Alvarus, Thomas, Liber de triplici motu, 1509

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                  <s xml:id="N2B3B6" xml:space="preserve">
                    <pb chead="Quarti tractatus." file="0266" n="266"/>
                  Patet hec ꝓpõ ex .2. replica dicti ſecūdi argumēti.
                    <lb/>
                    <note position="left" xlink:href="note-0266-01a" xlink:label="note-0266-01" xml:id="N2B617" xml:space="preserve">Correla.</note>
                  </s>
                  <s xml:id="N2B3C4" xml:space="preserve">¶ Ex hac ꝓpõne ſequit̄̄ /  aliqua eſt qualitas vni.
                    <lb/>
                  diffor. cuiꝰ ſcḋm aliquã diuiſiõeꝫ q̄lꝫ pars ꝓportio­
                    <lb/>
                  nalis eſt difformiter difformis. </s>
                  <s xml:id="N2B3CB" xml:space="preserve">pꝫ diuidēdo vnum
                    <lb/>
                  quadratū vniformiter difformē ꝑ lineas tranſuer-
                    <lb/>
                  ſales ſiue diametrales.
                    <note position="left" xlink:href="note-0266-02a" xlink:label="note-0266-02" xml:id="N2B61D" xml:space="preserve">4. ꝓpõ.</note>
                  </s>
                  <s xml:id="N2B3D7" xml:space="preserve">¶ Quarta ꝓpõ. </s>
                  <s xml:id="N2B3DA" xml:space="preserve">Qualitas
                    <lb/>
                  vnifor. diffor. nõ bñ diffinitur ſic. </s>
                  <s xml:id="N2B3DF" xml:space="preserve">Qualitas vnifor.
                    <lb/>
                  diffor. eſt illa q̄ ſic ſe hꝫ  ſecūdū aliquã eiꝰ diuiſio­
                    <lb/>
                  nē cuiuſlꝫ partis gradus medius .i. q̇ eſt ī medio .etc̃.
                    <lb/>
                  </s>
                  <s xml:id="N2B3E7" xml:space="preserve">Probat̄̄ / qr illa diffinitio ſic intellecta conuenit illi
                    <lb/>
                  qualitati q̄ nõ eſt vniformiter difformis de qua fit
                    <lb/>
                  mētio in .2. argumēto añ oppoſitū, eſto  illa diui-
                    <lb/>
                  datur ꝑ partes ꝓportionales ꝓportione dupla. vt
                    <lb/>
                  cõſtat intelligēti caſum.
                    <note position="left" xlink:href="note-0266-03a" xlink:label="note-0266-03" xml:id="N2B623" xml:space="preserve">5. propõ.</note>
                  </s>
                  <s xml:id="N2B3F7" xml:space="preserve">¶ Quinta ꝓpõ. </s>
                  <s xml:id="N2B3FA" xml:space="preserve">Qualitas
                    <lb/>
                  vnifor. diffor. nõ bene diffinit̄̄ ſic. </s>
                  <s xml:id="N2B3FF" xml:space="preserve">Qualitas vnifor.
                    <lb/>
                  diffor. eſt illa q̄ ſic ſe hꝫ  ſcḋm aliquã diuiſionē di­
                    <lb/>
                  uidendo ſecundū ṫuã dimēſionē cuiuſlibet partꝪ eiꝰ
                    <lb/>
                  gradus q̇ eſt in medio ſcḋm magnitudinē tantū ex-
                    <lb/>
                  ceditur a ſūmo: quãto etc̃. </s>
                  <s xml:id="N2B40A" xml:space="preserve">Probatur. </s>
                  <s xml:id="N2B40D" xml:space="preserve">q2 capto qua­
                    <lb/>
                  drato ꝑfecto cuiꝰ vna .3. in medio ꝓcedēs ab vno la-
                    <lb/>
                  tere in reliquū ſit vniformiter difformis ab .8. vſ
                    <lb/>
                  ad .4. </s>
                  <s xml:id="N2B416" xml:space="preserve">Et vna alia .3. ex trãſuerſo ꝓcedēs vſ ad alte­
                    <lb/>
                  ram ex vtro latere ꝑ modū crucis ſit etiã vnifor-
                    <lb/>
                  miter difformis ab .8. vſ ad .4. </s>
                  <s xml:id="N2B41D" xml:space="preserve">Et reſidue partes
                    <lb/>
                  ſint vniformis. </s>
                  <s xml:id="N2B422" xml:space="preserve">Tunc manifeſtū eſt illã qualitatem
                    <lb/>
                  non eſſe vniformiter difformē: et tñ illa diffinitio ei
                    <lb/>
                  cõuenit / vt patꝫ intelligēti caſum. </s>
                  <s xml:id="N2B429" xml:space="preserve">igr̄ illa diffinitio
                    <lb/>
                  nulla. </s>
                  <s xml:id="N2B42E" xml:space="preserve">Hoc videas clariꝰ in expõne .2. capi. Calcu. in
                    <lb/>
                  prīcipio.
