Alvarus, Thomas, Liber de triplici motu, 1509

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                    <pb chead="De difformium intenſione" file="0265" n="265"/>
                  duplo plus: et 3. in duplo plus ꝙ̄ .2. </s>
                  <s xml:id="N2B1BF" xml:space="preserve">Et .4. in duplo
                    <lb/>
                  pluſ̄ .3. </s>
                  <s xml:id="N2B1C4" xml:space="preserve">Et ſic ↄ̨ñter. </s>
                  <s xml:id="N2B1C7" xml:space="preserve">Tale corpus eſſet īfinite albuꝫ /
                    <lb/>
                  ſed ↄ̨ñs eſt falſum: igit̄̄ illud ex quo ſeq̇tur </s>
                  <s xml:id="N2B1CC" xml:space="preserve">Falſitas
                    <lb/>
                  ↄ̨ſequētis pꝫ / qr illud corpꝰ eſt finite albū: igit̄̄ </s>
                  <s xml:id="N2B1D1" xml:space="preserve">Pro­
                    <lb/>
                  batur añs. </s>
                  <s xml:id="N2B1D6" xml:space="preserve">Et pono gratia argumēti /  albedo pri­
                    <lb/>
                  me partis ꝓportionalis ſit vt .4. / et manifeſtum eſt /
                    <lb/>
                   ip̄a denominat totū vt .3. / igr̄ tota illa denominat
                    <lb/>
                  illud corpus vt .6. / et per ↄ̨ñs finite totū denoīat: et ex
                    <lb/>
                  cõſequēti illud corpus ē finite albū / qḋ fuit ꝓbãdum
                    <lb/>
                  </s>
                  <s xml:id="N2B1E2" xml:space="preserve">Probatur tñ ↄ̨ña: qr ſi albedo exiſtens in prīa par­
                    <lb/>
                  te ꝓportionali denoīat totū vt .3. </s>
                  <s xml:id="N2B1E7" xml:space="preserve">Et albedo exiſtēs
                    <lb/>
                  in .2. eſt in duplo intēſior: et eſt in ſubquadruplo ſub­
                    <lb/>
                  iecto: igr̄ denoīat in duplo minus ptꝫ ↄ̨ña: qr ſi eēt
                    <lb/>
                  abedo .2. partis equalis intēſiõis albedine prīe de­
                    <lb/>
                  noīaret in ſubquadruplo: ſꝫ mõ denoīat in duplo
                    <lb/>
                  plus cum ſit in duplo intēſior: ergo denoīat in du-
                    <lb/>
                  plo minus ꝙ̄ albedo prīe qr dupluꝫ ſubq̈drupli eſt
                    <lb/>
                  ſubduplū quadrupli. </s>
                  <s xml:id="N2B1F8" xml:space="preserve">Et eadē rõne albedo exiſtens
                    <lb/>
                  in .3. denoīat in ſubduplo minꝰ ꝙ̄ albedo exiſtens ī
                    <lb/>
                  2. </s>
                  <s xml:id="N2B1FF" xml:space="preserve">Et ſic cuiuſlibet ꝑtis ſequētis albedo denoīat in
                    <lb/>
                  duplo minus illud ſubiectū ꝙ̄ albedo īmediate p̄ce­
                    <lb/>
                  dentis ip̄am: igitur denoīato illiꝰ albedinis ↄ̨po-
                    <lb/>
                  nitur ex infinitis ↄ̨tinuo ſe habētibꝰ in ꝓportiõe du­
                    <lb/>
                  pla: et primū illoꝝ eſt vt .3. / ergo totū eſt vt ſex: pꝫ hec
                    <lb/>
                  ↄ̨ña ex ṗma parte huiꝰ libri. </s>
                  <s xml:id="N2B20C" xml:space="preserve">Sꝫ iam ꝓbo ſeq̄laꝫ: qr
                    <lb/>
                  ſi in prīa parte ꝓportionali alicuius corꝑis ꝓpor-
                    <lb/>
                  tiõe dupla diuiſi ponat̄̄ aliq̈ albedo: et in .2. duplo ī­
                    <lb/>
                  tenſior ꝑ totū ſiue mixtione ↄ̈rii in .3. in duplo intē-
                    <lb/>
                  ſior  in .2. et in .4. in duplo ītēſior ꝙ̄ in .3. / et ſic ↄ̨ſe-
                    <lb/>
                  quēter: tale corpus eēt infinite albū: igit̄̄ pari rõne
                    <lb/>
                  ſi diuidat̄̄ ꝓportione quadrupla: et in prima parte
                    <lb/>
                  ponatur aliqua albedo: et in .2. ī duplo intēſior etc.
