Alvarus, Thomas, Liber de triplici motu, 1509

Table of figures

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                <p xml:id="N2C419">
                  <s xml:id="N2C440" xml:space="preserve">
                    <pb chead="De difformium intenſione" file="0275" n="275"/>
                  minatiõis ab cxceſſu a ↄ̈ria denoīatiõe ſibi equali
                    <lb/>
                  īpedit̄̄: igr̄ ille exceſſus īmunis ab īpedimento ma-
                    <lb/>
                  nēs illud ſubiectū denoīat. </s>
                  <s xml:id="N2C44C" xml:space="preserve">Et ꝑ ↄ̨ñs penes illū ex-
                    <lb/>
                  ceſſum denominationis eſt mixti intenſio metien-
                    <lb/>
                  da: quod fuit probaudum.</s>
                </p>
                <note position="left" xml:id="N2C453" xml:space="preserve">8. ↄ̨cl° de
                  <lb/>
                diffo. q̈m
                  <lb/>
                calcula.
                  <lb/>
                negat.</note>
                <p xml:id="N2C45D">
                  <s xml:id="N2C45E" xml:space="preserve">Scḋa ↄ̨̨cluſio. </s>
                  <s xml:id="N2C461" xml:space="preserve">Aliqḋ eſt calidū īfinite
                    <lb/>
                  intenſum: et vna medietas eſt vniformis ſub certo
                    <lb/>
                  gradu et alia, nec calida, nec frigida. </s>
                  <s xml:id="N2C468" xml:space="preserve">Probatur: ſit
                    <lb/>
                  f. vnum quadratum diuiſum in .4. quadrata equa­
                    <lb/>
                  lia
                    <figure xlink:href="fig-0275-01a" xlink:label="fig-0275-01" xml:id="N2C4CD" number="13">
                      <image file="0275-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0275-01"/>
                    </figure>
                  a.b.c.d. / vt patet in figura:
                    <lb/>
                  et ſit quadratum b. infinite ca-
                    <lb/>
                  lidū, et a. frigidum vt .4. et c. et
                    <lb/>
                  d. vniformiṫ calida vt .4. </s>
                  <s xml:id="N2C47A" xml:space="preserve">Quo
                    <lb/>
                  poſito arguit̄̄ ſic / f. eſt īfinite ca-
                    <lb/>
                  lidum: cū vna quarta eius ſit in­
                    <lb/>
                  finite calida et nulla ſit in corpo­
                    <lb/>
                  re f. frigiditas īfinita: et vna eiꝰ
                    <lb/>
                  medietas eſt vniformiter calida
                    <lb/>
                  certo gradu puta vt .4. et alia nec calida nec frigi-
                    <lb/>
                  da / igr̄ ↄ̨cluſio vera. </s>
                  <s xml:id="N2C48B" xml:space="preserve">Cõſequētia pꝫ cū maiore, et mi­
                    <lb/>
                  nor ꝓbat̄̄ / q2 medietas cõpoſita ex c. et d. eſt vnifor-
                    <lb/>
                  miter calida vt .4. / vt pꝫ ex caſu: igr̄. </s>
                  <s xml:id="N2C492" xml:space="preserve">Sed  alia me­
                    <lb/>
                  dietas ſit nec calida nec frigida ꝓbat̄̄ / q2 medietas
                    <lb/>
                  ↄ̨poſita ex a. et c. nec eſt calida nec frigida: quia vna
                    <lb/>
                  medietas eiꝰ puta a. eſt frigida vt .4. et alia puta
                    <lb/>
                  c. calida et .4. / ergo medietas a.c. nec eſt calida nec
                    <lb/>
                  frigida: quod fuit probandum. </s>
                  <s xml:id="N2C49F" xml:space="preserve">Et ſic ptꝫ concluſio
                    <lb/>
                    <note position="left" xlink:href="note-0275-01a" xlink:label="note-0275-01" xml:id="N2C4D3" xml:space="preserve">9. ↄ̨° quã
                      <lb/>
                    calcula.
