Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N20F21" level="3" n="3" type="other" type-free="tractatus">
              <div xml:id="N20F2E" level="4" n="1" type="chapter" type-free="capitulum">
                <p xml:id="N22145">
                  <s xml:id="N2217F" xml:space="preserve">
                    <pb chead="Tertii tractatus" file="0185" n="185"/>
                  reſondeo negando ſequelã, et ad ꝓbationē ↄ̨cedo
                    <lb/>
                  añs: et nego conſequentiã: non em̄ maioris coloris
                    <lb/>
                  aut apparentie eſt illa ↄ̨ña  iſta in quolibet ma-
                    <lb/>
                  gno eſt īfinita paruitas / g̊ quodlibet magnū eſt īfi-
                    <lb/>
                  nite paruū, vel ꝙ̄ iſta in quolibet intenſo eſt īfini-
                    <lb/>
                  ta remiſſio capiendo ly īfinitū ſyncathegoreuma-
                    <lb/>
                  tice: g̊ quodlibet īfinitū eſt īfinite remiſſum: ſed ille
                    <lb/>
                  cõſequētie nichil valent / vt ſatis cõſtat: g̊ nec alte-
                    <lb/>
                  ra. </s>
                  <s xml:id="N22197" xml:space="preserve">Ad quintū / quod eſt cõtra ſecundã opinionē re-
                    <lb/>
                  ſpõdeo cõcedendo ſequelã vt bene ꝓbat argumen-
                    <lb/>
                  tum, et negando falſitatē conſequentis. </s>
                  <s xml:id="N2219E" xml:space="preserve">Cēſere em̄
                    <lb/>
                  aut iudicare aliquid eſſe minus aut magis rarum
                    <lb/>
                  ſecundū hanc opinionē ex maioritate aut minorita­
                    <lb/>
                  te quantitatis ſtante eadē materia: eſt a principio
                    <lb/>
                  huiꝰ opinionis plurimū deuiare. </s>
                  <s xml:id="N221A9" xml:space="preserve">Si tñ tu velis in-
                    <lb/>
                  telligere per rarefactionē, rarefactionē totius ſiue
                    <lb/>
                  īductionē raritatis qua totū rarefit, et ſic eo modo
                    <lb/>
                  nego iſtã ſequelã: qm̄ in caſu argumenti totū iſtud
                    <lb/>
                  corpus nõ rarefit: ſed efficitur minꝰ rarū vt bene ꝓ­
                    <lb/>
                  bat argumentū. </s>
                  <s xml:id="N221B6" xml:space="preserve">Si vero ꝑ rarefactionē intelligas
                    <lb/>
                  rarefactionē partialē qua aliqua pars illiꝰ corpo­
                    <lb/>
                  ris acq̇rit aliquos gradus illius qualitatis que eſt
                    <lb/>
                  raritas, et ſic eo modo concedo tibi ſequelã vt con-
                    <lb/>
                  ceſſi: nec iſtud cõſequens videtur afferre maiꝰ incon­
                    <lb/>
                  ueniens ꝙ̄ iſtud (ſuppoſito  caliditas vt in pluri-
                    <lb/>
                  bus augmentat ſiue maior at quantitatē) aliquod
                    <lb/>
                  calidū ꝑ ſolã calefactionē ſiue inductionē calidita-
                    <lb/>
                  tis et motū cõſequētem vt in pluribꝰ inductionē ca-
                    <lb/>
                  liditatis qui motus eſt augmentio efficitur minus
                    <lb/>
                  calidū: ſed iſtud cõſequēs nõ eſt incõueniens / vt pro­
                    <lb/>
                  babitur: igr̄ nec aliud ꝓbatur mīor: et poſito  vna
                    <lb/>
                  medietas corporis bipedalis ſit calida vt .12. et alia
                    <lb/>
                  vt duo, et acq̇rat medietas calida vt duo duos gra­
