Alvarus, Thomas, Liber de triplici motu, 1509

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                    <pb chead="De motu rarefactionis  condenſationis." file="0189" n="189"/>
                  a proportione dupla: quod patet quia proportio
                    <lb/>
                  dupla et tripla non ſe habent in proportione ra-
                    <lb/>
                  tionali / vt patet intuenti tractatum proportionum
                    <lb/>
                    <note position="left" xlink:href="note-0189-01a" xlink:label="note-0189-01" xml:id="N228D2" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N227A0" xml:space="preserve">¶ Et exinde deducitur  ſi quãtitatis alicuius cor-
                    <lb/>
                  poris ad ſuam materiam fuerit proportio tripla et
                    <lb/>
                  alterius corporis fuerit proportio dupla: rarita-
                    <lb/>
                  tes illorum corporum ſunt incõmenſurabiles
                    <note position="left" xlink:href="note-0189-02a" xlink:label="note-0189-02" xml:id="N228D8" xml:space="preserve">4. correĺ</note>
                  </s>
                  <s xml:id="N227AE" xml:space="preserve">¶ De­
                    <lb/>
                  ducitur vlterius  ſi quantitas alicuius corporis
                    <lb/>
                  rari ſine acquiſitione materie quadrupletur: ipſuꝫ
                    <lb/>
                  corpus quatuor gradus raritatis acquiret ſupra
                    <lb/>
                  raritatem prehabitam: quoniã talis raritas ipſi
                    <lb/>
                  proportioni quadruple correſpõdet: et ſi aliud cor-
                    <lb/>
                  pus rarum acquirat proportionē triplam ſue quã­
                    <lb/>
                  titatis ſine materie augmento aut decremento: ta-
                    <lb/>
                  le corpus acquiret maiorem raritem quam vt .2. in
                    <lb/>
                  nulla tamen proportione rationali maiorem ade-
                    <lb/>
                  quate. </s>
                  <s xml:id="N227C5" xml:space="preserve">Patet hoc / quia raritas vt duo correſpon-
                    <lb/>
                  det proportioni duple: maior igitur raritas corre­
                    <lb/>
                  ſpondet triple: cum ipſa ſit maior et cū ipſa in nul-
                    <lb/>
                  la proportione rationali ſit maior: ſequens eſt in
                    <lb/>
                  nulla proportione rationali ſibi maiorem rarita-
                    <lb/>
                  tem correſpondere quã duple. </s>
                  <s xml:id="N227D2" xml:space="preserve">Caute igitur reſpon­
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                  dendum eſt cum queritur quante raritatis eſt cor-
                    <lb/>
                  pus in quo quãtitatis ad materiam eſt proportio
                    <lb/>
                  tripla. </s>
                  <s xml:id="N227DB" xml:space="preserve">Non em̄ ſignanda eſt talis raritas per ali-
                    <lb/>
                  queꝫ numerū. </s>
                  <s xml:id="N227E0" xml:space="preserve">Quēadmodum ſi queratur quãta eſt
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                  velocitas correſpondens proportioni duple. </s>
                  <s xml:id="N227E5" xml:space="preserve">et di-
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                  catur exempli gratia  eſt vt .2. et deinde queratur
                    <lb/>
                  quantã eſt velocitas correſpondens proportioni
                    <lb/>
                  triple: nullo modo ſignanda eſt per aliquem nume­
                    <lb/>
                  rum: cum em̄ inter quoſcū numeros ſit proportio
                    <lb/>
                  rationalis / vt conſtat: et proportio velocitatum ſe-
                    <lb/>
                  quatur proportionem proportionū: naſceretur in
                    <lb/>
                  de proportionem triplam duple proportioni fore
                    <lb/>
                  cõmenſurabilem proportione ratiõali: quo nichil
                    <lb/>
                  in hac ſcientia falſiꝰ. </s>
                  <s xml:id="N227FA" xml:space="preserve">Et ſi queras an ſecundū hanc
                    <lb/>
                  opinionē raritas vel denſitas diſtinguatur ab ip-
                    <lb/>
                  ſa materia. </s>
                  <s xml:id="N22801" xml:space="preserve">¶ Reſpondeo  non. </s>
                  <s xml:id="N22804" xml:space="preserve">Nã quando dici­
                    <lb/>
                  mus iſtud corpus eſt rarum vt .2. adequate: volumꝰ
                    <lb/>
                  dicere /  ibi eſt proportio dupla quãtitatis ad ma­
                    <lb/>
                  teriam: eſto  proportioni duple correſpondeant
                    <lb/>
                  duo gradus raritatis: et ſic in aliis proportionibꝰ
                    <lb/>
                  exēplificandū eſt. </s>
                  <s xml:id="N22811" xml:space="preserve">ſēper tamen cauēdo proporti-
                    <lb/>
                  oni irrationali ad duplam aſſignes raritatē aliq̊
                    <lb/>
                  numero ſignatam: </s>
                  <s xml:id="N22818" xml:space="preserve">¶ Aduertendū eſt tertio /  ſcḋm
                    <lb/>
                  hanc opinionem ad diiuidicandū raritatē alicuius
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                  corporis ſiue vniformis ſiue difformis: aſpicienda
                    <lb/>
                  eſt totalis eius quantitas, et totalis eius materia.