                      <lb/>
                    negat.</note>
                  </s>
                  <s xml:id="N2C4A9" xml:space="preserve">¶ Ex q̊ ſequit̄̄ /  a. et b. ſūt ineq̄ intēſa: ita ꝙ̄ a. eſt in­
                    <lb/>
                  finite intenſū et b. īfinite remiſſū et q̄lꝫ pars finita ip­
                    <lb/>
                  ſius a. eſt eq̄ intēſa cū ꝑte corrñdente ipſiꝰ b. </s>
                  <s xml:id="N2C4B0" xml:space="preserve">Probr̄ /
                    <lb/>
                  ſit b. īfinitū in cuiꝰ ṗmo pedali ſint duo g̈dus calidi­
                    <lb/>
                  tatis et vnꝰ frigiditatis, et in ſecūdo pedali in duplo
                    <lb/>
                  plꝰ de caliditate et frigiditate ꝙ̄ in ṗmo, et in tertio
                    <lb/>
                  in duplo plus de caliditate et frigiditate ꝙ̄ in ſcḋo
                    <lb/>
                  et ſic deinceps: ſed a. ſit īfinitū in cuiꝰ ṗmo pedali ſit
                    <lb/>
                  vnꝰ g̈dus caliditatꝪ ꝑ totū, in ſcḋo duo, in tertio .4. /
                    <lb/>
                  et ſic ↄ̨ñter ſine admixtiõe ↄ̈rii / tūc a. eſt īfinite intēſū /
                    <lb/>
                  vt pꝫ ex p̄cedēti dubio, et b. īfinite rēiſſū, cū ī eo cali-
                    <lb/>
                  ditas et frigiditas īfinite ſe adeq̈te īpediãt: et q̄lꝫ ꝑs
                    <lb/>
                  finita ipſiꝰ a. eſt eque intēſa cū parte correſpõdēte
                    <lb/>
                  ipſiꝰ b. / vt pꝫ diligenter intuēti: igr̄ correlariū verū.</s>
                </p>
                <p xml:id="N2C4DD">
                  <s xml:id="N2C4DE" xml:space="preserve">Tertia ↄ̨̨cĺo. </s>
                  <s xml:id="N2C4E1" xml:space="preserve">A nūc eſt calidū qḋ non
                    <lb/>
                  ītēdet̄̄: nec remittet̄̄.
                    <note position="left" xlink:href="note-0275-02a" xlink:label="note-0275-02" xml:id="N2C520" xml:space="preserve">hanc ne-
                      <lb/>
                    gat cal.</note>
                  </s>
                  <s xml:id="N2C4EB" xml:space="preserve">Et tñ in fine manebit nõ calidū
                    <lb/>
                  hanc ↄ̨cĺonē negat Calcu. in capĺo de mixtoꝝ intē-
                    <lb/>
                  ſiõe. </s>
                  <s xml:id="N2C4F2" xml:space="preserve">Quã tñ ꝓbo ſic. </s>
                  <s xml:id="N2C4F5" xml:space="preserve">Sit a. diuiſū ꝑ partes ꝓporti-
                    <lb/>
                  onales ꝓportiõe dupla: et in ṗma ſit aliq̈ albedo: et
                    <lb/>
                  ī ſcḋa in duplo ītēſior: et in .3. in q̈druplo intēſior: et
                    <lb/>
                  in .4. in octuplo intēſior: et ſic in īfinitū ꝓcedēdo per
                    <lb/>
                  nūeros pariter pares. </s>
                  <s xml:id="N2C500" xml:space="preserve">Et deinde inducat̄̄ in quãlꝫ
                    <lb/>
                  partē ſubdupla frigiditas ſucceſſiue in hora īcipi-
                    <lb/>
                  piēdo a ṗma. </s>
                  <s xml:id="N2C507" xml:space="preserve">Tūc ex p̄dictis ptꝫ ↄ̨cĺo hoc addito / 
                    <lb/>
                  intēdi et remitti dicūt motū: et ſucceſſionē. </s>
                  <s xml:id="N2C50C" xml:space="preserve">¶ Ex hac
                    <lb/>
                  ſequit̄̄ /  a. nūc eſt nõ calidū: et nõ intēdet̄̄ nec remit­
                    <lb/>
                  tet̄̄: et tñ in fine manebit infinite calidū. </s>
                  <s xml:id="N2C513" xml:space="preserve">Ptꝫ in caſu
                    <lb/>
                  ↄ̨cĺonis poſito /  in hora ſequēti remittat̄̄ ſucceſſi-
                    <lb/>
                  ue frigiditas ad nõ gradū eo ordine quo ante indu­
                    <lb/>
                  cebatur: quo poſito ptꝫ correlariū pro fine tēporis</s>
                </p>
                <p xml:id="N2C528">
                  <s xml:id="N2C529" xml:space="preserve">Quarta ↄ̨̨cĺo. </s>
                  <s xml:id="N2C52C" xml:space="preserve">A. nõ eſt calidum. </s>
                  <s xml:id="N2C52F" xml:space="preserve">Et tñ
                    <lb/>
                  eiꝰ ſcḋm certã diuiſionē q̄lꝫ pars eſt infinite calida.