                    <lb/>
                  dus caliditatis: ita vt efficiatur calida vt quatuor
                    <lb/>
                  alia medietate quieſcente: et efficiat̄̄ alia medietas
                    <lb/>
                  minꝰ calida qñ acq̇rit illos duos gradus in duplo
                    <lb/>
                  maior. </s>
                  <s xml:id="N221DB" xml:space="preserve">quo poſito iſtud corpꝰ efficitur minꝰ calidū
                    <lb/>
                  ̄ antea, et hoc ſolū ꝑ īductionē caliditatis et motū
                    <lb/>
                  vt in pluribꝰ cõſequentē inductionē caliditatis: igr̄
                    <lb/>
                  ꝓpoſitū. </s>
                  <s xml:id="N221E4" xml:space="preserve">Cõſequētia ptꝫ cū minore, et argr̄ maior:
                    <lb/>
                  q2 iſtud corpus in principio inductionis illiꝰ calidi­
                    <lb/>
                  tatis eſt calidū vt ſeptē, et in fine eſt calidū vt ſex cū
                    <lb/>
                  duabꝰ tertiis: vt ptꝫ ex mõ ꝓbãdi quarti argumēti
                    <lb/>
                  quod modo ſoliumꝰ: igr̄. </s>
                  <s xml:id="N221EF" xml:space="preserve">Alio modo etiã põt nega­
                    <lb/>
                  ri ſequela ſimpliciter, et hoc ſi teneamꝰ intenſionē
                    <lb/>
                  qualitatis correſpondere ſuo gradui ſummo: qm̄
                    <lb/>
                  id oportebit dicere ſecundū hanc opinionē de rari­
                    <lb/>
                  tate difformi: qm̄ ſecundū eã raritas qualitas eſt.
                    <lb/>
                  </s>
                  <s xml:id="N221FB" xml:space="preserve">¶ Ad ſextū / quod eſt etiã cõtra ſcḋam opinionē re-
                    <lb/>
                  ſpondeo negando ſequelã, et ad ꝓbationē admiſſo
                    <lb/>
                  caſu, concedo  in fine illud corpus manebit rarū
                    <lb/>
                  vt ſex: et nego  manebit rariꝰ ꝙ̄ ſit modo, et ad ꝓ-
                    <lb/>
                  bationē nego hanc cõſequentiã: maiorē quantita-
                    <lb/>
                  tem acq̇rit ꝙ̄ deꝑdit manente eadem materia: g̊ eſt
                    <lb/>
                  rariꝰ. </s>
                  <s xml:id="N2220A" xml:space="preserve">Et ratio eſt: q2 intenſio raritatis nõ ſequitur
                    <lb/>
                  maiorationē ꝓportionis quantitatis ad materiã:
                    <lb/>
                  ſed ſequitur additionē gradus raritatis ſequētis
                    <lb/>
                  gradibꝰ p̄cedentibꝰ: ſicut fit de albedine et nigredīe
                    <lb/>
                  </s>
                  <s xml:id="N22214" xml:space="preserve">Rariꝰ autē m modū huiꝰ opinionis eſt illud  hꝫ
                    <lb/>
                  raritatē magis denominantē ipſum: ſiue habeat
                    <lb/>
                  plus de quantitate ſiue minꝰ nõ eſt cura. </s>
                  <s xml:id="N2221B" xml:space="preserve">¶ Ad ſepti­
                    <lb/>
                  mū argumentū quod eſt cõtra tertiã opinionē cuiꝰ
                    <lb/>
                  fundamēta et prīcipia nõ exacte capio nõ reſpõdeo
                    <lb/>
                  nec decreui ad argumeuta eã expugnantia reſpon­
                    <lb/>
                  dere: nec illi opinioni ſuppetias dare.</s>
                </p>
                <p xml:id="N22226">
                  <s xml:id="N22227" xml:space="preserve">Notandū eſt ſcḋo circa materiã ſecñ-
                    <lb/>
                  di argumenti principalis ante oppoſitū:  vt ex-
                    <lb/>
