Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N25905" level="3" n="4" type="other" type-free="tractatus">
              <div xml:id="N2AEE0" level="4" n="4" type="chapter" type-free="capitulum">
                <p xml:id="N2C06A">
                  <s xml:id="N2C06E" xml:space="preserve">
                    <pb chead="De difformium intenſione" file="0273" n="273"/>
                  prime ꝑtis ꝓportiõalis qua totū denoīat: ibi tota
                    <lb/>
                  q̈litas reducta ad vniformitatē eſt incõmēſurabi-
                    <lb/>
                  lis intēſioni ṗme ꝑtis ꝓportiõalis poſt̄ ꝑ totū ex-
                    <lb/>
                  tendit̄̄. </s>
                  <s xml:id="N2C07E" xml:space="preserve">Probat̄̄ / q2 ſemꝑ totalis intēſio difformis
                    <lb/>
                  q̈litatis poſt̄ reducit̄̄ ad vniformitatē corrñdet in
                    <lb/>
                  g̈du totali denoīatiõi ipſiꝰ: et denoīatio qua prima
                    <lb/>
                  pars ꝓportiõalis totū denoīat: et q̈litas eiꝰ iã re-
                    <lb/>
                  miſſa et extenſa ꝑ totū ſiĺr corrñdent in gradu: g̊ cõ­
                    <lb/>
                  cluſio vera. </s>
                  <s xml:id="N2C08B" xml:space="preserve">Sed ad cognoſcendã intenſionē diffor-
                    <lb/>
                  mis infiniti quãtitatiue: pono aliquas ↄ̨cluſiones.</s>
                </p>
                <p xml:id="N2C090">
                  <s xml:id="N2C091" xml:space="preserve">Quīta ↄ̨̨cluſio. </s>
                  <s xml:id="N2C094" xml:space="preserve">Cuiuſlꝫ īfiniti diffor-
                    <lb/>
                  mis in quo nõ ſunt q̈litates ſe īpediētes intenſio d3
                    <lb/>
                  attendi penes maximū gradū vniformē ꝑ īfinita eiꝰ
                    <lb/>
                  pedalia extēſum: aut penes gradū qui nõ extēdit̄̄
                    <lb/>
                  ꝑ infinita eiꝰ pedalia. </s>
                  <s xml:id="N2C09F" xml:space="preserve">ſed quilꝫ quē ille gradꝰ exce-
                    <lb/>
                  dit extēdit̄̄ ꝑ īfinita eiꝰ pedalia vniformiṫ. </s>
                  <s xml:id="N2C0A4" xml:space="preserve">Nõ dico /
                    <lb/>
                  aut penes minimū gradū qui nõ extēdit̄̄ ꝑ infinita
                    <lb/>
                  eiꝰ pedalia ꝓpter gradū īfinitū qui nõ eſt paruus.
                    <lb/>
                    <note position="left" xlink:href="note-0273-01a" xlink:label="note-0273-01" xml:id="N2C12A" xml:space="preserve">correĺ.</note>
                  </s>
                  <s xml:id="N2C0B2" xml:space="preserve">¶ Ex hac ↄ̨cĺone ſequit̄̄ primo /  corpꝰ infinitū cuiꝰ
                    <lb/>
                  primū pedale eſt vt .4. et .2. vt .5. et .3. vt quin cū di-
                    <lb/>
                  midio, et .4. vt .5. cū duabꝰ primis partibꝰ ꝓportio-
                    <lb/>
                  nabilibꝰ vniꝰ, et .5. vt quī cū .3. primis ꝑtibꝰ ꝓpor-
                    <lb/>
                  tionabilibꝰ vniꝰ (intelligo ꝓportione dupla) </s>
                  <s xml:id="N2C0BD" xml:space="preserve">Et .6.
                    <lb/>
                  vt quī cū .4, primis partibꝰ ꝓportionalibꝰ vniꝰ / et
                    <lb/>
                  ſic ↄ̨ñter eſt intenſum vt .6. </s>
                  <s xml:id="N2C0C4" xml:space="preserve">Probat̄̄ / q2 ille vt .6. eſt
                    <lb/>
                  gradꝰ qui nõ extēdit̄̄ ꝑ īfinita eiꝰ pedalia: ſed quilꝫ
                    <lb/>
                  quē ſex excedūt extēdit̄̄ vniformiṫ ꝑ īfinita eiꝰ peda-
                    <lb/>
                  lia: vt ↄ̨ſtat: igr̄ ex .5. ↄ̨cĺone tale corpꝰ infinitū eſt vt
                    <lb/>
                  6.