                    <lb/>
                  </s>
                  <s xml:id="N22822" xml:space="preserve">Et deinde inſpiciēda eſt ꝓportio totius quãtitatis
                    <lb/>
                  ad totã eius materiã: et ſecundã illam metiri opor-
                    <lb/>
                  tet raritatem talis corporis: vt ſi ſit vnū bipedale
                    <lb/>
                  cuius vna medietas ſit rara vt .2. et alia vt .4. ad vi­
                    <lb/>
                  dendum quanta eſt totius bipedalis raritas: capi­
                    <lb/>
                  enda eſt tota materia illius bipedalis que vt ↄ̨ſtat
                    <lb/>
                  ex predictis eſt vt .3. et deinde capienda eſt tota quã-
                    <lb/>
                  titas, que eſt vt .8. cum bipedale contineat .4. q̈rtas
                    <lb/>
                  pedalis: et aſſerendū eſt talem raritatem eſſe tantã
                    <lb/>
                  quãta ꝓportioni .8. ad .3. que eſt dupla ſuperbipar-
                    <lb/>
                  tiens tertias correſpondet. </s>
                  <s xml:id="N22839" xml:space="preserve">Et ſic īuenietur totam
                    <lb/>
                  raritatem illius corporis non eſſe vt .3. ſed minorē:
                    <lb/>
                  vt patet ex deductione tertii argumenti huiꝰ dubii.
                    <lb/>
                    <note position="left" xlink:href="note-0189-03a" xlink:label="note-0189-03" xml:id="N228DE" xml:space="preserve">.1. correĺ.</note>
                  </s>
                  <s xml:id="N22847" xml:space="preserve">¶ Ex quo ſequitur ſecundū / hanc opinionē rarita-
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                  tem difformiter difformē cuius vtra medietas eſt
                    <lb/>
                  vniformis vel vniformiter difformis nõ correſpon­
                    <lb/>
                  dere ſuo gradui medio vt argumentū tertiū p̄alle-
                    <lb/>
                  gatū bene oſtendit.
                    <note position="left" xlink:href="note-0189-04a" xlink:label="note-0189-04" xml:id="N228E4" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N22857" xml:space="preserve">¶ Ex quo ſequitur vlteriꝰ /  ra-
                    <lb/>
                  ritas difformis nõ eſt iudicanda penes reductioneꝫ
                    <lb/>
                  ad vniformitatē ſui: ſed penes reductionē ad vnifor­
                    <lb/>
                  mitatē ſue materie: vt ſi vna medietas cuiuſdã bi-
                    <cb chead="De motu rarefactionis  condenſationis."/>
                  pedalis habeat vnū gradū materie et alia habeat
                    <lb/>
                  duos capienda eſt vna medietas vniꝰ gradus illo-
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                  rum duoꝝ et addenda eſt alteri medietati ipſiꝰ bi-
                    <lb/>
                  pedalis et illud manebit vniformiter rarum et eque
                    <lb/>
                  rarū ſicut antea: (volo em̄ /  nulla fiat deperditio
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                  aut acquiſitio quãtitatis aut materie). </s>
                  <s xml:id="N2286D" xml:space="preserve">Et eodē mö
                    <lb/>
                  debet fieri ſi prima pars ꝓportionalis, et ſecunda
                    <lb/>
                  haberet in quadruplo minꝰ quã prima, et tertia in
                    <lb/>
                  quadruplo minꝰ quã ſcḋa, et ſic cõſequenter: tūc re-
                    <lb/>
                  ducenda eſt materia ad vniformitatē et videndū eſt
                    <lb/>
                  quãta eſt tota materia et tota quãtitas: et penes ꝓ-
                    <lb/>
                  portionē totiꝰ quãtitatis ad totã materiã diiudica­
                    <lb/>
                  bitur raritas. </s>
                  <s xml:id="N2287E" xml:space="preserve">Eſt iſto etiã modo metienda eſt denſi­
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                  tas corporis denſi penes videlicet ꝓportionē to-
                    <lb/>
                  tius materie ad totã quãtitatē: et nõ penes denomi­
                    <lb/>
                  nationē quēadmodū fit in qualitatibꝰ difformibꝰ
                    <lb/>
                  </s>
                  <s xml:id="N22888" xml:space="preserve">Quod diligenter aīaduerte ſi hanc opinionē de-
                    <lb/>
                  fenſare affectas.
                    <note position="right" xlink:href="note-0189-05a" xlink:label="note-0189-05" xml:id="N228EA" xml:space="preserve">Queſtio</note>
                  </s>
                  <s xml:id="N22892" xml:space="preserve">¶ Sed nõ abs requireres quomõ
                    <lb/>
                  iudicanda eſt et mēſuranda materia corporis rari
                    <lb/>
                  aut denſi in quo eſt infinita difformitas ita  diui­
                    <lb/>
                  ſo tali corpore ꝓportione dupla nulla pars ꝓpor-
                    <lb/>
                  tionalis ſecundū talē diuiſionē ſit ita rara aut den­
                    <lb/>
                  ſa ſicut alia vt tangitur in quarto argumēto huiꝰ
                    <lb/>
                  queſtionis.