                    <lb/>
                  tale corpus erit infinite albū. </s>
                  <s xml:id="N2B21F" xml:space="preserve">Patꝫ ↄ̨ña / qr nõ vide­
                    <lb/>
                  tur maior ratio de vno ꝙ̄ de altero. </s>
                  <s xml:id="N2B224" xml:space="preserve">Probat̄̄ añs:
                    <lb/>
                  et pono gr̄a argumenti /  albedo prime partis ſit
                    <lb/>
                  vt .2. deīde volo /  in prīa parte ꝓportionabili vniꝰ
                    <lb/>
                  hore capiãtur .4. gradus exiſtētes ī .2. parte ꝓpor-
                    <lb/>
                  tionali illiꝰ corporis q̄ eſt vna quarta: et ponatur
                    <lb/>
                  quilibet illoꝝ in diuerſa quarta. </s>
                  <s xml:id="N2B231" xml:space="preserve">Et in .2. ꝑte hore
                    <lb/>
                  ponatur q̇lꝫ .8. graduū exiſtentiū in .3. parte corpo-
                    <lb/>
                  ris que eſt vna octaua in diuerſa octaua illius cor­
                    <lb/>
                  ris. </s>
                  <s xml:id="N2B23A" xml:space="preserve">Et in .3. parte hore capiat̄̄ q̇lꝫ ſexdecim graduū
                    <lb/>
                  exiſtentiū in quarta ꝑte corꝑis et ponat̄̄ in diuerſa
                    <lb/>
                  decimaſexta: et ſic ↄ̨ñter: quo poſito in fine hore illḋ
                    <lb/>
                  corpus habebit ꝑ totū infinitã albedinē / vt cõſtat: et
                    <lb/>
                  erit reductū ad vniformitatē: igitur illud corpꝰ mõ
                    <lb/>
                  ante reductionē ad vniformitatē eſt infinite album /1
                    <lb/>
                  quod fuit ꝓbandum.</s>
                </p>
                <p xml:id="N2B249">
                  <s xml:id="N2B24A" xml:space="preserve">In oppoſitum arguitur ſic </s>
                  <s xml:id="N2B24D" xml:space="preserve">Sit a. dif­
                    <lb/>
                  forme: et pono /  reducatur ad vniformitatem nul-
                    <lb/>
                  la facta rarefactiõe aut condēſatione qualitatis in
                    <lb/>
                  parte aut in tota: nulla qualitate poſita in maiori
                    <lb/>
                  aut minori parte ꝙ̄ erat antea etc. </s>
                  <s xml:id="N2B258" xml:space="preserve">Et tūc manifeſtū
                    <lb/>
                  eſt /  tale corpus eſt vniforme. </s>
                  <s xml:id="N2B25D" xml:space="preserve">Sit igitur vniforme
                    <lb/>
                  c. gradu. </s>
                  <s xml:id="N2B262" xml:space="preserve">Et arguo ſic / a. eſt intenſum c. gradu: et eſt
                    <lb/>
                  ita intenſuꝫ ſicut erat ante reductionē ad vniformi-
                    <lb/>
                  tatē: igit̄̄ ante reductionē ad vniformitatē erat a. in­
                    <lb/>
                  tenſum c. gradu. </s>
                  <s xml:id="N2B26B" xml:space="preserve">Et ꝑ ↄ̨ñs eius intēſio et pari ratio-
                    <lb/>
                  ne cuiuſcū difformis mēſuranda eſt penes redu-
                    <lb/>
                  ctionē ad vniformitatē. </s>
                  <s xml:id="N2B272" xml:space="preserve">Minor ꝓbatur / qr a. nullaꝫ
                    <lb/>
                  intenſionē acq̇ſiuit aut ꝑdidit / qr quantã ꝑdidit vna
                    <lb/>
                  eiꝰ pars tantã acquiſiuit ſibi equalis: g̊ a. eſt ita in­
                    <lb/>