                  ſcrinio calculatorio in capite de raritate et denſita­
                    <cb chead="Capitulū primū."/>
                  te colligi põt (et quidē aperte) duplex eſt opinio ra-
                    <lb/>
                  tione fulcita: penes quid habeat attendi: et cõmen­
                    <lb/>
                  ſurari raritatis aut denſitatis maioritas. </s>
                  <s xml:id="N22235" xml:space="preserve">quaruꝫ
                    <lb/>
                  prior eſt /  ipſa raritas attenditur penes ꝓporti-
                    <lb/>
                  onē quantitatis ſubiecti ad eiꝰ materiã et maiori-
                    <lb/>
                  tas raritatis penes maiorē ꝓportionē quantitatꝪ
                    <lb/>
                  ad materiã. </s>
                  <s xml:id="N22240" xml:space="preserve">Denſitas autē penes ꝓportionē mate-
                    <lb/>
                  rie ad quantitatē, et eiuſdē raritas penes maiorem
                    <lb/>
                  ꝓportionē materie ad quantitatē (et loquor de pro­
                    <lb/>
                  portione maioris inequalitatis) </s>
                  <s xml:id="N22249" xml:space="preserve">Exemplū vt ſi īter
                    <lb/>
                  quantitatē vniꝰ pedalis et ſuã materiã ſit ꝓportio
                    <lb/>
                  dupla illud eſt rarū: et ſi alteriꝰ pedalis quãtitatis
                    <lb/>
                  ad materiã eſſet ꝓportio maior dupla illud eſt ma­
                    <lb/>
                  gis rarū: q2 ꝓportio eſt maior: et ſi vniꝰ alteriꝰ pe-
                    <lb/>
                  dalis materie ad quantitatē eſt ꝓpoportio dupla
                    <lb/>
                  illud eſt denſum: et ſi ꝓportio materie ad quantita­
                    <lb/>
                  tem maioretur illud efficeretur denſius. </s>
                  <s xml:id="N2225A" xml:space="preserve">Poſterior
                    <lb/>
                  autē opinio diiudicat raritatē penes quantitatem
                    <lb/>
                  in cõparationē ad materiã vel (vt verbis calculato­
                    <lb/>
                  riis loquar) in materia ꝓportionata. </s>
                  <s xml:id="N22263" xml:space="preserve">differentiam
                    <lb/>
                  autē inter has duas opinationes talis ferme a cal­
                    <lb/>
                  culatore ſignatur loco preallegato: nã prima opi-
                    <lb/>
                  natio aſſeuerat ad duplationē raritatis non ſequi
                    <lb/>
                  duplationē quantitatis: nec ad ſexq̇alterationem
                    <lb/>
                  raritatis etiã ſequi quantitatē effici in ſexquialte­
                    <lb/>
                  ro maiorē: ſed dicit ad duplationem raritatis ſiue
                    <lb/>
                  ſexquialterioneꝫ ſequi duplationem proportio­
                    <lb/>
                  nis quãtitatis ad materiam ſiue ſexquialteratio-
                    <lb/>
                  nem et ſic de aliis proportionibus. </s>
                  <s xml:id="N22278" xml:space="preserve">¶ Secunda vc-
                    <lb/>
                  ro aſſerit ſemper ad duplationem ſequi duplatio-
                    <lb/>
                  nem quantitatis: et ad triplationem raritatis ſe-
                    <lb/>
                  qui idemtidam triplationem quantitatis. </s>
                  <s xml:id="N22281" xml:space="preserve">Exem-
                    <lb/>
                  plum vt eſto  vniꝰ pedalis ꝓportio quãtitatis ad
                    <lb/>
                  materiam ſit ſexq̇altera et dupletur eius raritas:
                    <lb/>
                  tunc ſecundū hanc opinionem eius quantitas non
                    <lb/>
                  efficitur in duplo maior (et ſi raritas ad duplum
                    <lb/>
                  maioretur) ſed duplatur ꝓportio quantitatis ad
                    <lb/>
                  materiã: ita  efficitur ꝓportio quantitatis ad ma­
                    <lb/>
                  teriam dupla ad ſexquialterã cuiuſmodi eſt ꝓpor-
                    <lb/>
                  tio dupla ſexq̇quarta qualis eſt nomē ad quatuor
                    <lb/>
                  et ſic illa quantitas effecta eſt in ſexquialtero ma-
                    <lb/>
                  ior vt pote pedalis cū dimidia. </s>
                  <s xml:id="N22298" xml:space="preserve">Sed ſi tale pedale
                    <lb/>
                  ſecundū alteram opinionē efficitur in duplo rariꝰ
                    <lb/>
                  eius quantitas duplabitur et efficietur bipedalis:
                    <lb/>
                  et ſic ptꝫ /  ſecundã priorem opinionem  ad dupla­
                    <lb/>
                  tionē raritatis nõ ſequitur duplatio quantitatis.
                    <lb/>
                  </s>
                  <s xml:id="N222A4" xml:space="preserve">Secundū alterã vero ſemꝑ ſequitur duplatio quã­
                    <lb/>
                  titatis raritatis duplicationem. </s>
                  <s xml:id="N222A9" xml:space="preserve">Et vt hec opinio
                    <lb/>
                  clarius intelligatur et eius fundamenta et baſes co­
                    <lb/>
                  gnoſcant̄̄. </s>
                  <s xml:id="N222B0" xml:space="preserve">¶ Quero vtrū ipſa poſſit vera ſuſtētari.</s>
                </p>
                <p xml:id="N222B3">
                  <s xml:id="N222B4" xml:space="preserve">Et argr̄ primo  nõ. </s>
                  <s xml:id="N222B7" xml:space="preserve">Qm̄ ſi ipſa eſſet
                    <lb/>
                  a ſequeretur /  quelibet ꝓportio quantitatis ad
                    <lb/>
                  materiam certos gradus raritatis ꝓduceret ita 
                    <lb/>
                  vbicun eſſet proportio dupla quantitatis ad ma­
                    <lb/>
                  teriam: ibi eſſent certi gradus raritatis q̇ ſint duo
                    <lb/>
                  gratia exēpli et vbi eſſet ꝓportio quadrupla quã-
                    <lb/>
                  titatis ad materiã ibi eſſent in duplo plures gra-
                    <lb/>
                  dus raritatis. </s>
                  <s xml:id="N222C8" xml:space="preserve">Et vbi eſſet ſexq̇altera ꝓportio quã-
                    <lb/>
                  titatis ad materiã: ibi eſſet raritas nata ꝓuenite a
                    <lb/>
                  ꝓportiõe ſexq̇altera que ſe habet ad raritatē natã
                    <lb/>
                  ꝓuenire a ꝓportione dupla ſicut ſe hꝫ ſexquialtera
                    <lb/>
                  ꝓportio ad ꝓportionē duplã: ſed hoc couſequens
                    <lb/>
                  eſt falſum: igr̄ et illud ex quo ſequitur. </s>
                  <s xml:id="N222D5" xml:space="preserve">Sequela pro­
                    <lb/>
                  batur / qm̄ m hanc opinionē certa ꝓportio quãti-
                    <lb/>
                  tatis ad materiã certã raritatē ꝓducit: et in duplo
                    <lb/>
                  maior ꝓportio in duplo maiorē raritatē, et in ſexq̇­
                    <lb/>
                  altero maior ꝓportio ī ſexq̇altero maiorē rarita-
                    <lb/>
                  tem: igr̄ in quacū ꝓportione ſe hñt ꝓportiones </s>
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