                    <note position="right" xlink:href="note-0189-06a" xlink:label="note-0189-06" xml:id="N228F0" xml:space="preserve"> Solutio
                      <lb/>
                    q̄ſtionis.</note>
                  </s>
                  <s xml:id="N228A6" xml:space="preserve">¶ Reſpõdeo breuiter /  aliquando ma­
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                  teria talis corporis ſe habet continuo in certa
                    <lb/>
                  propoſitione: ita  materie prime ad materiã ſcḋe
                    <lb/>
                  partis ſit aliqua ꝓportio: et materie ſecūde ad ma­
                    <lb/>
                  teriam tertie ſit eadē ꝓportio: et ſic cõſeqnēter: ali-
                    <lb/>
                  quando vero nõ eadē cõtinuo ꝓportio obſeruatur
                    <lb/>
                  ſed in infinitum variatur puta ſi materie prime ad
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                  materiã ſecūde ſit ꝓportio dupla: et materie partꝪ
                    <lb/>
                  ſecūde ad materiã tertie ſit ꝓportio tripla: et ma-
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                  terie tertie ad materiã quarte ſit quadrupla: et ſic
                    <lb/>
                  cõſequēter aſcendendo per ſpecies ꝓportiõis mul-
                    <lb/>
                  tiplicis: et tūc nõ eſt poſſibile capacitati intellectus
                    <lb/>
                  finite adequate illã materiam menſurare vt iam in
                    <lb/>
                  ſimili dictū eſt circa materiã de motu locali penes
                    <lb/>
                  effectū. </s>
                  <s xml:id="N228C5" xml:space="preserve">Sed ſi materie illarū partiū ꝓportionaliū
                    <lb/>
                  cõtinuo ſe habeant in eadē proportione: facile erit
                    <lb/>
                  diiudicare totalem materiam ex concluſionibus et
                    <lb/>
                  correlariis quīti capitis prime partis huiꝰ operis</s>
                </p>
                <p xml:id="N228F8">
                  <s xml:id="N228F9" xml:space="preserve">Ad ratiões ante oppoſitū huiꝰ dubii.
                    <lb/>
                  </s>
                  <s xml:id="N228FD" xml:space="preserve">Ad primã reſponſū eſt ibi vſ ad replicã ad quam
                    <lb/>
                  reſpõdeo ↄ̨cedēdo ſequelã, q2 illud ↄ̨ñs manifeſte
                    <lb/>
                  ſequit̄̄ ex hac poſitiõe: et negat̄̄ falſitas ↄ̨ñtis: et ad
                    <lb/>
                  ꝓbationē: datis illis duobus corporibꝰ equalibus
                    <lb/>
                  quãtitatiue et īequalibꝰ in raritate et cū ſic argr̄ eq̄
                    <lb/>
                  ꝓportionabiliṫ ſicut iſta duo corpora acquirūt de
                    <lb/>
                  quãtitate acquirūt de raritate: negat̄̄ illud m hãc
                    <lb/>
                  opinionē: īmo dico /  oīa corpora ſiue eq̈lia quãti-
                    <lb/>
                  tatiue, ſiue īeq̈lia, ſiue eq̄ rara ſiue nõ, q̄ eque ꝓpor­
                    <lb/>
                  tionabiliṫ acquir̄t de quãtitate eq̈liṫ oīno acquir̄t
                    <lb/>
                  de raritate: qm̄ eq̈les ꝓportiones acquirūt, et ſemꝑ
                    <lb/>
                  ab equalibꝰ ꝓportionibꝰ eq̈les raritates nate ſunt
                    <lb/>
                  ꝓuenire / vt dictū eſt. </s>
                  <s xml:id="N22918" xml:space="preserve">¶ Ad ſecundã rationē reſpõſū
                    <lb/>
                  eſt ibi vſ ad replicam: ad quam reſpondeo conce­
                    <lb/>
                  dendo ſequelam: et negando falſitatem conſequen­
                    <lb/>
                  tis. </s>
                  <s xml:id="N22921" xml:space="preserve">Et ad probationem negatur hec conſequentia
                    <lb/>
                  in qua eſt vis rationis: vna medietas huius bipe-
                    <lb/>
                  dalis eſt denſa vt duo adequate, et alia rara vt duo
                    <lb/>
                  adequate: et raritas et denſitas non ſe compatiunt̄̄
                    <lb/>
                  immo ſe cohabent ſicut cecitas et viſus; / igitur illud
                    <lb/>
                  corpus nec eſt rarum non eſt denſum: et ad probationē
                    <lb/>
                  que conſiſtit in quadam ſimilitudine concedo an-
                    <lb/>
                  tecedens: et nego conſequentiam: quia non eſt oīno
                    <lb/>
                  ſimile de illis qualitatibus et de raritate et denſi-
                    <lb/>
                  tate que ſunt duo oppoſita priuatiue: nam ſi </s>
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