ex ꝓpor­
                    <lb/>
                  tione tēporis maioris ad tēpus minꝰ tripla et velo-
                    <lb/>
                  citatis tēporis maioris ad velocitatē tēporis mi-
                    <lb/>
                  noris quadrupla eſt duodecupla, vt patet in his
                    <lb/>
                  terminis .12.4.1. et quodlibet totū diuiſuꝫ ꝑ partes
                    <lb/>
                  ꝓportionales ꝓportione duodecupla ſe habet ad
                    <lb/>
                  primã ſui partē ꝓportionalē in ꝓportione ſexqui
                    <lb/>
                  vndecima, vt ptꝫ ex prima parte: igitur ſpaciū per­
                    <lb/>
                  tranſitū a mobili in totali tēpore ſe habet ad ſpa­
                    <lb/>
                  cium ꝑtranſitum in prima parte proportionali in
                    <lb/>
                  proportione ſexquivndecima. </s>
                  <s xml:id="N1FB07" xml:space="preserve">Patet cõſequentia
                    <lb/>
                  ex octaua concluſione.</s>
                </p>
                <p xml:id="N1FB1C">
                  <s xml:id="N1FB1D" xml:space="preserve">Nona concluſio. </s>
                  <s xml:id="N1FB20" xml:space="preserve">Diuiſa hora per par­
                    <lb/>
                  tes ꝓportiõales q̈uis ꝓportione, et in certa ꝓpor-
                    <lb/>
                  tiõe ↄ̨tinuo mobile velociꝰ moueat̄̄ ī qualibet parte
                    <cb chead="Capitulū tertiū."/>
                  pari ſequenti quã in pari īmediate precedenti eaꝫ
                    <lb/>
                  et ſimiliter in certa proportione equali maiori, vel
                    <lb/>
                  minori, continuo in qualibet parte ſequente impa­
                    <lb/>
                  ri velocius moueatur quã in impari īmediate pre-
                    <lb/>
                  cedenti: ſpaciū pertranſitū in totali hora erit infi-
                    <lb/>
                  nitū dūmodo ꝓportio velocitatū ſit equalis pro-
                    <lb/>
                  portioni tempoꝝ vel maior: et ſi ꝓportio velocita-
                    <lb/>
                  tum partiū pariuꝫ, et ꝓportio velocitatū partium
                    <lb/>
                  impariū fuerit minor ꝓportione tempoꝝ: tunc ſpa­
                    <lb/>
                  cium pertranſitū in omnibus partibus paribus ſe
                    <lb/>
                  habet ad ſpaciū pertranſitū in prima illaꝝ pariū
                    <lb/>
                  in ꝓportione qua ſe habet aliquod totum diuiſuꝫ
                    <lb/>
                  per partes ꝓportionales ꝓportione per quã pro-
                    <lb/>
                  portio tempoꝝ excedit ꝓportionē velocitatum ad
                    <lb/>
                  primã partē ꝓportionale eiuſdē totius. </s>
                  <s xml:id="N1FB46" xml:space="preserve">Et ſimili-
                    <lb/>
                  ter dicendū eſt de ſpacio ꝑtranſito in omnibꝰ par-
                    <lb/>
                  tibus imparibus. </s>
                  <s xml:id="N1FB4D" xml:space="preserve">Declaratur hec cõcluſio iſto mo­
                    <lb/>
                  do: diuidatur hora per partes proportionales
                    <lb/>
                  proportione dupla, et capiantur ex vno latere oēs
                    <lb/>
                  ꝑtes pares: et ex alio oēs īpares, et in qualibet īpa­
                    <lb/>
                  ri ſequente moueatur a. mobile in quadruplo velo­
                    <lb/>
                  cius quã in impari īmediate precedenti eam: tunc
                    <lb/>
                  dicit prima pars concluſionis /  illud mobile in­
                    <lb/>
                  finitū ſpaciū ꝑtranſit et etiã infinitū ſpaciū tranſi-
                    <lb/>
                  ret ſi in qualibet ſequēti impari moueretur in quī-
                    <lb/>
                  tuplo velocius quã in impari īmediate precedenti
                    <lb/>
                  eam quia ꝓportio velocitatū eſt ibi maior vel equa­
                    <lb/>
                  lis ꝓportioni tempoꝝ. </s>
                  <s xml:id="N1FB66" xml:space="preserve">Tēpora em̄ illa continuo ſe
                    <lb/>
