Alvarus, Thomas, Liber de triplici motu, 1509
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                    <pb chead="Tertii tractatus" file="0199" n="199"/>
                  in fine eſt tripla. </s>
                  <s xml:id="N238A3" xml:space="preserve">Si vero duo pedalia acquirant
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                  duos gradus denſitatis eque velociter: tūc minus
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                  denſum maiorem quantitatem deperdit in pro-
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                  portione ſuperbipartiente tertias: quia denſita-
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                  tes illorum ſe habebunt in fine in proportione ſu-
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                  perbipartiente tertias qualis eſt decem ad ſex.</s>
                </p>
                <note position="left" xml:id="N238BA" xml:space="preserve">2. nöbile</note>
                <p xml:id="N238BE">
                  <s xml:id="N238BF" xml:space="preserve">¶ Secundū notabile: ſi ſint duo inequalia in quã-
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                  titate et in denſitate, et ſicut eſt vnuꝫ alio maius ita
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                  ſit eodem denſius que eque velociter acquirant de
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                  denſitate: tunc denſius deperdit maiorem quanti-
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                  tatem in ea proportione per quam proportio den-
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                  ſitatum in principio excedit proportionem denſi-
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                  tatum in fine. </s>
                  <s xml:id="N238CE" xml:space="preserve">Si vero eque velociter deperdant de
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                  denſitate: tunc denſius minorem quantitatem ac-
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                  quirit in proportione per quam proportio denſi-
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                  tatum in fine excedit proportionem denſitatum in
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                  principio deperditionis denſitatum. </s>
                  <s xml:id="N238D9" xml:space="preserve">Exemplum /
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                  vt ſi ſit bipedale denſum vt .8. et pedale denſum vt
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                  quatuor: et acquirat vtrum illoruꝫ duos gradus
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                  dēſitatis eque velociter: tūc dico /  quantitas quã
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                  deperdit denſius excedit quantitatem quã deper-
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                  dit minus denſum in proportione ſexquiquinta.
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                  </s>
                  <s xml:id="N238E7" xml:space="preserve">Illa em̄ eſt proportio per quã dupla excedit pro-
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                  portionem ſuperbipartientem tertias que eſt pro-
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                  portio denſitatum in fine. </s>
                  <s xml:id="N238EE" xml:space="preserve">Exemplum ſecundi: vt ſi
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                  illa duo corpora puta bipedale et pedale deperdãt
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                  duos gradus denſitatis eque velociter: tunc denſiꝰ
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                  minorem quantitatem acquirit ꝙ̄ minus denſum
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                  in proportione ſexquialtera per quam tripla pro-
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                  portio denſitatum in fine excedit duplam propor­
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                  tionem denſitatum in principio.
                    <note position="left" xlink:href="note-0199-01a" xlink:label="note-0199-01" xml:id="N23AC2" xml:space="preserve">3. nöbile</note>
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                  <s xml:id="N23902" xml:space="preserve">¶ Tercium nota-
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                  bile. </s>
                  <s xml:id="N23907" xml:space="preserve">Si ſint duo inequalia et inequaliter denſa. </s>
                  <s xml:id="N2390A" xml:space="preserve">ita
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                  tamen  maius ſit denſius: et  proportio quanti­
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                  tatis vnius ad quantitatem alterius ſit maior
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                  proportione denſitatis vnius ad denſitatem alte-
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                  rius: que eque velociter acquirant de denſita-
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                  te: tunc denſius maiorem quautitatem deper-
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                  dit in ea proportione per quam proportio quanti­
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                  tatis in principio excedit proportionem denſita-
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                  tis in fine acquiſitionis: hoc eſt per quam propor-
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                  tio que eſt inter quantitates in principio talis ac-
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                  quiſitionis excedit proportionem que eſt inter dē-
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                  ſitates in fine. </s>
                  <s xml:id="N23923" xml:space="preserve">Si vero illa talia eque velociter de-
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                  perdant de dēſitate: et proportio denſitatū in fine
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                  ſit minor proportione quantitatum in principio:
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                  tunc denſius maiorem quantitatē acquirit in pro-
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                  portione per quam proportio quantitatū in prin-
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                  cipio excedit proportionem denſitatum in fine. </s>
                  <s xml:id="N23930" xml:space="preserve">Si
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                  vero proportio denſitatū in fine fuerit equalis ꝓ-
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                  portioni quantitatum in principio: tunc equalem
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                  quantitatem acquirunt. </s>
                  <s xml:id="N23939" xml:space="preserve">Si autem proportio den-
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                  ſitatum in fine ſit maior proportione quantitatuꝫ
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                  in principio: tunc minus denſum maiorem quanti­
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                  tatem acquirit in ea proportione per quam pro-
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                  portio denſitatū in fine excedit proportionē quan-
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                  titatum in principio. </s>
                  <s xml:id="N23946" xml:space="preserve">Exemplum primi: vt ſi bipe-
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                  dale denſum vt .8. et pedale denſum vt .6. eque velo­
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                  citer acquirant de denſitate acquirendo duos gra­
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                  dus: tunc denſius deperdet maiorem quantitatem
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                  ̄ minus denſum in proportione ſupertripartien-
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                  te quintas: quia illa eſt proportio per qnam pro-
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                  portio dupla quantitatum in principio excedit ꝓ-
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                  portionem denſitatum in fine que eſt ſexquiquarta
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                  </s>
                  <s xml:id="N23958" xml:space="preserve">Exemplū ſecundi / vt eodem exemplo perdat vtrū
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                  duos gradus denſitatis eque velociter: tunc denſiꝰ
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                  maiorem quantitatem acquirit in proportione ſer­
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                  quitertia: quia illa eſt proportio per quam propor­
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                  tio quantitatum in principio que eſt dupla excedit
