Alvarus, Thomas, Liber de triplici motu, 1509
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            <div xml:id="N20F21" level="3" n="3" type="other" type-free="tractatus">
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                <p xml:id="N21D56">
                  <s xml:id="N21D9A" xml:space="preserve">
                    <pb chead="Tertii tractatus" file="0183" n="183"/>
                  ſex. cū duabꝰ tertiis: ergo totū eſt rarum vt ſex cum
                    <lb/>
                  duabꝰ tertiis / quod fuit ꝓbandū. </s>
                  <s xml:id="N21DA8" xml:space="preserve">Et hoc eſt optimū
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                  argumētū cõtra iſtã opinionē quod apparētiſſime
                    <lb/>
                  impugnat eã ſiue teneatur ſecundum iſtam opnionē
                    <lb/>
                  raritatem eſſe qualitatem ſiue non: dummodo di-
                    <lb/>
                  catur raritas poſitiue.</s>
                </p>
                <p xml:id="N21DB3">
                  <s xml:id="N21DB4" xml:space="preserve">Sexto ↄ̨̨tra eandē ſcḋam opinionem
                    <lb/>
                  argr̄. </s>
                  <s xml:id="N21DB9" xml:space="preserve">Si raritas eſſet qualitas aut poſitiue dicere­
                    <lb/>
                  tur: ſeq̄retur /  difformiter difforme cuius vtra
                    <lb/>
                  medietas eſſet vniformis nõ correſpõderet ſuo gra­
                    <lb/>
                  dui medio: ſed ↄ̨ñs eſt falſum:. igr̄ / et illud ex quo ſe-
                    <lb/>
                  quit̄̄. </s>
                  <s xml:id="N21DC4" xml:space="preserve">Seq̄la ꝓbat̄̄: et pono /  ſit vnū bipedale cuiꝰ
                    <lb/>
                  vna medietas ſit rara vt octo, et alia vt q̈tuor, et ar­
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                  guit̄̄ ſic / raritas iſtiꝰ corꝑis nõ correſpõdet ſuo g̈dui
                    <lb/>
                  medio que eſt vt ſex: igr̄. </s>
                  <s xml:id="N21DCD" xml:space="preserve">Argr̄ añs: et volo /  medie­
                    <lb/>
                  tas rara vt octo deꝑdat duos g̈dus raritatis: et tm̄
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                  acq̇rat medietas minꝰ rara vniiformiter in eodem
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                  tēpore quo poſito in fine totū illud manebit vnifor­
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                  me vt ſex, et manebit rariꝰ ꝙ̄ eſt modo: g̊ raritas eiꝰ
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                  nõ correſpondet g̈dui medio q̄ eſt raritas vt ſex. </s>
                  <s xml:id="N21DDA" xml:space="preserve">Sꝫ
                    <lb/>
                  iam ꝓbo minorē vcꝫ  illud corpus in fine manebit
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                  rariꝰ ꝙ̄ ſit modo: q2 illa medietas q̄ eſt rara vt qua­
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                  tuor acq̇ret proportionē ſexq̇altera raritatis ſupra
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                  ſe, et eſt vnū pedale: igr̄ acq̇ret ſemipedale: medie-
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                  tas vero rarior deꝑdet ꝓportionē ſexq̇tertiã rari-
                    <lb/>
                  tatis et eſt pedalis: igr̄ deꝑdet vnã quartã pedalis:
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                  ergo ſequit̄̄ / ꝙ̄ maiorē quantitatē acq̇rit totū illud
                    <lb/>
                  corpꝰ ꝙ̄ deꝑdit: et ꝑ ↄ̨ñs eſt rariꝰ ꝙ̄ antea: et eſt rarū
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                  vniformiter vt ſex puta g̈du medio inter .4. et .8. igr̄
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                  antea qñ erat difforme erat minus rarū ꝙ̄ ſit gra-
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                  dus mediꝰ : et ſic ſua raritas non correſpõdebit ſuo
                    <lb/>
                  gradui medio, quod fuit probandum.</s>
                </p>
                <p xml:id="N21DF5">
                  <s xml:id="N21DF6" xml:space="preserve">Septimo. </s>
                  <s xml:id="N21DF9" xml:space="preserve">Contra tertiã opinionē ar­
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                  guitur ſic: et ſignãter contra primã ꝓpoſitionē quã
                    <lb/>
                  addit opinio vcꝫ  ex vniformi rarefactiõe ſiue ac-
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                  quiſitione raritatis per tēpus ſequit̄̄ vniformis ac­
                    <lb/>
                  quiſitio quantitatis q2 ſi ita eſt: capio vnū pedale
                    <lb/>