                    <note position="left" xlink:href="note-0266-04a" xlink:label="note-0266-04" xml:id="N2B629" xml:space="preserve">6. ꝓpõ.</note>
                  </s>
                  <s xml:id="N2B438" xml:space="preserve">¶ Sexta ꝓpõ. </s>
                  <s xml:id="N2B43B" xml:space="preserve">Qualitas vnifor. diffor. bñ
                    <lb/>
                  diffinit̄̄ ſic.
                    <note position="left" xlink:href="note-0266-05a" xlink:label="note-0266-05" xml:id="N2B62F" xml:space="preserve">q̇d quali­
                      <lb/>
                    tas vni.
                      <lb/>
                    diffor.</note>
                  </s>
                  <s xml:id="N2B445" xml:space="preserve">Qualitas vniformiter diffor. eſt quali-
                    <lb/>
                  tas ita ſe hñs  in ea ꝓportõe in qua queuis om̄ia
                    <lb/>
                  puncta eiꝰ intrīſeca equalis intēſiõis magis diſtãt
                    <lb/>
                  quãtitatiue a gradu euius ſūmo in ea ꝑ maiorē la-
                    <lb/>
                  titudinē diſtãt intēſiue ab eodē gradu ſūmo: ita 
                    <lb/>
                  in quacū ꝓportiõe vna pars eius eſt maior alte-
                    <lb/>
                  ra ̄titatiue (inequalis tñ intēſiõis) in ea extremū
                    <lb/>
                  eius intēſiꝰ ꝑ maiorē latitudinē excedit extremū re­
                    <lb/>
                  miſſiꝰ eiuſdem. </s>
                  <s xml:id="N2B458" xml:space="preserve">exēplū / vt capta latitudine vniformi­
                    <lb/>
                  ter difformi. </s>
                  <s xml:id="N2B45D" xml:space="preserve">ab .8. vſ ad nõ gradū manifeſtuꝫ eſt /
                    <lb/>
                   punctus vt .4. iu duplo plꝰ diſtat ̄titatiue ꝙ̄ pū­
                    <lb/>
                  ctus vt .6. a gradu .8. et etiã ꝑ in duplo maiorem la­
                    <lb/>
                  titudinē gradus octauus excedit .4. ꝙ̄ .6. / vt ſatis cõ­
                    <lb/>
                  ſtat. </s>
                  <s xml:id="N2B468" xml:space="preserve">et ſic de aliis gradibꝰ et punctis poteris facile
                    <lb/>
                  exēplificare. </s>
                  <s xml:id="N2B46D" xml:space="preserve">Itē capta medietate intēſiori que ē ab
                    <lb/>
                  octauo vſ ad .4. et prīa quarta alteriꝰ medietatꝪ
                    <lb/>
                  q̄ eſt a .4. vſ ad .2. manifeſtū eſt  in ea ꝓportione
                    <lb/>
                  puta dupla q̈ in medietas ē maior illa quarta ī ea
                    <lb/>
                  ꝑ maiorē latitudinē extremū intēſius eiꝰ excedit eiꝰ
                    <lb/>
                  extremū remiſſius ꝙ̄ extremū intēſius ipſius quar­
                    <lb/>
                  te excedat eius extremū remiſſius. </s>
                  <s xml:id="N2B47C" xml:space="preserve">Hanc diffinitio­
                    <lb/>
                  nē nõ aliter ſufficiētē ꝓbo niſi q2 nõ video defectuꝫ
                    <lb/>
                  in ea.
                    <note position="left" xlink:href="note-0266-06a" xlink:label="note-0266-06" xml:id="N2B639" xml:space="preserve">phūs .6.
                      <lb/>
                    thopi.</note>
                  </s>
                  <s xml:id="N2B488" xml:space="preserve">difficile em̄ eſt cõſtruere diffinitionē vt inquit
                    <lb/>
                  phūs .6. thopi.