                    <note position="left" xlink:href="note-0273-02a" xlink:label="note-0273-02" xml:id="N2C130" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N2C0D4" xml:space="preserve">¶ Sequit̄̄ .2°. /  corpꝰ infinitū cuiꝰ primū pedale
                    <lb/>
                  eſt vt .6. et .2. vt .5. et .3. vt .5. cū dimidio, et .4. vt .5. cum
                    <lb/>
                  vna quarta, et .6. vt .5. cū vua octaua, et .7. vt .5. cum
                    <lb/>
                  vna decimaſexta: et ſic ↄ̨ñter eſt intēſum vt .5. </s>
                  <s xml:id="N2C0DD" xml:space="preserve">Pro-
                    <lb/>
                  bat̄̄ / q2 gradꝰ quītꝰ maximꝰ gradꝰ vniformis qui
                    <lb/>
                  extēdit̄̄ ꝑ infinita eiꝰ pedalia / vt ptꝫ. </s>
                  <s xml:id="N2C0E4" xml:space="preserve">igr̄ ex ↄ̨cĺone
                    <lb/>
                  illud infinitū eſt intēſum vt .5.
                    <note position="left" xlink:href="note-0273-03a" xlink:label="note-0273-03" xml:id="N2C136" xml:space="preserve">.3. correĺ.</note>
                  </s>
                  <s xml:id="N2C0EE" xml:space="preserve">¶ Sequit̄̄ .3. /  corpꝰ
                    <lb/>
                  īfinitū cuiꝰ primū pedale eſt vt vnū, et .2. vt duo, et .3.
                    <lb/>
                  vt tria, et .4. et quatuor: et ſic in infinitū aſcendendo
                    <lb/>
                  ꝑ oēs nūeros eſt īfinite intēſuꝫ ſemꝑ excludo ↄ̈rias
                    <lb/>
                  q̈litates. </s>
                  <s xml:id="N2C0F9" xml:space="preserve">Probat̄̄ / q2 īfinitꝰ gradꝰ nõ extēdit̄̄ ꝑ infi­
                    <lb/>
                  nita eiꝰ pedalia: et quilꝫ quē gradꝰ īfinitꝰ excedit ex-
                    <lb/>
                  tēdit̄̄ ꝑ infinita eiꝰ pedalia / vt ↄ̨ſtat: g̊ ex .5. ↄ̨cluſione
                    <lb/>
                  illud corpꝰ eſt infinite intēſum.
                    <note position="left" xlink:href="note-0273-04a" xlink:label="note-0273-04" xml:id="N2C13C" xml:space="preserve">4. correĺ.</note>
                  </s>
                  <s xml:id="N2C107" xml:space="preserve">¶ Sequit̄̄ .4. /  infi-
                    <lb/>
                  tū cuiꝰ primū pedale vel queuis pars finita eſt īfini­
                    <lb/>
                  te alba et totū reſiduū eſt vt .4. eſt albū vt .4. </s>
                  <s xml:id="N2C10E" xml:space="preserve">Pro-
                    <lb/>
                  bat̄̄ / q2 gradꝰ vt quatuor eſt maximꝰ extēſus ꝑ īfini­
                    <lb/>
                  ta eius pedalia: igr̄.