                  rarū vt quatuor / et volo /  acquirat vniformiter per
                    <lb/>
                  horam quatuor gradus raritatis: et argr̄ ſic / in illa
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                  hora totale illud pedale difformiter acquirit quanti­
                    <lb/>
                  tatē: et vniformiter raritatē: igr̄ illa ꝓpoſitio falſa
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                  </s>
                  <s xml:id="N21E0D" xml:space="preserve">Maior ꝓbatur vcꝫ /  difformiter acq̇rit ̄titatē q2
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                  bene ſequitur vniformiter acq̇rit raritatē: ergo vni­
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                  formiter deꝑdit denſitatē. </s>
                  <s xml:id="N21E14" xml:space="preserve">Patet ↄ̨ña / quia nichil
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                  aliud eſt vniformiter acq̇rere raritatē ꝙ̄ vniformi-
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                  ter deꝑdere denſitatē (raritas em̄ ſecundū hanc o-
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                  pinionē priuatiue dr̄) et vltra vniformiter deperdit
                    <lb/>
                  denſitatē: g̊ difformiter acq̇rit quantitatem: añs eſt
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                  verū : g̊ et ↄ̨ñs. </s>
                  <s xml:id="N21E21" xml:space="preserve">Probo tñ hanc vltimã cõſequentiam /
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                  q2 cõtinuo in equali tēpore tale corpus maiorē ꝓ-
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                  portionē denſitatis deꝑdit: igr̄ continuo in equali
                    <lb/>
                  tēpore maiorē quantitatē acq̇rit. </s>
                  <s xml:id="N21E2A" xml:space="preserve">Conſequētia ptꝫ /
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                  q2 eque ꝓportionabiliter ſicut deꝑditur denſitas
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                  maioratur quantitas: et añs ꝓbatur / q2 ↄ̨tinuo illa
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                  denſitas qñ deꝑditur eſt minor: et cõtinuo eque velo­
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                  citer deꝑditur: g̊ cõtinuo maiorē ꝓportionē deꝑdit
                    <lb/>
                  </s>
                  <s xml:id="N21E36" xml:space="preserve">pꝫ ↄ̨ña ex ſcḋa ꝑte q̈rto capite octaua ſuppoſitiõe
                    <lb/>
                    <note position="left" xlink:href="note-0183-01a" xlink:label="note-0183-01" xml:id="N21E86" xml:space="preserve">ↄ̨firma.</note>
                  </s>
                  <s xml:id="N21E40" xml:space="preserve">¶ Confirmatur / q2 ſecūda ꝓpoſitio quã addit hec ſe-
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                  tunda opinio: videlicet  ſi rarius et denſius equa­
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                  lia eque velociter rarefiant: cõtinuo denſiꝰ maioreꝫ
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                  quantitatē acquirit ꝙ̄ rarius repugnat alteri pro­
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                  poſitioni quã addit quã immediate ꝓcedens argu-
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                  mentum impugnat: igitur illa opinio non coheret
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                  ſibi ipſi: arguitur antecedens et capio duo pedalia
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                  vnū denſum vt quatuor et aliud denſum vt duo et ma­
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                  nifeſtum eſt ſecundam iſtam opinionem  denſum
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                  vt duo ē magꝪ raꝝ / volo igit̄̄ /  vtrū illoꝝ rarefiat
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                  eque velociter acquirendo infinitam raritatem in
                    <cb chead="Capitulū primū."/>
                  hora. </s>
                  <s xml:id="N21E5A" xml:space="preserve">quo poſito arguo ſic / vtrum illorum in hora
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                  acquiſiuit equalē quantitatem quia infinitam cum
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                  vtrum ſit infinite rarum in fine et vniformiter acq̇­
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                  rebat raritatem ſicut quantitatem / vt dicit prima
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                  ꝓpoſitio: et tamen vnum illorum erat denſius et ali­
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                  ud rariꝰ et eque velociter rare fiebant per illud tem­