                  tenſum ſicut erat añ reductionē ad vniformitatē.</s>
                </p>
                <p xml:id="N2B27B">
                  <s xml:id="N2B27C" xml:space="preserve">Quatuor articuli hãc queſtionē abſol­
                    <lb/>
                  uent: primꝰ notabit: ſcḋs cõcluſiões inducet: tertius
                    <lb/>
                  dubitabit: quartꝰ vero ratiões añ oppoſitū ſoluet. </s>
                </p>
                <p xml:id="N2B283">
                  <s xml:id="N2B284" xml:space="preserve">Notandum eſt primo tangendo ma-
                    <cb chead="De difformium intenſione"/>
                  teriam primi argumēti: iſti termini paruitas et ma­
                    <lb/>
                  gnitudo ſunt termini ſe habentes ꝑ modū priuati-
                    <lb/>
                  ui et poſitiui: et ſimiĺr iſti intenſio et remiſſio: et iſti
                    <lb/>
                  multitudo et paucitas. </s>
                  <s xml:id="N2B290" xml:space="preserve">Et ꝓ eadē reverificant̄̄: omīs
                    <lb/>
                  eī magnitudo ē paruitas et oīs paruitas eſt magni­
                    <lb/>
                  tudo. </s>
                  <s xml:id="N2B297" xml:space="preserve">Quãuis tamē idē ſit magnitudo et paruitas
                    <lb/>
                  nichilominus nõ ſequit̄̄ hec magnitudo efficit̄̄ ma-
                    <lb/>
                  ior: et hec magnitudo eſt paruitas: g̊ paruitas effi­
                    <lb/>
                  citur maior. </s>
                  <s xml:id="N2B2A0" xml:space="preserve">Sed debet cõcludi: ergo paruitas effi-
                    <lb/>
                  citur maior magnitudo. </s>
                  <s xml:id="N2B2A5" xml:space="preserve">Et qm̄ iſti termini diſtan-
                    <lb/>
                  tia et propinq̇tas etiã eodē mõ ſe habent ſicut ma-
                    <lb/>
                  gnitudo et paruitas: dico /  oīs diſtantia eſt ꝓpin­
                    <lb/>
                  quitas: et oīs ꝓpinquitas eſt diſtantia. </s>
                  <s xml:id="N2B2AE" xml:space="preserve">Tñ iſtã ↄ̨ña
                    <lb/>
                  nõ valet iſta ꝓpinq̇tas efficitur maior. </s>
                  <s xml:id="N2B2B3" xml:space="preserve">Et iſta ꝓpī-
                    <lb/>
                  quitas eſt iſta diſtãtia: g̊ iſta diſtãtia efficit̄̄ maior.
                    <lb/>
                  </s>
                  <s xml:id="N2B2B9" xml:space="preserve">Sꝫ debet cõcludi: g̊ iſta diſtãtia efficit̄̄ maior ꝓprin-
                    <lb/>
                  quitas.
                    <note position="right" xlink:href="note-0265-01a" xlink:label="note-0265-01" xml:id="N2B320" xml:space="preserve">Aduerte.</note>
                  </s>
                  <s xml:id="N2B2C3" xml:space="preserve">Aduerte vlteriꝰ /  intēſionem attēdi penes
                    <lb/>
                  maiorē diſtãtia a nõ gradu nichil aliud eſt ꝙ̄ maio­
                    <lb/>
                  ritatē intenſiõis cognoſci mediãte veritate huiꝰ ꝓ-
                    <lb/>
                  poſitionis. </s>
                  <s xml:id="N2B2CC" xml:space="preserve">Quanta diſtãtia qualitatis a nõ gra-
                    <lb/>
                  du eſt maior tanto intēſio qualitatis eſt maior. </s>
                  <s xml:id="N2B2D1" xml:space="preserve">ma­
                    <lb/>
                  gnitudo aūt diſtantie attēditur penes multitudinē
                    <lb/>
                  graduū eiuſdē intenſionis ipſius qualitatis.