                  habent in ꝓportione quadrupla. </s>
                  <s xml:id="N1FB6B" xml:space="preserve">Si vero mobile
                    <lb/>
                  in qualibet parte ſequeti impari moueretur in du-
                    <lb/>
                  plo velociꝰ preciſe ꝙ̄ in parte īmediate precedenti
                    <lb/>
                  impari, diuiſione ſic facta in partes ꝓportionales
                    <lb/>
                  ꝓportione dupla: tunc ſpaciū ꝑtranſitū in omnibꝰ
                    <lb/>
                  partibus paribus ſe habet ad ſpaciū ꝑtrauſitū
                    <lb/>
                  in prima pari in ꝓportione dupla: et ſpaciū ꝑtran­
                    <lb/>
                  ſitum in omnibus partibus imparibus etiã ſe ha-
                    <lb/>
                  bet ad ſpaciū pertranſitū in prima impari in pro-
                    <lb/>
                  portione dupla: quia proportio tempoꝝ quadru-
                    <lb/>
                  pla excedit ꝓportionem velocitatū duplam ꝑ du-
                    <lb/>
                  plam: et corpus diuiſum per partes ꝓportionales
                    <lb/>
                  ꝓportione dupla ſe habet ad primã partē propor­
                    <lb/>
                  tionalem etiam in ꝓportione dupla, et etiã veloci-
                    <lb/>
                  tas maior eſt coextenſa tempori minori. </s>
                  <s xml:id="N1FB8A" xml:space="preserve">Ideo to-
                    <lb/>
                  tum ſpaciū pertranſitū in omnibus partibus im-
                    <lb/>
                  paribus eſt duplū ad ſpaciū ꝑtranſitū in prima
                    <lb/>
                  illarū impariū. </s>
                  <s xml:id="N1FB93" xml:space="preserve">Et conſimiliter dicendum eſt de pa­
                    <lb/>
                  ribus. </s>
                  <s xml:id="N1FB98" xml:space="preserve">Probatur hec concluſio ex predictis, et hoc
                    <lb/>
                  generaliter: et primo patet prima pars ex ſexta
                    <lb/>
                  concluſione: et ſecunda ex ſeptima.
                    <note position="right" xlink:href="note-0161-02a" xlink:label="note-0161-02" xml:id="N1FC5A" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N1FBA4" xml:space="preserve">¶ Ex hac conclu­
                    <lb/>
                  ſione ſequitur primo /  partita hora per partes ꝓ­
                    <lb/>
                  portionales ꝓportione dupla: et in prima illarum
                    <lb/>
                  mobile moueatur aliquanta velocitate vuiformi-
                    <lb/>
                  ter, et in ſecūda moueat̄̄ vniformiter intēdendo mo­
                    <lb/>
                  tū ſuū a gradu quo mouetur in prima vſ ad gra-
                    <lb/>
                  dum duplū: et in tertia moueatur illo gradu duplo
                    <lb/>
                  vniformiter: et in quarta intendat vniformiter mo-
                    <lb/>
                  tum ſuū ab illo gradu duplo vſ ad gradū duplū
                    <lb/>
                  illius, ita  in omnibus partibus imparibus mo-
                    <lb/>
                  ueatur vniformiter continuo in duplo velocius in
                    <lb/>
                  ſequente impari ꝙ̄ īmediate precedenti impari, et
                    <lb/>
                  in qualibet parte pari moueatur intendendo mo-
                    <lb/>
                  tum ſuum vniformiter a gradu partis imparis im­
                    <lb/>
                  mediate precedentis vſ ad gradum partis paris
                    <lb/>
                  īmediate ſequentis: ita  velocitates partium im-
                    <lb/>
                  parium reducte ad vniformieatem etiam ſi habe-
                    <lb/>
                  ant continuo in proportione dupla: tunc ſpacium
                    <lb/>
                  totale pertranſitum in hora ſe habebit in propor-
                    <lb/>
                  tione tripla ſexquialtera ad ſpacium pertranſi-
                    <lb/>
                  tum in prima parte proportionali impari. </s>
                  <s xml:id="N1FBCF" xml:space="preserve">Pro- </s>
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