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                  pus / ergo non ſi rariꝰ et denſius equalis quantita­
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                  tis eque velociter rarefiant denſius maiorem quan­
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                  titatem acquirit ꝙ̄ rarius q2 in caſu illo acquirit
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                  equalem. </s>
                  <s xml:id="N21E6F" xml:space="preserve">vel ſi ſic iam non vniformiter ſicut acq̇rit̄̄
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                  raritas acquiritur quantitas: et ꝑ ↄ̨ñs vna ꝑs repu­
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                  gnat alteri
                    <note position="right" xlink:href="note-0183-02a" xlink:label="note-0183-02" xml:id="N21E8C" xml:space="preserve">Dicitur</note>
                  </s>
                  <s xml:id="N21E7B" xml:space="preserve">¶ Dices forte /  hec opinio intelligit dū­
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                  modo vtrum acquirit finitam raritatem modo
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                  in propoſitio vtrum acquirit īfinitam.</s>
                </p>
                <p xml:id="N21E92">
                  <s xml:id="N21E93" xml:space="preserve">Sed contra. </s>
                  <s xml:id="N21E96" xml:space="preserve">Quia eſto  vtrū ac-
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                  quirit finitam raritatem rarius videlicet et denſiꝰ
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                  adhuc tamen rarius maiorem quantitatem acqui­
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                  rit / igitur ſolutio nulla. </s>
                  <s xml:id="N21E9F" xml:space="preserve">Arguitur antecedēs et volo /
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                   ſint duo pedalia a. et b.a. denſum vt quattuor
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                  b. denſum vt octo et tam a. ꝙ̄ b. acquirat duos gra­
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                  dus raritatꝪ / quo poſito arguitur ſic / a. maiorē quã­
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                  titatem acquirit quã b. et eſt rarius b. et eque velo-
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                  citer rarefit cum b. / igitur quãdo rarius et denſius
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                  eque velociter rare fiunt rarius maiorem quantita­
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                  tem acquirit ꝙ̄ denſius. </s>
                  <s xml:id="N21EB0" xml:space="preserve">Probat̄̄ maiori / q2 ſi a. ac-
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                  quirit duos g̈dus raritatis: et b. ſimiliter: ſequit̄̄ / 
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                  vtrū illoꝝ deꝑdit duos g̈dus denſitatis: et ſic a.
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                  efficitur in duplo minꝰ dēſum, et per ↄ̨ñs efficitur in
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                  duplo maiꝰ, et acq̇rit vnū pedale, b. vero cū deꝑdat
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                  duos g̈dus denſitatis et ſit vt octo, deꝑdit ꝓporti-
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                  onē ſexq̇tertia denſitatis, et ſic efficit̄̄ in ſexq̇tertio
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                  maiꝰ, et per ↄ̨ñs acq̇rit vnã tertiã pedalis: et aliud
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                  rariꝰ acq̇rit vnū pedale / vt dictū eſt: igr̄ maiorē quã­
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                  titatē acq̇rit rarius ꝙ̄ denſius eq̈le qñ et eque velo-
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                  citer rarefiūt: quod fuit ꝓbandū. </s>
                  <s xml:id="N21EC7" xml:space="preserve">Et hec ferme ſunt
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                  ex ſubtili minerua
                    <note position="right" xlink:href="note-0183-03a" xlink:label="note-0183-03" xml:id="N21EDC" xml:space="preserve">calcula.</note>
                  </s>
                  <s xml:id="N21ED1" xml:space="preserve">Calculatoris excerpta qui mul-
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                  ta alia in has tres opiniones argumenta coniecit
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                  que apud eum poteris conſpicere.</s>
                </p>
                <note position="right" xml:id="N21EE2" xml:space="preserve">cõmē. 7.