                    <note position="left" xlink:href="note-0266-07a" xlink:label="note-0266-07" xml:id="N2B641" xml:space="preserve">Aulꝰ ge.
                      <lb/>
                    i. nocttuꝫ
                      <lb/>
                    atti. c. 25.</note>
                  </s>
                  <s xml:id="N2B492" xml:space="preserve">Si q̇s aūt defectū inuenerit: aut eo
                    <lb/>
                  affectu excuſet Aulus geliꝰ .i. nocti. atti. varro­
                    <lb/>
                  nē in cõplete inducias diffiniētē excuſat: aut corri-
                    <lb/>
                  gat.
                    <note position="left" xlink:href="note-0266-08a" xlink:label="note-0266-08" xml:id="N2B64B" xml:space="preserve">Augu. i.
                      <lb/>
                    de trini.
                      <lb/>
                    3. reg. 8.</note>
                  </s>
                  <s xml:id="N2B4A0" xml:space="preserve">Nõ em̄ (vt cū Auguſto .i. de trini. loquar) pude­
                    <lb/>
                  bit me ſicubi heſito querere aut ſicubi erro diſcere.
                    <lb/>
                  </s>
                  <s xml:id="N2B4A6" xml:space="preserve">Nõ eī eſt hõ q̇ nõ peccet .3. regū .8.
                    <note position="left" xlink:href="note-0266-09a" xlink:label="note-0266-09" xml:id="N2B655" xml:space="preserve">eſaie .53.</note>
                  </s>
                  <s xml:id="N2B4AE" xml:space="preserve">Oēs eī errauimꝰ
                    <lb/>
                  Eſaie .53. qḋ et de volūtatis et etiã intellectꝰ errore
                    <lb/>
                  ſatis cõmode intelligi põt. </s>
                  <s xml:id="N2B4B5" xml:space="preserve">¶ Qualitas aūt vnifor­
                    <lb/>
                  miter difformis eſt duplex: q̄dã eī terminat̄̄ ad gra­
                    <lb/>
                  dū. </s>
                  <s xml:id="N2B4BC" xml:space="preserve">q̄dã vero ad nõ gradū. </s>
                  <s xml:id="N2B4BF" xml:space="preserve">Qualitas vnifor. diffor.
                    <lb/>
                  terminata ad nõ gradū eſt qualitas vnifor. diffor.
                    <lb/>
                  cuiꝰ oīa puncta ↄ̨ſimilis intēſionis in ea ꝓportiõe
                    <lb/>
                  plus diſtant quãtitatiue a nõ gradu in q̈ ſunt inten­
                    <lb/>
                  ſiora: et econtra. </s>
                  <s xml:id="N2B4CA" xml:space="preserve">vt qualitas vniformiter diffor. ab
                    <lb/>
                  octauo vſ ad nõ gradū.
                    <note position="left" xlink:href="note-0266-10a" xlink:label="note-0266-10" xml:id="N2B65B" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N2B4D4" xml:space="preserve">¶ Ex hac diffinitione ſeq̇­
                    <lb/>
                  tur  in omni qualitate vnifor. diffor. termīata ad
                    <cb chead="Capitulum quartum"/>
                  non gradū et vniformiū dimēſionū in ea ꝓportio-
                    <lb/>
                  ne in qua puncta magis diſtant a nõ gradu ſecūdū
                    <lb/>
                  longitudinē: in ea ſunt maioris intenſiõis.
                    <note position="right" xlink:href="note-0266-11a" xlink:label="note-0266-11" xml:id="N2B661" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N2B4E5" xml:space="preserve">¶ Seq̇-
                    <lb/>
                  tur ſcḋo / quedaꝫ ꝓprietas qualitatis vnifor. diffor.
                    <lb/>
                  ad gradū termīate que et diffinitio eſt v3 qualitas
                    <lb/>
                  vnifor. diffor. ad gradū termīate ē q̈litas vniformi­
                    <lb/>
                  ter diffor. inter cuiꝰ gradus maior eſt ꝓpõ intēſionū
                    <lb/>
                  ̄ diſtentiaꝝ ab extremo eius remiſſiori: hoc facile
                    <lb/>
                  ꝓbatur ex diffinitiõe qualitatis vni. diffor. ad non
                    <lb/>
                  gradū terminate. </s>
                  <s xml:id="N2B4F6" xml:space="preserve">hoc addito /  quelꝫ qualitas vni.
                    <lb/>
                  diffor. põt eſſe in potētia ꝓpinqua pars vni: diffor.