                    <note position="left" xlink:href="note-0273-05a" xlink:label="note-0273-05" xml:id="N2C142" xml:space="preserve">Calcula.</note>
                  </s>
                  <s xml:id="N2C11A" xml:space="preserve">Et hoc correlariū eſt de mente
                    <lb/>
                  Calculatoris in .2. capĺo. </s>
                  <s xml:id="N2C11F" xml:space="preserve">Nã ſcḋm eū q̈litas īfinita
                    <lb/>
                  extenſa ꝑ partē finitã p̄ciſe alicuiꝰ corporis infiniti
                    <lb/>
                  nõ confert aliq̇d ad denoīationē corporis infiniti.</s>
                </p>
                <p xml:id="N2C148">
                  <s xml:id="N2C149" xml:space="preserve">Sexta ↄ̨̨cĺo. </s>
                  <s xml:id="N2C14C" xml:space="preserve">Quã
                    <gap/>
                  īfiniti difformis
                    <lb/>
                  intēſio nõ ſit penes reductionē ad vniformitatē at-
                    <lb/>
                  tendenda et cognoſcēda: ſed mõ dicto in .5. ↄ̨cĺone:
                    <lb/>
                  nichilominꝰ põt ad vniformitatē ſue denoīationis
                    <lb/>
                  reduci. </s>
                  <s xml:id="N2C159" xml:space="preserve">Prima ꝑs ꝓbat̄̄: q2 tota reductio ad vnifor­
                    <lb/>
                  mitatē fundat̄̄ in hoc  tm̄ põt qualitas extenſa ꝑ
                    <lb/>
                  partē denoīare totū ſicut extēſa ſub mīori intēſiõe
                    <lb/>
                  ꝑ totū. </s>
                  <s xml:id="N2C162" xml:space="preserve">Sed hoc nõ hꝫ locū in corꝑe īfinito: vt ptꝫ ex
                    <lb/>
                  4. correlario .5. ↄ̨cĺonis: igr̄ nõ d3 ↄ̨mēſurari ītēſio
                    <lb/>
                  īfiniti difformis penes reductionē ad vniformitatē
                    <lb/>
                  </s>
                  <s xml:id="N2C16A" xml:space="preserve">¶ Scḋa pars ꝓbat̄̄: q2 q̄lꝫ q̈litas põt ad quãcū in­
                    <lb/>
                  tenſionē reduci: vt ptꝫ ex p̄mo capĺo huiꝰ tractatus
                    <lb/>
                  vbi agit̄̄ ḋ poña rei: igr̄. </s>
                  <s xml:id="N2C171" xml:space="preserve">Cõcĺo reſpõſiua ad dubiū
                    <lb/>
                  ptꝫ ex dictis ↄ̨cluſionibus. </s>
                  <s xml:id="N2C176" xml:space="preserve">¶ Ad rationem ante op-
                    <lb/>
                  poſitum reſpondent ↄ̨cluſiones et correlaria.</s>
                </p>
                <p xml:id="N2C17B">
                  <s xml:id="N2C17C" xml:space="preserve">Ad ſcḋm dubiū argr̄ pars negatiua:
                    <lb/>
                  q2 ſi pars affirmatiua eēt a: ſeq̄ret̄̄ /  pedale hñs
                    <lb/>
                  ꝑ totū caliditatē et .6. et frigiditatē vt .8. eēt frigidū
                    <lb/>
                  et .2. / ſed ↄ̨ñs eſt fim̄: igr̄ illud ex q̊ ſequit̄̄. </s>
                  <s xml:id="N2C185" xml:space="preserve">Seq̄la ptꝫ /
                    <lb/>
                  q2 .8. excedūt .6. per .2. et falſitas ↄ̨ñtis. </s>
                  <s xml:id="N2C18A" xml:space="preserve">Probat̄̄. </s>
                  <s xml:id="N2C18D" xml:space="preserve">q2
                    <cb chead="De difformium intenſione"/>
                  illud eſt frigidū vt .8. igr̄. </s>
                  <s xml:id="N2C193" xml:space="preserve">Añs ꝓbat̄̄ / q2 aliq̇ .2. gra­
                    <lb/>
                  dus frigiditatꝪ denominãt illud pedale frigidū vt
                    <lb/>
                  2. vt ↄ̨ſtat: et nõ eſt maior rõ de aliq̇bꝰ ꝙ̄ de q̇buſcū-
                    <lb/>
                   aliis .2. / igr̄ q̇lꝫ duo denominãt vt .2. / et ꝑ ↄ̨ñs oēs
                    <lb/>
                  8. collectiue denoīant vt .8. </s>
                  <s xml:id="N2C19E" xml:space="preserve">Maior eſt nõ, et minor
                    <lb/>
                  ꝓbat̄̄: q2 nõ eſt maior rõ  īpediãt̄̄ ſeptimꝰ et octa-
                    <lb/>
                  uus, ꝙ̄ primꝰ et ſcḋs: ſcḋs et tertiꝰ .etc̃.
                    <note position="right" xlink:href="note-0273-06a" xlink:label="note-0273-06" xml:id="N2C1C7" xml:space="preserve">Dicitur</note>
                  </s>
                  <s xml:id="N2C1AA" xml:space="preserve">¶ Dices et bñ
                    <lb/>
                  ↄ̨cedēdo qḋ infert̄̄: et negãdo falſitatē ↄ̨ñtis et ad cū
                    <lb/>
                  ꝓbat̄̄ negat̄̄ añs: et cū ꝓbat̄̄: nego maiorē. </s>
                  <s xml:id="N2C1B1" xml:space="preserve">Dico em̄ /
                    <lb/>
                   nulli 2. gradꝰ denoīant illḋ pedale frigidū vt .2.
