Alvarus, Thomas, Liber de triplici motu, 1509

Table of figures

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                <p xml:id="N214A2">
                  <s xml:id="N21511" xml:space="preserve">
                    <pb chead="De motu rarefactionis et condenſationis." file="0178" n="178"/>
                  ante inſtans medium totius temporis. </s>
                  <s xml:id="N21519" xml:space="preserve">incipiet tale
                    <lb/>
                  corpus rarefieri poſt̄ condēſabit̄̄: igitur inſtans
                    <lb/>
                  mediū illius temporis non eſt inſtans in quo tale
                    <lb/>
                  corpus incipit rarefieri poſt̄ antea condenſabat̄̄.
                    <lb/>
                  </s>
                  <s xml:id="N21523" xml:space="preserve">Conſequētia pꝫ et arguit̄̄ añs et volo /  illa medie-
                    <lb/>
                  tas denſior deperdat vniformiter duos gradꝰ den­
                    <lb/>
                  ſitatis et illos acq̇rat medietas minus denſa / et ma­
                    <lb/>
                  nifeſtum eſt /  medietas denſior efficitur in ſexqui­
                    <lb/>
                  quinto minus denſa et ſic acquirit ſupra ſe vnam
                    <lb/>
                  quintam pedalis: et alia medietas efficitur in quī-
                    <lb/>
                  tuplo denſior ꝙ̄ erat antea et ſic deꝑdit q̈tuor quin­
                    <lb/>
                  tas ſui et manet p̄ciſe vna quīta pedalis: volo dein­
                    <lb/>
                  de  medietas dēſior ꝑdat medietatem vnius gra-
                    <lb/>
                  dus et tm̄ acq̇rat medietas minꝰ denſa eq̄ velociter:
                    <lb/>
                  </s>
                  <s xml:id="N21539" xml:space="preserve">Et argr̄ ſic / in tꝑe illo in q̊ pars denſior deperdit me­
                    <lb/>
                  dietate vnius gradus et pars minꝰ denſa tm̄ acq̇rit
                    <lb/>
                  iã totū rarefit. </s>
                  <s xml:id="N21540" xml:space="preserve">et illud tp̄s eſt añ inſtans medium vt
                    <lb/>
                  pꝫ ex ſe: igr̄ añ inſtãs mediū totiꝰ tꝑis īcipit tale cor­
                    <lb/>
                  pus rarefieri poſt̄ cõdēſabat̄̄. </s>
                  <s xml:id="N21547" xml:space="preserve">pꝫ ↄ̨ña et argr̄ ma­
                    <lb/>
                  ior / q2 in tp̄e illo pars dēſior q̄ ē maior pedali deꝑ-
                    <lb/>
                  dit ꝓportionē ſexquidecimã nonnã in dēſitate et ſic
                    <lb/>
                  acq̇rit vnã decimã nonã vniꝰ pedalis et plus. </s>
                  <s xml:id="N21550" xml:space="preserve">Pars
                    <lb/>
                  vero minus denſa efficit̄̄ in ſexquiquīto denſior, et
                    <lb/>
                  ꝑ ↄ̨ñs in ſexq̇quinto minor et ſic perdit vnã ſextã ſui
                    <lb/>
                  et ipſa eſt vna quinta pedalis. </s>
                  <s xml:id="N21559" xml:space="preserve">g̊ perdit vnã ſextam
                    <lb/>
                  quinte pedalis: et ſexta vnius quīte pedalis eſt vna
                    <lb/>
                  trigeſima pedalis / vt pꝫ intuenti: igr̄ illḋ totale cor­
                    <lb/>
                  pus ꝑdit vnã trigeſimã vniꝰ pedalis et acq̇rit pluſ̄
                    <lb/>
                  vnã decimã nona in tp̄e illo añ inſtãs mediū: igitur
                    <lb/>
                  plus acq̇rit de quãtitate ꝙ̄ deperdit et per cõſeq̄ns
                    <lb/>
                  rarefit / quod fuit probandum.</s>
                </p>
                <p xml:id="N21572">
                  <s xml:id="N21573" xml:space="preserve">Quīto prīcipaliṫ argr̄ ſic </s>
                  <s xml:id="N21576" xml:space="preserve">Si raritas
                    <lb/>
                  et denſitas eēnt poſſibiles. </s>
                  <s xml:id="N2157B" xml:space="preserve">Seq̄ret̄̄ /  datis duobꝰ
                    <lb/>
                  corporibꝰ inequalibus maiore plus continente de
                    <lb/>
                  materia ꝙ̄ minus ſemꝑ maius eſſet dēſius minore.