                    <lb/>
                  ad nõ gradū terminate. </s>
                  <s xml:id="N2B4FD" xml:space="preserve">Et  vtro termino ꝓpor­
                    <lb/>
                  tionis maioris inequalitatis equaliter decreſcēte
                    <lb/>
                  ꝓportio augetur
                    <note position="right" xlink:href="note-0266-12a" xlink:label="note-0266-12" xml:id="N2B667" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N2B509" xml:space="preserve">¶ Seq̇tur .3. /  ſi q̈litas vniformis
                    <lb/>
                  addatur q̈litati vnifor. dif. oīno eq̈lium dimēſionū:
                    <lb/>
                  reſultabit qualitas vniformiter difformis. </s>
                  <s xml:id="N2B510" xml:space="preserve">Proba­
                    <lb/>
                  tur. </s>
                  <s xml:id="N2B515" xml:space="preserve">q2 facta tali vnione adhuc puncta oīo eodē mo­
                    <lb/>
                  do ſe excedēt ſicut añ ſe excedebãt in illa q̈litate vni­
                    <lb/>
                  formiter diffor. </s>
                  <s xml:id="N2B51C" xml:space="preserve">Sꝫ in illa qualitate vniformi. dif.
                    <lb/>
                  puncta eo mõ ſe excedūt ſicut ſufficit ad qualitateꝫ
                    <lb/>
                  vni. dif. / igit̄̄ facta tali vniõe illa qualitas manet vni­
                    <lb/>
                  for. dif. </s>
                  <s xml:id="N2B525" xml:space="preserve">Minor pꝫ. </s>
                  <s xml:id="N2B528" xml:space="preserve">et maior ꝓbat̄̄ ꝑ hoc /  qñcun
                    <lb/>
                  aliqua ſe excedūt: et equalē latitudinē oīo acquirūt
                    <lb/>
                  cõtinuo equali exceſſu ſe excedūt. </s>
                  <s xml:id="N2B52F" xml:space="preserve">vt facile eſt demõ­
                    <lb/>
                  ſtrare.
                    <note position="right" xlink:href="note-0266-13a" xlink:label="note-0266-13" xml:id="N2B66D" xml:space="preserve">4. correĺ.</note>
                  </s>
                  <s xml:id="N2B539" xml:space="preserve">¶ Sequit̄̄ .4. </s>
                  <s xml:id="N2B53C" xml:space="preserve">Si due q̈litates vnifor. dif. ad
                    <lb/>
                  non gradū terminate: et ↄ̨ſimiliū oīno dimēſionum
                    <lb/>
                  nõ gradibus ſimul vnitis: et extremis aliis etiã ad
                    <lb/>
                  inuicem vnitis: reſultabit qualitas totalis vni. dif.
                    <lb/>
                  </s>
                  <s xml:id="N2B546" xml:space="preserve">Probatur / q2 puncta correſpõdētia in vna illaruꝫ
                    <lb/>
                  ſe habēt oīo in eadē ꝓportiõe quo ad intēſionē et
                    <lb/>
                  diſtantiã a nõ gradu: ſicut ſe habēt correſpõdentia
                    <lb/>
                  in altera: ergo ipſa ſimul vnita manebūt in eadem
                    <lb/>
                  ꝓportiõe: et ꝑ ↄ̨ñs illa totalis q̈litas manebit vni.
                    <lb/>
                  dif. </s>
                  <s xml:id="N2B553" xml:space="preserve">Patet hec ↄ̨ña auxilio huius / qḋ in .2. parte de­
                    <lb/>
                  monſtratū eſt /  v3 talis eſt ꝓportio cõiunctorū qua­
                    <lb/>
                  lis eſt diuiſorū.
                    <note position="right" xlink:href="note-0266-14a" xlink:label="note-0266-14" xml:id="N2B673" xml:space="preserve">5. correĺ.</note>
                  </s>
                  <s xml:id="N2B55F" xml:space="preserve">¶ Seq̇t̄̄ .5. /  ſi q̈litati vni. dif. oīno
                    <lb/>
                  equaliū dimēſionū extremis ītēſioribꝰ ad inuiceꝫ
                    <lb/>
                  iūctꝪ: et remiſſoribꝰ ad īuicē ſiĺr iūctꝪ addat̄̄ q̈li. vni.