                    <lb/>
                  ſed oēs .8. collectiue. </s>
                  <s xml:id="N2C1B8" xml:space="preserve">Nã quãuis .6. gradꝰ īpediant̄̄
                    <lb/>
                  a q̈litate ↄ̈ria nõ tñ totaliṫ: ſed q̄lꝫ dualitas illiꝰ fri­
                    <lb/>
                  giditatꝪ aliq̇ mõ denoīat puta vt vna medietas: et
                    <lb/>
                  qualibet gradus vt vna quarta vbi ſine contrarii
                    <lb/>
                  permixtione denominaret vt vnum.</s>
                </p>
                <p xml:id="N2C1CD">
                  <s xml:id="N2C1CE" xml:space="preserve">Sed ↄ̨̨tra. </s>
                  <s xml:id="N2C1D1" xml:space="preserve">Q2 ſi hoc eſſet verū ſeq̄ret̄̄
                    <lb/>
                  aliquã frigiditatē extēſam ꝑ aliqḋ corpꝰ ↄ̨tinuo re­
                    <lb/>
                  mitti: et corpꝰ ↄ̨tinuo eſſe frigidꝰ: ſed ↄ̨ñs videt̄̄ im-
                    <lb/>
                  poſſibile: igr̄ illud ex q̊ ſeqnit̄̄. </s>
                  <s xml:id="N2C1DA" xml:space="preserve">Seq̄la ꝓbat̄̄: et pono /
                    <lb/>
                   ſucceſſiue ꝑ vnã horã remittat̄̄ frigiditas et cali-
                    <lb/>
                  ditas illiꝰ pedalis: ita tñ  qñ frigiditas ꝑdit ali-
                    <lb/>
                  quē gradū caliditas ꝑdat duplū ad illū. </s>
                  <s xml:id="N2C1E3" xml:space="preserve">Quo po-
                    <lb/>
                  ſito illud pedale ꝑ illã horã erit frigidiꝰ et frigidiꝰ:
                    <lb/>
                  et tñ ↄ̨tinuo frigiditas eiꝰ ꝑ totū remittit̄̄: igr̄ pro-
                    <lb/>
                  poſitū. </s>
                  <s xml:id="N2C1EC" xml:space="preserve">Coña ptꝫ cū mīore: et argr̄ maior / q2 ↄ̨tinuo
                    <lb/>
                  exceſſus frigiditatis ſupra caliditatem erit maior
                    <lb/>
                  </s>
                  <s xml:id="N2C1F2" xml:space="preserve">Nã qñ remittet̄̄ vnꝰ gradꝰ frigiditatꝪ remittentur
                    <lb/>
                  duo caliditatꝪ: et ſic qñ frigiditas erit vt .7. calidi-
                    <lb/>
                  tas erit vt .4. / igr̄ frigiditas excedit, tūc caliditateꝫ
                    <lb/>
                  ꝑ .3. gradꝰ: et aña p̄ciſe excedebat ꝑ duos. </s>
                  <s xml:id="N2C1FB" xml:space="preserve">Itē qñ fri­
                    <lb/>
                  giditas ꝑdiderit duos gradꝰ: caliditas ꝑdidit .4.
                    <lb/>
                  ex caſu: igr̄ cū frigiditas erit vt .6. caliditas erit vt
                    <lb/>
                  2, et ſic exceſſus erit .4. gradus: igitur continuo ex-
                    <lb/>
                  ceſſus augetur / quod fuit probandum.