                    <lb/>
                  </s>
                  <s xml:id="N21583" xml:space="preserve">ↄ̨ñs eſt falſū. </s>
                  <s xml:id="N21586" xml:space="preserve">igr̄ et añs </s>
                  <s xml:id="N21589" xml:space="preserve">Seq̄la ſuadet̄̄ q2 capto cor-
                    <lb/>
                  pore bipedali vniformiter qḋ habeat tres gradus
                    <lb/>
                  materie. </s>
                  <s xml:id="N21590" xml:space="preserve">et pedali  habeat vnum gradū materie
                    <lb/>
                  dūtaxat manifeſtū eſt  maius eſt dēſius mīore q2
                    <lb/>
                  ſi manente eadem quãtitate maius ꝑderet vnū gra­
                    <lb/>
                  dū materie. </s>
                  <s xml:id="N21599" xml:space="preserve">ipſū rarefieret: et in fine maneret vnifor­
                    <lb/>
                  miter eq̄ denſū cū pedali. </s>
                  <s xml:id="N2159E" xml:space="preserve">igr̄ mõ eſt denſius illo pe­
                    <lb/>
                  dali / qḋ fuit ꝓbãdū </s>
                  <s xml:id="N215A3" xml:space="preserve">Falſitas tñ ↄ̨ñtis ꝓbat̄̄ et capio
                    <lb/>
                  vnū pedale qḋ habeat duos gradus materie: et vnū
                    <lb/>
                  bipedale vniforme qḋ habeat tres / et argr̄ ſic / illud
                    <lb/>
                  pedale ē dēſius illo bipedali maiori continēte plus
                    <lb/>
                  de materia: igr̄ nõ ſi aliq̇d eſt maiꝰ plꝰ ↄ̨tinēs de ma­
                    <lb/>
                  teria ꝙ̄ aliud minꝰ eo ipſū ē eo: dēſiꝰ. </s>
                  <s xml:id="N215B0" xml:space="preserve">Probat̄̄ añs
                    <lb/>
                  et volo /  ſtãte quãtitate ipſius pedalis perdat me-
                    <lb/>
                  dietatē vniꝰ gradꝰ materie. </s>
                  <s xml:id="N215B7" xml:space="preserve">q̊ poſito illḋ pedale ra­
                    <lb/>
                  refit vt notū eſt et in fine manebit eq̄ dēſū cū bipeda­
                    <lb/>
                  li: igr̄ antea erat dēſius. </s>
                  <s xml:id="N215BE" xml:space="preserve">Coña pꝫ cū maiore et argr̄
                    <lb/>
                  minor / q2 illud pedale in fine manebit eq̄ dēſū ſicut
                    <lb/>
                  medietas illius bipedalis q2 cõtinebit tm̄ de mate­
                    <lb/>
                  ria adeq̈te ſicut medietas illius bipedalis: et bipe-
                    <lb/>
                  dale eſt vniforme vt ponit̄̄: g̊ illud pedale eſt ita dē­
                    <lb/>
                  ſū ſicut bipedale / qḋ fnit ꝓbãdū.
                    <note position="left" xlink:href="note-0178-01a" xlink:label="note-0178-01" xml:id="N215DB" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N215D0" xml:space="preserve">¶ Dices et bñ negã­
                    <lb/>
                  do ſeq̄lã īmo aliqñ minꝰ ē dēſius maiore: et eↄ̈: et ali­
                    <lb/>
                  qñ eq̄ denſum vt apparere poteſt ex argumento.</s>
                </p>
                <p xml:id="N215E1">
                  <s xml:id="N215E2" xml:space="preserve">Sꝫ ↄ̨̨tra </s>
                  <s xml:id="N215E5" xml:space="preserve">Q2 tūc ſeq̄ret̄̄ /  nõ poſſet da­
                    <lb/>
                  ri certa regula ad ſciēdū qñ vnū e denſius altero: et
                    <lb/>
                  qñ maius eſt dēſius minore vel econtra: quod ſi ne-
                    <lb/>
                  ges des illam. </s>
                  <s xml:id="N215EE" xml:space="preserve">ſed cõſequēs eſt falſum: igitur illud
                    <lb/>
                  ex quo ſequitur.</s>
                </p>
                <p xml:id="N215F3">
                  <s xml:id="N215F4" xml:space="preserve">Sexto prīcipaliṫ argr̄ ſic  hoc tãgen­
                    <lb/>
                  do rara difformia. </s>