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                phi. c. 15.</note>
                <p xml:id="N21EE8">
                  <s xml:id="N21EE9" xml:space="preserve">In oppoſitum arguit̄̄ / pro prima opi-
                    <lb/>
                  nione auctorttate cõmentatoris ſeptimo phiſicorū
                    <lb/>
                  cõmenento quindecimo vt ſuperius allegatum ē. </s>
                  <s xml:id="N21EF0" xml:space="preserve">Itē
                    <lb/>
                  raritas et denſitas videntur effectus qualitatū pri­
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                  marum: igitur ſunt qualitates ſecunde.</s>
                </p>
                <p xml:id="N21EF7">
                  <s xml:id="N21EF8" xml:space="preserve">Pro ſecunda opinione arguit̄̄ ſic / ſem­
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                  per ad inductionē raritatis ſequitur acquiſitio ali­
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                  cuius poſitiui puta quantitatis: igitur raritas eſt
                    <lb/>
                  quoddã poſitiuuꝫ. </s>
                  <s xml:id="N21F01" xml:space="preserve">Colorat̄̄ ↄ̨ña / q2 nullū priuatiuū
                    <lb/>
                  neceſſario eſt cauſa alicuiꝰ poſitiui: hoc eſt nõ eſt ne­
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                  ceſſe  ad priuationē alicuiꝰ poſitiui ſequat̄̄ neceſ-
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                  ſario neceſſitate ſimpliciter acq̇ſitio alteriꝰ poſitiui /
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                  g̊ ſi raritas eſſet ſiue diceret̄̄ priuatiue: nun̄ ad ac­
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                  q̇ſitionē eiꝰ neceſſario ſimpliciter ſeq̄retur acq̇ſitio
                    <lb/>
                  quãtitatis aut alicuiꝰ alteriꝰ poſitiui.
                    <note position="right" xlink:href="note-0183-04a" xlink:label="note-0183-04" xml:id="N21F34" xml:space="preserve">cõfirma.</note>
                  </s>
                  <s xml:id="N21F15" xml:space="preserve">¶ Et ↄ̨firmat̄̄
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                  hoc inductiue nun̄ enim ad acquiſitionem ſilentii /
                    <lb/>
                  ſequitur neceſſario acquiſitio alicuius poſitiui: nec
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                  ad acquiſitionem tenebrarum, nec ad acquiſitionē
                    <lb/>
                  paruitatis: et ſimiliter remiſſionis: et ſic de ſingu-
                    <lb/>
                  lis priuatiuis: igitur ſi raritas eſſꝫ priuatiuū nõ ne­
                    <lb/>
                  ceſſario ad acquiſitionem raritatis ſequeretur ac-
                    <lb/>
                  quiſitio alicuiꝰ poſitiui </s>
                  <s xml:id="N21F26" xml:space="preserve">Patet hec cõſequentia a ſi­
                    <lb/>
                  mili. </s>
                  <s xml:id="N21F2B" xml:space="preserve">¶ Pro tertia opinione non arguo / quia nõ in-
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                  tendo ea deffenſare quamuis forte ſit deffēſabilis.</s>
                </p>
                <p xml:id="N21F3A">
                  <s xml:id="N21F3B" xml:space="preserve">Pro ſolutione huius dubitationis ad­
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                  uertendum eſt  cum occurrit contrapugnantia et
                    <lb/>
                  opinionum diuerſitas de entitate alicuius rei tunc
                    <lb/>
                  diuerſimode opinantes diuerſas talis rei couſtitu­
                    <lb/>
                  unt diffinitiões. </s>
                  <s xml:id="N21F46" xml:space="preserve">et proprietates vt cū occurrit diffi- </s>
                </p>
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