                    <lb/>
                  </s>
                  <s xml:id="N2C535" xml:space="preserve">Sit a. corpꝰ finitū diuiſū in duas medietates ſcḋm
                    <lb/>
                  latitudinē: et ſit vna illaꝝ medietatū īfinite calida ꝑ
                    <lb/>
                  totū vniformiter ſiue ↄ̈rii coextēſione. </s>
                  <s xml:id="N2C53C" xml:space="preserve">Et alteriꝰ me­
                    <lb/>
                  dietatis ṗma pars ſit aliqualr̄ frigida, et .2. in du­
                    <lb/>
                  plo plus, et .3. in q̈druplo) et .4. in octuplo, et ſic in
                    <lb/>
                  īfinitū ꝓcedēdo ſus extremū ipſiꝰ a. </s>
                  <s xml:id="N2C545" xml:space="preserve">Et deīde diui­
                    <lb/>
                  datur totū a. ex tranſuerſo ꝑ partes proportiona­
                    <lb/>
                  les quauis proportione. </s>
                  <s xml:id="N2C54C" xml:space="preserve">Et patet concluſio.</s>
                </p>
                <p xml:id="N2C54F">
                  <s xml:id="N2C550" xml:space="preserve">Quīta ↄ̨̨cĺo. </s>
                  <s xml:id="N2C553" xml:space="preserve">Diuiſo a. ꝑ partes ꝓpor­
                    <cb chead="De difformium intenſione"/>
                  tionales ꝓportiõe dupla: et in p̄ma pari ponant̄̄ .4.
                    <lb/>
                  g̊dus albedīs. </s>
                  <s xml:id="N2C55B" xml:space="preserve">Et in .2. pari .8. </s>
                  <s xml:id="N2C55E" xml:space="preserve">Et in .3. pari .16. / et ſic
                    <lb/>
                  ↄ̨ñter aſcēdendo ꝑ nūeros pariṫ pares </s>
                  <s xml:id="N2C563" xml:space="preserve">Et in prima
                    <lb/>
                  in pari ponant̄̄ .4. nigredīs, et in .2.8. </s>
                  <s xml:id="N2C568" xml:space="preserve">Et in .3.16. / et
                    <lb/>
                  ſic ↄ̨ñter: vt fit in paribꝰ. </s>
                  <s xml:id="N2C56D" xml:space="preserve">Totū a. eſt nigrū vt duo.
                    <lb/>
                  </s>
                  <s xml:id="N2C571" xml:space="preserve">Ptꝫ / q2 tota deneīatio nata ꝓuenire ab illa albe-
                    <lb/>
                  dine non ꝑmixta ↄ̈rio eſt vt duo. </s>
                  <s xml:id="N2C576" xml:space="preserve">Et tota denoīatio
                    <lb/>
                  nata ꝓuedire ab illa nigredīe eſt vt .4. ceteris pari-
                    <lb/>
                  bus remoto īpedimento: g̊ ex prima ↄ̨cĺone totū a.
                    <lb/>
                  eſt nigrū vt duo. </s>
                  <s xml:id="N2C57F" xml:space="preserve">Añs pꝫ calculãti facile: ex p̄dictis
                    <lb/>
                    <note position="right" xlink:href="note-0275-03a" xlink:label="note-0275-03" xml:id="N2C5CE" xml:space="preserve">Correĺ.</note>
                  </s>
                  <s xml:id="N2C589" xml:space="preserve">¶ Ex hac ↄ̨cĺone ſequit̄̄ /  ſi in caſu eiꝰ ṗma ꝑs par
                    <lb/>
                  rarefiat acq̇rēdo aliquã ̄titatē </s>
                  <s xml:id="N2C58E" xml:space="preserve">Et .2. par ſubduplã
                    <lb/>
                  </s>
                  <s xml:id="N2C592" xml:space="preserve">Et .3. par ſubq̈druplã, et ſic ↄ̨ñter: ita  q̄lꝫ ſequens
                    <lb/>
                  acq̇rat in duplo mīorē quãtitatē ꝙ̄ p̄cedes. </s>
                  <s xml:id="N2C597" xml:space="preserve">Tūc in
                    <lb/>
                  fine illud manebit infinite album. </s>
                  <s xml:id="N2C59C" xml:space="preserve">Ptꝫ ex modo ꝓ-
                    <lb/>
                  bande .6. ↄ̨cĺonis q̄ſtiõis. </s>
                  <s xml:id="N2C5A1" xml:space="preserve">Et iſto mõ poteris īfinita
                    <lb/>
                  talia īferre: q̄ oīa ex p̄dictis facilē ſortiunt̄̄ ꝓbatio­