                  <s xml:id="N215F9" xml:space="preserve">Q2 ſi raritas et denſitas eſſent
                    <lb/>
                  poſſibiles ſeq̄ret̄̄ /  dabile eēt raꝝ vniformiter dif­
                    <lb/>
                  forme ab aliquo gradu vſ ad non gradū: et eiꝰ ra­
                    <cb chead="De motu rarefactionis et condenſationis."/>
                  ritas correſponderat gradui medio: ſed ↄ̨ñs eſt fal­
                    <lb/>
                  ſum: igitur et antecedēs. </s>
                  <s xml:id="N21605" xml:space="preserve">Sequela ꝓbatur / quia da­
                    <lb/>
                  bile eſt rarum vniformiter difforme a certo gradu
                    <lb/>
                  vſ ad nõ gradū: g̊ etiã pari forma dabile eſt rarū
                    <lb/>
                  vniformiter difforme a certo gradu vſ ad nõ gra­
                    <lb/>
                  dū. </s>
                  <s xml:id="N21610" xml:space="preserve">Sed falſitas conſequentis ꝓbatur / q2 ex illo ſe-
                    <lb/>
                  quitur aliquid eē rarū et idē non eē rarum / quod eſt
                    <lb/>
                  impoſſibile: </s>
                  <s xml:id="N21617" xml:space="preserve">Sequela ꝓbatur / q2 capto tali corpo-
                    <lb/>
                  re vniformiter difformiter raro a gradu quarto vſ­
                    <lb/>
                   ad non gradū: tale corpus eſt raꝝ vt duo ꝑ te cū
                    <lb/>
                  eius raritas correſpondeat ſuo gradui medio: et eſt
                    <lb/>
                  nõ rarū cū ſit infinite dēſum: igr̄ intentū: minor pro­
                    <lb/>
                  batur / q2 prīa ꝑs ꝓportionalis illiꝰ corporis ꝓpor­
                    <lb/>
                  tione dupla eſt aliq̈liter denſa. </s>
                  <s xml:id="N21626" xml:space="preserve">et ſecunda in duplo
                    <lb/>
                  denſior et tertia in quadruplo et ſic in infinitū: igit̄̄
                    <lb/>
                  illud corpus eſt infinite dēſum: et per ↄ̨ñs non rarum.
                    <lb/>
                  </s>
                  <s xml:id="N2162E" xml:space="preserve">Q, ſecunda pars ꝓportiõalis ſit in duplo den-
                    <lb/>
                  ſior prīa patet / q2 eſt in ſubduplo rarior;: g̊ in duplo
                    <lb/>
                  denſior: pꝫ ↄ̨ña qm̄ ī quacū ꝓportione raritas ē
                    <lb/>
                  minor: in eadem denſitas ē maior. </s>
                  <s xml:id="N21637" xml:space="preserve">vt ſatis facile ꝓ­
                    <lb/>
                  bari p̄t ex diffinitionibꝰ magis rari et magis denſi
                    <lb/>
                  et añs pꝫ / q2 prīa ꝑs ꝓportionalis eſt rara vt tria,
                    <lb/>
                  cū eius raritas ſit vniformiter difformis a quatuor
                    <lb/>
                  vſ ad duo: et ſcḋa pars proportionalis eſt rara vt
                    <lb/>
                  vnū cū dimidio: ſꝫ vnū cū dimidio eſt ſubdupluꝫ ad
                    <lb/>
                  tria. </s>
                  <s xml:id="N21646" xml:space="preserve">igr̄ ſcḋa pars ꝓportionalis eſt in ſubduplo ra­
                    <lb/>
                  rior ꝙ̄ prima / qḋ fuit ꝓbãdū. </s>
                  <s xml:id="N2164B" xml:space="preserve">Et ſic ꝓbabis /  tertia
                    <lb/>
                  eſt in duplo denſior ꝙ̄ ſcḋa et quarta in duplo den-
                    <lb/>
                  ſior ꝙ̄ tertia: et ſic in infinitū. </s>
                  <s xml:id="N21652" xml:space="preserve">igit̄̄ totū cõtinet infini­
                    <lb/>
                  tã materiã ſub finita quantitate: et ꝑ ↄ̨ñs non eſt ra-
                    <lb/>
                  rū. </s>
                  <s xml:id="N21659" xml:space="preserve">Oīs em̄ pars illius ꝓportionalis tantū cõtinet
                    <lb/>
                  de materia ſicut prīa / vt pꝫ calculatanti igit̄̄.