                    <note position="right" xlink:href="note-0265-02a" xlink:label="note-0265-02" xml:id="N2B326" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N2B2DD" xml:space="preserve">¶ Ex
                    <lb/>
                  quo ſequit̄̄ primo /  meliꝰ cognoſcit̄̄ intenſiõis ma­
                    <lb/>
                  ioritas penes multitudinē graduū: ꝙ̄ penes diſtan­
                    <lb/>
                  tiã a nõ gradu: qñ quidē ipſius diſtantie maioritas
                    <lb/>
                  penes multitudinē graduū tandē cognoſcit̄̄ de hoc
                    <lb/>
                  plura in expoſitiõe ṗmi capitis calculatoris.
                    <note position="right" xlink:href="note-0265-03a" xlink:label="note-0265-03" xml:id="N2B32C" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N2B2EF" xml:space="preserve">¶ Se­
                    <lb/>
                  quitur ſcḋo / hanc ↄ̨ñam nõ valere iutēſio attēditur
                    <lb/>
                  penes maiorē diſtantiã a nõ gradu: et oīs diſtãtia
                    <lb/>
                  eſt ꝓpinq̇tas: igitur intenſio attēdit̄̄ penes ꝓpīqui­
                    <lb/>
                  tatē ad nõ gradū. </s>
                  <s xml:id="N2B2FA" xml:space="preserve">Probat̄̄ / q2 cõuertit̄̄ cū iſta mala
                    <lb/>
                  ↄ̨ña intenſio mēſuratur mediãte veritate huiꝰ ꝓpo­
                    <lb/>
                  ſitiõis: quãto diſtãtia a nõ gradu eſt maior tanto ī-
                    <lb/>
                  tenſio eſt maior: et oīs diſtãtia eſt ꝓpinq̇tas: igit̄̄ in­
                    <lb/>
                  tenſio mēſuratur mediante itate huiꝰ ꝓpoſitiõis
                    <lb/>
                  </s>
                  <s xml:id="N2B306" xml:space="preserve">Quanto ꝓpinq̇tas ad nõ gradū eſt maior tanto in­
                    <lb/>
                  tenſio eſt maior. </s>
                  <s xml:id="N2B30B" xml:space="preserve">Et ꝑ hoc ſoluirur prmū argumen-
                    <lb/>
                  tū ante oppoſitū
                    <note position="right" xlink:href="note-0265-04a" xlink:label="note-0265-04" xml:id="N2B332" xml:space="preserve">3. correĺ.</note>
                  ¶ Seq̇tur .3. gradum ſummū eē re­
                    <lb/>
                  miſſum. </s>
                  <s xml:id="N2B317" xml:space="preserve">Patꝫ hoc correlariū ex confirmatione pri­
                    <lb/>
                  mi argumenti.</s>
                </p>
                <p xml:id="N2B338">
                  <s xml:id="N2B339" xml:space="preserve">Notandum eſt ſecundo / circa materiã
                    <lb/>
                  ſecundi argumēti inq̇rendo diffinitionē qualitatis
                    <lb/>
                  vniformiṫ difformis /  duplex eſt qualitas quedaꝫ
                    <lb/>
                  eſt vniformis: q̄dã eſt difformis. </s>
                  <s xml:id="N2B342" xml:space="preserve">Qualitas vnifor-
                    <lb/>
                  mis eſt illa cuius oēs partes ̄titatiue ſunt eque in­
                    <lb/>
                  tenſe. </s>
                  <s xml:id="N2B349" xml:space="preserve">Sed qualitas difformis eſt qualitas cuiꝰ nõ
                    <lb/>
                  om̄s partes equales quãtitatiue ſunt eque intenſe
                    <lb/>
                  </s>
                  <s xml:id="N2B34F" xml:space="preserve">Hec aūt eſt duplex: quia q̄dã eſt vniformiter diffor-
                    <lb/>
                  mis: quedã vero vniformiter difformis. </s>
                  <s xml:id="N2B354" xml:space="preserve">Sꝫ q2 qua­
                    <lb/>
                  litas vniformiter difformis diuerſi mode a diuer-
                    <lb/>
                  ſis diffinitur: ideo ad inq̇rendã diffinitionē eiꝰ po-
                    <lb/>
                  no aliquas ꝓpoſitiones.