                    <lb/>
                  nē. </s>
                  <s xml:id="N2C5A8" xml:space="preserve">Et ſic pꝫ rñſio ad dubiū. </s>
                  <s xml:id="N2C5AB" xml:space="preserve">¶ Ad rõnes dubii. </s>
                  <s xml:id="N2C5AE" xml:space="preserve">Ad
                    <lb/>
                  primã rñſum eſt ibi vſ ad replicã: ad quam rñdeo
                    <lb/>
                  cõcedendo qḋ īfert̄̄. </s>
                  <s xml:id="N2C5B5" xml:space="preserve">¶ Et ſiĺr ad ↄ̨firmationē rñdeo
                    <lb/>
                  ↄ̨cedēdo illatū nec illud eſt incõueniēs. </s>
                  <s xml:id="N2C5BA" xml:space="preserve">¶ Ad ſcḋam
                    <lb/>
                  rõnē rñdeo ↄ̨cedendo illatū et nego illud eſſe incõue-
                    <lb/>
                  niēs. </s>
                  <s xml:id="N2C5C1" xml:space="preserve">¶ Ad ↄ̨firmationē nego ſequelã: nec eſt ſimile:
                    <lb/>
                  īmo dico /  iutenſio talis mixti debet attēdi penes
                    <lb/>
                  exceſſum vnius denominationis ſuper alteram / vt
                    <lb/>
                  patet ex prima concluſione huius dubii.</s>
                </p>
                <p xml:id="N2C5D4">
                  <s xml:id="N2C5D5" xml:space="preserve">Ad tertiū dubiū. </s>
                  <s xml:id="N2C5D8" xml:space="preserve">Argr̄ /  nõ ſit dabi-
                    <lb/>
                  lis q̈litas nulliꝰ intēſionis etc̈. </s>
                  <s xml:id="N2C5DD" xml:space="preserve">Q2 tūc ſeq̄ret̄̄ illam
                    <lb/>
                  nõ eſſe q̈litatē. </s>
                  <s xml:id="N2C5E2" xml:space="preserve">Sed ↄ̨ñs eſt flm̄: igr̄ illud ex q̊ ſequit̄̄.
                    <lb/>
                  </s>
                  <s xml:id="N2C5E6" xml:space="preserve">Seq̄la ꝓbat̄̄ / q2 oīs q̈litas eſt intenſa cū illud ſit ei
                    <lb/>
                  ꝓpriū. </s>
                  <s xml:id="N2C5EB" xml:space="preserve">¶ Et ↄ̨firmat̄̄ / q2 tū ſeq̄ret̄̄ illã eſſe qualitatē
                    <lb/>
                  nõ intenſibilē. </s>
                  <s xml:id="N2C5F0" xml:space="preserve">Sed ↄ̨ñs eſt flm̄: igr̄ illud ex q̊ ſequit̄̄.
                    <lb/>
                  </s>
                  <s xml:id="N2C5F4" xml:space="preserve">Seq̄la ꝓbat̄̄ / q2 illa q̈litas eſſet intēſibilis cū q̄lꝫ
                    <lb/>
                  eiꝰ pars ſit nõ ītenſa: tūc ex nõ ītenſis cõponeret̄̄ in­
                    <lb/>
                  tēſū: qḋ eſt manifeſte flm̄. </s>
                  <s xml:id="N2C5FB" xml:space="preserve">¶ In oppoſitū argr̄ / q2 p̄t
                    <lb/>
                  dari quãtitas nulliꝰ extenſiõis: igr̄ põt dari q̈litas
                    <lb/>
                  nulliꝰ intēſionis. </s>
                  <s xml:id="N2C602" xml:space="preserve">pꝫ ↄ̨ña / a ſiĺi et añs cõiter cõcedit̄̄
                    <lb/>
                  de benedicto corpore chriſti in ſacramēto altaris.
                    <lb/>
                  </s>
                  <s xml:id="N2C608" xml:space="preserve">Item hoc non implicat: igitur. </s>
                  <s xml:id="N2C60B" xml:space="preserve">¶ Pro ſolutione
                    <lb/>
                  huiꝰ dubitationis. </s>
                  <s xml:id="N2C610" xml:space="preserve">Pono aliquas coucluſiones.</s>
                </p>
                <p xml:id="N2C613">
                  <s xml:id="N2C614" xml:space="preserve">Prima ↄ̨̨cĺo. </s>
                  <s xml:id="N2C617" xml:space="preserve">Nõ eſt poſſibĺe naturalr̄
                    <lb/>
                  dare q̈litatē nulliꝰ intēſiõis. </s>
                  <s xml:id="N2C61C" xml:space="preserve">hãc paſſim oēs admit-
                    <lb/>
                  tūt. </s>
                  <s xml:id="N2C621" xml:space="preserve">Et ei experiētia ſuffragat̄̄.