                    <note position="right" xlink:href="note-0178-02a" xlink:label="note-0178-02" xml:id="N2167B" xml:space="preserve">Dicitur</note>
                  </s>
                  <s xml:id="N21663" xml:space="preserve">¶ Dices
                    <lb/>
                  et bñ negando ſequelã et ad ꝓbationē conceſſo añte
                    <lb/>
                  negãdo ↄ̨ñam / q2 ad raꝝ vniformiter difformi a cer­
                    <lb/>
                  to gradu vſ ad non gradū ſeq̇tur ipſum eſſe rarū
                    <lb/>
                  et non rarum vt bene ꝓbat argumentum. </s>
                  <s xml:id="N2166E" xml:space="preserve">Ad rarū
                    <lb/>
                  vero vniformiṫ difforme a gradu vſ certū gradū
                    <lb/>
                  illḋ nõ ſeq̇tur: nec aliud etiam incõueniens iõ negã-
                    <lb/>
                  da eſt ſimilitudo.</s>
                </p>
                <p xml:id="N21681">
                  <s xml:id="N21682" xml:space="preserve">Sꝫ ↄ̨̨tra </s>
                  <s xml:id="N21685" xml:space="preserve">Q2 eadē rõe ſeq̄ret̄̄ /  nõ poſ­
                    <lb/>
                  ſet dari denſū vniformiter difforme a certo gradu
                    <lb/>
                  vſ ad non gradū: ſed ↄ̨ñs ē falſū: igr̄ et añs. </s>
                  <s xml:id="N2168C" xml:space="preserve">Seq̄­
                    <lb/>
                  la pꝫ / q2 non eſt maior ratio de raritate vniformiṫ
                    <lb/>
                  difformi a gradu vſ ad nõ gradū quã de dēſitate
                    <lb/>
                  vniformiter difformi a gradu vſ ad nõ graduꝫ: g̊
                    <lb/>
                  ſi vnū nõ eſt dabile: nec aliud cõcedēdū erit. </s>
                  <s xml:id="N21697" xml:space="preserve">Sꝫ iã ꝓ­
                    <lb/>
                  bat̄̄ falſitas conſequentis / q2 ad denſum vniformi-
                    <lb/>
                  ter difforme a certo gradu vſ ad nõ gradū nulluꝫ
                    <lb/>
                  ſeq̇tur incõueniens: igr̄ denſū vniformiter difforme
                    <lb/>
                  a certo gradu vſ ad nõ gradū ē poſſiblle. </s>
                  <s xml:id="N216A2" xml:space="preserve">Et ſi ne­
                    <lb/>
                  gas  ad illud nullū ſequat̄̄ īcõueuiēs des illud / igr̄
                    <lb/>
                  inconueniēs / qḋ ſeq̇tur. </s>
                  <s xml:id="N216A9" xml:space="preserve">et nõ poteris. </s>
                  <s xml:id="N216AC" xml:space="preserve">q2 nõ ſequitur
                    <lb/>
                  illud quod ſequitur ad rarum vniformiter diffor-
                    <lb/>
                  me a certo gradu vſ ad non gradum: nec aliquod
                    <lb/>
                  aliud: igitur. </s>
                  <s xml:id="N216B5" xml:space="preserve">Antecedens probatur / quia licet talis
                    <lb/>
                  vniformiter difformiter denſi etc. ſecunda pars pro­
                    <lb/>
                  portionalis ꝓportione dupla ſit in ſubduplo den­
                    <lb/>
                  ſior et per conſequens duplo rarior ꝙ̄ prima et ter-
                    <lb/>
                  tia in duplo rarior ꝙ̄ ſecunda: et quarta ꝙ̄ tertia et
                    <lb/>
                  ſic in infinitum: non tamen eo illud denſum vnifor-
                    <lb/>
                  miter difformiter etc. eſt infinite rarum. </s>
                  <s xml:id="N216C4" xml:space="preserve">Continet
                    <lb/>
                  enim ſub finita quantitate aliquam materiam: vt
                    <lb/>
                  patet. </s>
                  <s xml:id="N216CB" xml:space="preserve">igitur non ſequitur tale inconueniens / quod
                    <lb/>
                  fuit probandum.
                    <note position="right" xlink:href="note-0178-03a" xlink:label="note-0178-03" xml:id="N21727" xml:space="preserve">.1. confir.</note>
                  </s>
                  <s xml:id="N216D5" xml:space="preserve">¶ Et confirmatur </s>
                  <s xml:id="N216D8" xml:space="preserve">Quia
                    <lb/>
                  ſi raritas et denſitas eſſent poſſibiles ſequeretur / 
                    <lb/>
                  poſſet dari infinite denſum / ſed conſequens eſt fal-
                    <lb/>
                  ſum. </s>
                  <s xml:id="N216E1" xml:space="preserve">igitur illud ex quo ſequitur falſitas conſequē­
                    <lb/>
                  tio oſtenditur / q2 illud denſum īfinite eēt aliq̈liṫ ma­
                    <lb/>
                  gnū. </s>
                  <s xml:id="N216E8" xml:space="preserve">et poſſet eiꝰ pūcta adhuc mag approxīari et ad </s>
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