                    <lb/>
                  dif. reſultabit q̈litas vni. dif. (ſꝑ abigo muſcas). </s>
                  <s xml:id="N2B568" xml:space="preserve">ꝓ­
                    <lb/>
                  bat̄̄ / q2 vel vtra illaꝝ termīat̄̄ ad nõ g̈dū. </s>
                  <s xml:id="N2B56D" xml:space="preserve">et ſic ex .4.
                    <lb/>
                  corre. manebit vni. dif. aut vna terminat̄̄ ad nõ gra­
                    <lb/>
                  dum: et alia nõ: et tūc dematur ab illa termīata ad
                    <lb/>
                  gradū maximꝰ gradus vniformis ꝑ totū: et tunc vt
                    <lb/>
                  conſtat manebit totū reſiduū qualitas vni. diffor.
                    <lb/>
                  ad nõ gradū terminata: vniat̄̄ igit̄̄ alteri termina­
                    <lb/>
                  te ad nõ gradū: et ex .4. corre. manebit qualitas vni.
                    <lb/>
                  diffor. addatur / ergo illa qualitas vni. diffor. gra-
                    <lb/>
                  dui vniformi dēpto a q̈litate terminata ad graduꝫ
                    <lb/>
                  et ex .3. corre. manebit qualitas vni. dif. / igit̄̄ ſi quali­
                    <lb/>
                  tati vni. diffor. addat̄̄ etc. reſultabit quali. vni dif.
                    <lb/>
                  </s>
                  <s xml:id="N2B585" xml:space="preserve">Patꝫ igit̄̄ corre.
                    <note position="right" xlink:href="note-0266-15a" xlink:label="note-0266-15" xml:id="N2B679" xml:space="preserve">Calcula.</note>
                  </s>
                  <s xml:id="N2B58D" xml:space="preserve">Et hec eſt .4. cal. in .c. de inductione
                    <lb/>
                  gradus ſū. </s>
                  <s xml:id="N2B592" xml:space="preserve">quã longis ambagibus ꝓbat.
                    <note position="right" xlink:href="note-0266-16a" xlink:label="note-0266-16" xml:id="N2B67F" xml:space="preserve">6. correĺ</note>
                  </s>
                  <s xml:id="N2B59A" xml:space="preserve">¶ Sequi­
                    <lb/>
                  tur .6. /  ſemꝑ ex vnione duarū qualitū vni. diffor-
                    <lb/>
                  miū oīno equaliū et ↄ̨ſimiliū dimēſionū reſultat q̈-
                    <lb/>
                  litas vniformis vel vniformiter dif. hanc facile eſt
                    <lb/>
                  ex predictis demõſtrare. </s>
                  <s xml:id="N2B5A5" xml:space="preserve">¶ Sequit̄̄ .7. </s>
                  <s xml:id="N2B5A8" xml:space="preserve">Qñcū eadē
                    <lb/>
                  latitudo vel oīno ↄ̨ſimilis vni. dif. extendit̄̄ ꝑ duo
                    <lb/>
                  ſubiecta inequalia: in ꝓportione qua vnū ſubiectū
                    <lb/>
                  eſt maius alio in ea puncta ↄ̨ſimilia ī maiori plꝰ
                    <lb/>
                  diſtaut ̄titatiue a gradu ſūmo q̈ eis ſimilia ī mi­
                    <lb/>
                  nori. </s>
                  <s xml:id="N2B5B5" xml:space="preserve">exemplū / vt ſi latitudo ab .8. vſ ad .4. exten-
                    <lb/>
                  datur in pedali et in ſemipedali punctus vt .6. in du­
                    <lb/>
                  plo plus diſtat a ſūmo in pedali ꝙ̄ in ſemipedali
                    <lb/>
                  </s>
                  <s xml:id="N2B5BD" xml:space="preserve">Probatur / ſit a. lati. vni. diffor. extenſa ꝑ aliqḋ ſub­
                    <lb/>
                  iectū. </s>
                  <s xml:id="N2B5C2" xml:space="preserve">et b. oīo cõſimilis lati. extenſa ꝑ ſubiectum in
                    <lb/>
                  f. ꝓportiõe minus: et ſit .c. punctꝰ in a. et d. cõſimilis
                    <lb/>
                  in b. et excedat gradus ſummꝰ in g. ꝓportione ma-
                    <lb/>
                  iori exceſſu extrema illaꝝ latitu. ꝙ̄ ipſa puncta c.d:
                    <lb/>
                  </s>
                  <s xml:id="N2B5CC" xml:space="preserve"/>
                </p>
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