                    <note position="right" xlink:href="note-0265-05a" xlink:label="note-0265-05" xml:id="N2B5FF" xml:space="preserve">1. propõ.</note>
                  </s>
                  <s xml:id="N2B362" xml:space="preserve">¶ Prima ꝓpõ. </s>
                  <s xml:id="N2B365" xml:space="preserve">Qualitas
                    <lb/>
                  vnifor. diffor. non bene ſic diffinit̄̄. </s>
                  <s xml:id="N2B36A" xml:space="preserve">Qualitas vni-
                    <lb/>
                  for. diffor. eſt qualitas difformis cuiꝰ om̄s partes
                    <lb/>
                  immediate ſcḋm extenſionē ſunt īmediate ſecundū
                    <lb/>
                  intēſionē: vt declaratū eſt in .2. argumēto. </s>
                  <s xml:id="N2B373" xml:space="preserve">Ptꝫ hec
                    <lb/>
                  ꝓpoſitio ex eodē .2. argumēto añ oppoſitū.
                    <note position="right" xlink:href="note-0265-06a" xlink:label="note-0265-06" xml:id="N2B605" xml:space="preserve">2. propõ.</note>
                  </s>
                  <s xml:id="N2B37D" xml:space="preserve">¶ Secū­
                    <lb/>
                  da ꝓpõ. </s>
                  <s xml:id="N2B382" xml:space="preserve">Qualitas vnifor. diffor. non bene diffinit̄̄
                    <lb/>
                  ſic. </s>
                  <s xml:id="N2B387" xml:space="preserve">Qualitas vnifo. diffor. ē illa que ſic ſe habet 
                    <lb/>
                  cuiuſlibet partis eius gradus medius .i. qui eſt ī me­
                    <lb/>
                  dio tanto exceditur a ſummo quanto excedit infini­
                    <lb/>
                  um.
                    <note position="right" xlink:href="note-0265-07a" xlink:label="note-0265-07" xml:id="N2B60B" xml:space="preserve">ↄ̨tra cal.</note>
                  </s>
                  <s xml:id="N2B395" xml:space="preserve">Et hoc eſt cõtra calcula in c. de inductiõe gradꝰ
                    <lb/>
                  ſummi. </s>
                  <s xml:id="N2B39A" xml:space="preserve">pꝫ hoc ꝓpõ ex deductiõe prime replice di-
                    <lb/>
                  cti .2 argu. ante oppoſitum.
                    <note position="right" xlink:href="note-0265-08a" xlink:label="note-0265-08" xml:id="N2B611" xml:space="preserve">3. propõ.</note>
                  </s>
                  <s xml:id="N2B3A4" xml:space="preserve">¶ Tertia ꝓpõ. </s>
                  <s xml:id="N2B3A7" xml:space="preserve">Quali-
                    <lb/>
                  tas vnifor. diffor. nõ bene diffinitur ſic. </s>
                  <s xml:id="N2B3AC" xml:space="preserve">Qualitas
                    <lb/>
                  vnifor. diffor eſt illa que ſic ſe habet  cuiuſlꝫ part-
                    <lb/>
                  tis eius gradus medius .i. qui eſt in medio ſecundū
                    <lb/>
                  magnitudinem tanto exceditur a ſūmo quantum etc.
                    <lb/>
                  </s>
                  <s xml:id="N2B3B6" xml:space="preserve"/>
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