                    <cb chead="Capitulū primum."/>
                  proportionē denſitatum in fine que eſt ſexquialte-
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                  ra / vt patet. </s>
                  <s xml:id="N23968" xml:space="preserve">Exemplum tertii / vt eodem exemplo re­
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                  tento perdat vtrum: 4. gradus denſitatis tunc e-
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                  qualem quantitatē acquirunt quia proportio dē-
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                  ſitatum in fine que eſt dupla eſt equalis proportiõi
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                  quantitatū in principio cum etiam ſit dupla. </s>
                  <s xml:id="N23973" xml:space="preserve">Exē-
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                  plum .4. / vt retento eodem deperdat vtrum illoꝝ
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                  quin gradus denſitatis: tunc minus denſum ac-
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                  quirit maiorem quantitatem in proportione ſex-
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                  quialtera que eſt proportio per quam tripla pro-
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                  portio denſitatum in fine excedit proportionē du-
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                  plam quantitatum in principio
                    <note position="right" xlink:href="note-0199-02a" xlink:label="note-0199-02" xml:id="N23AC8" xml:space="preserve">.4. nöbile</note>
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                  <s xml:id="N23987" xml:space="preserve">¶ Quartum nota­
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                  bile. </s>
                  <s xml:id="N2398C" xml:space="preserve">Si ſint duo inequalia in quantitate et in den-
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                  ſitate, maiore exiſtente denſiore: et proportio denſi­
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                  tatis vnius ad denſitatem alterius excedat ꝓpor-
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                  tionem quantitatis eiuſdem ad quantitatem alte-
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                  rius que eque velociter deperdant de dēſitate: tūc
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                  minus denſum maiorem quantitatem acquirit ̄
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                  magis denſum in proportione per quam propor-
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                  tio denſitatum in fine talis deperditionis excedit
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                  proportionem quantitatum in principio. </s>
                  <s xml:id="N2399F" xml:space="preserve">Si vero
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                  illa duo equaliter acquirant de denſitate, et eque
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                  velociter: : et proportio denſitatum in fine maneat
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                  maior ꝙ̄ ſit proportio quantitatum in principio:
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                  tunc minus denſum deperdit maiorem quantitatē
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                  in proportione per quam proportio denſitatuꝫ in
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                  fine excedit proportioneꝫ que eſt inter quantitates
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                  in principio talis acquiſitionis ipſius denſitatis.
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                  </s>
                  <s xml:id="N239B1" xml:space="preserve">Et ſi ꝓportio denſitatis in fine fuerit equalis pro-
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                  portioni quantitatis in principio: tūc et magis dē­
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                  ſum et minus denſum equalem quantitatem deper­
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                  duut. </s>
                  <s xml:id="N239BA" xml:space="preserve">Si autem proportio denſitatum in fine exce-
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                  dit proportionem quantitatum in principio: tunc
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                  magis denſum maiorem quantitatē deperdit quã
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                  minus denſum in ea proportione per quam pro-
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                  portio quantitatis in principio excedit proporti-
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                  onem denſitatum in fine. </s>
                  <s xml:id="N239C7" xml:space="preserve">Exemplum primi / vt ſi ſit
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                  vnū bipedale denſum vt .8. et vnum pedale denſum
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                  vt .2. et eque velociter deperdant vnum gradū den-
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                  ſitatis: tunc minus denſum maiorem quantitatē
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                  acquiret ꝙ̄ magis denſum in proportione tripla
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                  ſexquialtera qualis eſt .7. ad .2. quia proportio dē­
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                  ſitatum in fine que eſt ſeptupla excedit proportio-
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                  nem duplam quantitatis que eſt in principio per
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                  proportionem triplam ſexquialteram. </s>
                  <s xml:id="N239DA" xml:space="preserve">Exemplum
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                  ſecundi in eodem exemplo / ſi vtrum illorum ac-
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                  quirat duos gradus denſitatis: tunc minus denſū
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                  maiorem quantitatem deperdet in ea proportiõe
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                  per quam proportio denſitatum in fine que eſt du­
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                  pla ſexquialtera excedit proportionem quantita-
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                  tum in principio que eſt dupla: et quia illa propor-
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                  tio per quam dupla ſexquialtera excedit propor-
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                  tionem duplã eſt ſexquiquarta. </s>
                  <s xml:id="N239ED" xml:space="preserve">Ideo minus den-
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                  ſum maiorem quantitatem acquiret in proporti-
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                  one ſexquiquarta. </s>
                  <s xml:id="N239F4" xml:space="preserve">Exemplum tertii / vt in eodem ca­
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                  ſu. </s>
                  <s xml:id="N239F9" xml:space="preserve">ſi vtrum illorum corporum acquirat .4. gra-
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                  dus denſitatis: tunc equaliter deperdent de denſi-
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                  tate: quia proportio denſitatum in fine erit equa-
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                  lis proportioni quantitatum in principio. </s>
                  <s xml:id="N23A02" xml:space="preserve">Exem-
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                  plum quarti / vt in eodem exemplo. </s>
                  <s xml:id="N23A07" xml:space="preserve">ſi vtrum il-
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                  lorum corporū acquirat quī gradus denſitatis
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                  tunc magis denſum maiorem quantitatem deper-
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                  dit in proportione ſexquitridecimo quoniam pro-
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                  portio quantitatum in principio que eſt dupla pro­
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                  portionem denſitatum exuperat que eſt proportio
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                  ſuperſextipartiens ſeptimas ꝑ proportionē ſex-
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                  quitridecimam: vt ſatis conſtat. </s>
                  <s xml:id="N23A18" xml:space="preserve">Hec notabilia que
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                  numero quaternario abſoluūtur tanta ſubtilita- </s>
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