                    <note position="right" xlink:href="note-0275-04a" xlink:label="note-0275-04" xml:id="N2C636" xml:space="preserve">pḣus de
                      <lb/>
                    ſomno et
                      <lb/>
                    vigi.</note>
                  </s>
                  <s xml:id="N2C629" xml:space="preserve">Qḋ aūt ab oībꝰ dr̄
                    <lb/>
                  p̄ſtat fidē de itate ex libro de ſomno et vigi. (ab oī­
                    <lb/>
                  bus ) q2 qḋ parū deeſt ꝓ nichilo reputat̄̄ ex .2.
                    <lb/>
                  phiſicoꝝ: hac ſuaſione hec ↄ̨° ſuã ſūmat apparētiã</s>
                </p>
                <p xml:id="N2C640">
                  <s xml:id="N2C641" xml:space="preserve">Scḋa ↄ̨̨cĺo. </s>
                  <s xml:id="N2C644" xml:space="preserve">Poſſibile eſt ſimpĺr dare
                    <lb/>
                  q̈litatē nulliꝰ ītēſiõis. </s>
                  <s xml:id="N2C649" xml:space="preserve">Probat̄̄: et ſigno vnã q̈lita­
                    <lb/>
                  tē īfinitã extēſiue diuiſam ꝑ partes ꝓportiõales ꝓ­
                    <lb/>
                  portiõe q̈drupla aſcēdendo. </s>
                  <s xml:id="N2C650" xml:space="preserve">Et ṗma eiꝰ pars puta
                    <lb/>
                  primū pedale ſit ītenſū vt vnū: et ſcḋa puta .4. ſeq̄n­
                    <lb/>
                  tia pedalia vt dimidiū, et .3. puta .16. pedalia vt vna
                    <lb/>
                  q̈rta: </s>
                  <s xml:id="N2C659" xml:space="preserve">Et .4. puta .64. vt vna octaua: et ſic ↄ̨ñter ſub-
                    <lb/>
                  duplando intēſionē. </s>
                  <s xml:id="N2C65E" xml:space="preserve">Quo poſito manifeſtū eſt illã
                    <lb/>
                  qualitatē nulliꝰ eſſe intenſionis q2 nullꝰ gradꝰ certe
                    <lb/>
                  intenſionis eſt ꝑ infinita eiꝰ pedalia extēſus: igitur
                    <lb/>
                  ex .5. ↄ̨cluſiõe p̄cedētis dubii illa nõ eſt alicuiꝰ inten­
                    <lb/>
                  ſionis.
                    <note position="right" xlink:href="note-0275-05a" xlink:label="note-0275-05" xml:id="N2C6CF" xml:space="preserve">Correĺ.</note>
                  </s>
                  <s xml:id="N2C66E" xml:space="preserve">¶ Ex hac ↄ̨cluſiõe ſeqnit̄̄ /  a. eſt nõ intenſuꝫ.
                    <lb/>
                  </s>
                  <s xml:id="N2C672" xml:space="preserve">Et ꝓportionabilr̄ ſicut ſua q̈litas partialis exten­
                    <lb/>
                  det̄̄ ꝑ mīores ꝑtes ita ꝓportiõabilr̄ fiet intēſior: et
                    <lb/>
                  in fine erit īfinite intenſum. </s>
                  <s xml:id="N2C679" xml:space="preserve">Probat̄̄ poſito /  a. ſit
                    <lb/>
                  corpꝰ de quo fit mentio in caſu ↄ̨cluſions īmediate
                    <lb/>
                  p̄cedentis. </s>
                  <s xml:id="N2C680" xml:space="preserve">Et cuiuſlꝫ illaꝝ partiū ſe habentiū in ꝓ-
                    <lb/>
                  portione quadrupla totalis qualitas ponatur in
                    <lb/>
                  primo eiꝰ pedali: et ꝓportionãbiliter ſicut ponitur
                    <lb/>
                  in minori parte ꝓportiõabiliter fiat intēſior. </s>
                  <s xml:id="N2C689" xml:space="preserve">Quo
                    <lb/>
                  poſito a. in fine manebit infinite intenſum: et modo
                    <lb/>
                  eſt nõ intenſum: et ꝓportionabiliter ſicut ſua quali­
                    <lb/>
                  tas partialis etc̈. / igr̄ correlariū verum. </s>
                  <s xml:id="N2C692" xml:space="preserve">Sed ꝓbatur / </s>
                </p>
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