                    <note position="right" xlink:href="note-0273-07a" xlink:label="note-0273-07" xml:id="N2C214" xml:space="preserve">Dicitur</note>
                  </s>
                  <s xml:id="N2C20B" xml:space="preserve">¶ Dices et be­
                    <lb/>
                  ne ↄ̨cedendo quod infert̄̄ tan̄ correlariū ſequēs.</s>
                </p>
                <p xml:id="N2C21A">
                  <s xml:id="N2C21B" xml:space="preserve">Sed ↄ̨̨tra. </s>
                  <s xml:id="N2C21E" xml:space="preserve">Q2 ꝑ idē ſeq̄ret̄̄ /  a.  b. pe­
                    <lb/>
                  dalia ſunt mõ equalr̄ frigida: et ↄ̨tinuo ꝑ horã futu­
                    <lb/>
                  rã a. erit frigidiꝰ b. et tñ frigiditas ipſiꝰ a. ↄ̨tinuo ꝑ
                    <lb/>
                  horã remittet̄̄: frigiditas o ipſiꝰ b. ↄ̨tinuo intēdet̄̄
                    <lb/>
                  ꝑ horã: ſed hoc eſt īpoſſibile: igr̄. </s>
                  <s xml:id="N2C229" xml:space="preserve">Probat̄̄ tñ ſeq̄la:
                    <lb/>
                  et volo /  a. et b. pedalia habeãt ꝑ totū caliditatē vt
                    <lb/>
                  6. et frigiditatē vt .8. et a. vniformiṫ in iſta hora ꝑ-
                    <lb/>
                  dat duos gradꝰ frigiditatis et .4. caliditatꝪ .b. vero
                    <lb/>
                  vniformiṫ in eadē hora acq̇rat duos frigiditatꝪ et
                    <lb/>
                  4. caliditatis. </s>
                  <s xml:id="N2C236" xml:space="preserve">Quo poſito a. et b. pedalia ſūt eq̈liṫ
                    <lb/>
                  frigida: et cõtinuo ꝑ horã futurã a. erit frigidꝰ b. et
                    <lb/>
                  ↄ̨tinuo ꝑ eandē horã remittet̄̄ frigiditas ipſiꝰ a. et
                    <lb/>
                  intēdit̄̄ frigiditas ipſiꝰ b. / igr̄ ꝓpoſitū. </s>
                  <s xml:id="N2C23F" xml:space="preserve">Cõſequētia
                    <lb/>
                  ptꝫ cū maiore: et argr̄ mīor: q2 a ↄ̨tinuo intendet̄̄ in
                    <lb/>
                  frigiditate: et b. ↄ̨tinuo remittet̄̄ / vt pꝫ intuenti, et in
                    <lb/>
                  principio ſunt eq̄ frigida: igr̄ ↄ̨tinuo a. erit frigidꝰ
                    <lb/>
                  b. / qḋ fuit ꝓbandū. </s>
                  <s xml:id="N2C24A" xml:space="preserve">¶ Itē ſeq̄ret̄̄ /  in aliq̊ frigido cõ­
                    <lb/>
                  tinuo intēderet̄̄ frigiditas: et tñ ipſū in infinitū re-
                    <lb/>
                  mitteret̄̄: qḋ eſt īpoſſibile. </s>
                  <s xml:id="N2C251" xml:space="preserve">Seq̄la ꝓbat̄̄ et volo /  a.
                    <lb/>
                  hñs frigiditatē vt .6. et caliditatē vt .4. vniformiter
                    <lb/>
                  in iſta hora acq̇rat duos gradꝰ frigiditatꝪ, et .4. ca­
                    <lb/>
                  liditatis. </s>
                  <s xml:id="N2C25A" xml:space="preserve">Quo poſito in īfinitū remittet̄̄ ipſū a: cū
                    <lb/>
                  in īfinitū paruus erit exceſſus frigiditatꝪ ſupra ca-
                    <lb/>
                  liditatē: igr̄.
                    <note position="right" xlink:href="note-0273-08a" xlink:label="note-0273-08" xml:id="N2C2BF" xml:space="preserve">ↄ̨fir̄atio.</note>
                  </s>
                  <s xml:id="N2C266" xml:space="preserve">¶ Et ↄ̨firmat̄̄ / q2 tūc ſeq̄ret̄̄ /  aliquod
                    <lb/>
                  corpꝰ calidū efficeret̄̄ nec calidū nec frigidū ſine de­
                    <lb/>
                  ꝑditione aut acq̇ſitiõe caliditatis aut frigiditatis /
                    <lb/>
                  qḋ īplicat. </s>
                  <s xml:id="N2C26F" xml:space="preserve">Seq̄la ꝓbat̄̄ / et ſit a. corpꝰ diuiſū ꝑ par-
                    <lb/>
                  tes ꝓportionales ꝓportiõe dupla, et in ṗma eiꝰ ꝑte
                    <lb/>
                  ꝓportiõali ſit caliditas vt .2. et frigiditas vt vnū, et
                    <lb/>
                  in ſcḋa ꝑte ꝓportiõali ſit caliditas et frigiditas in
                    <lb/>
                  duplo maior ꝙ̄ in ṗma, et in tertia ſit caliditas et
                    <lb/>
                  frigiditas in triplo maior ꝙ̄ in prima / et ſic ↄ̨ñter.
                    <lb/>
                  </s>
                  <s xml:id="N2C27D" xml:space="preserve">Quo poſito manifeſtū eſt expõne et ṗma ↄ̨cluſione
                    <lb/>
                  q̄ſtiõs /  a. corpꝰ eſt calidū vt duo cū tota ſua cali- </s>
                </p>
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