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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                  <s xml:id="N21375" xml:space="preserve">
                    <pb chead="Tertii tractatus" file="0177" n="177"/>
                  ad vniformitatē reduci medietate rariori tãtum de­
                    <lb/>
                  perdente quantū minus rara medietas acquirit ip­
                    <lb/>
                  ſo difformi manēte cõtinuo ſub eodē gradu rarita­
                    <lb/>
                  tis: ſed bene p̄t fieri  reducat̄̄ ad vniformitatē ſub
                    <lb/>
                  eodē gradu ſub quo eſt puta ſub gradu medio in to­
                    <lb/>
                  to tꝑe: ̄uis in tp̄e medio ſit magis raruꝫ. </s>
                  <s xml:id="N21387" xml:space="preserve">hoc eſt in
                    <lb/>
                  quolibet inſtanti intrīſeco. </s>
                  <s xml:id="N2138C" xml:space="preserve">Uolo dicere /  poſt̄
                    <lb/>
                  pars minꝰ rara acq̇ſiuerit medietatē exeſſꝰ ꝑ queꝫ
                    <lb/>
                  medietas magis rara excedit eã tunc totum mane-
                    <lb/>
                  bit eq̄ rarum ſicut erat in principio qñ erat difformi-
                    <lb/>
                  ter difforme cuiꝰ vtra medietas erat vniformis.</s>
                </p>
                <p xml:id="N21397">
                  <s xml:id="N21398" xml:space="preserve">Sꝫ ↄ̨̨tra </s>
                  <s xml:id="N2139B" xml:space="preserve">Q2 volo /  in hora illa medie­
                    <lb/>
                  tas q̄ eſt vt octo deꝑdat duos gradꝰ et tm̄ acq̇rat me­
                    <lb/>
                  dietas minus rara puta vt quatuor quo poſito in fi­
                    <lb/>
                  ne pars minꝰ rara acq̇ſiuit medietatē exeeſſus per
                    <lb/>
                  quē exceſſū pars magis rara excedebat eã: et totum
                    <lb/>
                  manet vniforme ſub gradu medio inter octauum et
                    <lb/>
                  quartū q̇ ē vt ſex et tūc totale corpꝰ eſt rarius ꝙ̄ erat
                    <lb/>
                  in principio qñ erat difformiter difforme cuiꝰ vtra­
                    <lb/>
                   medietas eſt vniformis. </s>
                  <s xml:id="N213AE" xml:space="preserve">igr̄ antea erat minus ra­
                    <lb/>
                  rū ꝙ̄ vt ſex. / et ꝑ ↄ̨ñs ſolutio nulla: </s>
                  <s xml:id="N213B3" xml:space="preserve">Coña pꝫ cū maio-
                    <lb/>
                  re: et argr̄ minor v3  tale corpꝰ rarefit. </s>
                  <s xml:id="N213B8" xml:space="preserve">q2 in fine ē
                    <lb/>
                  maius ꝙ̄ erat antea et nullã materiã acq̇ſiuit: igr̄ ra­
                    <lb/>
                  refit: </s>
                  <s xml:id="N213BF" xml:space="preserve">Argr̄ maior / q2 medietas eiꝰ puta rarior effe-
                    <lb/>
                  cta eſt in ꝓportione ſexq̇tertia minus rara: et ꝑ ↄ̨ñs
                    <lb/>
                  in eadē ꝓportione minor: et ſic ip̄a deꝑdit vnã quar­
                    <lb/>
                  tã ſui q̄ ē vna octaua pedalis: medietas vero minꝰ
                    <lb/>
                  rara effecta eſt in ſexq̇altero rarior / vt pꝫ ex caſu igr̄
                    <lb/>
                  effecta ē ī ſexquialtero maior: et ſic ipſa acq̇ſiuit medie­
                    <lb/>
                  tatē ſui ſupra ſe q̄ medietas eiꝰ eſt vna quarta peda­
                    <lb/>
                  lis: igr̄ totū illud corpꝰ in duplo maiorē quãtitatē
                    <lb/>
                  acq̇ſiuit ꝙ̄ deꝑdit: igr̄ eſt maiꝰ: qḋ fuit probandum.
                    <lb/>
                    <note position="left" xlink:href="note-0177-01a" xlink:label="note-0177-01" xml:id="N213F3" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N213D9" xml:space="preserve">¶ Dices forte et bene /  nõ p̄t ſic / rarū vniformiṫ dif­
                    <lb/>
                  forme cuiꝰ vtra medietas eſt vniformis ad vnifor­
                    <lb/>
                  mitatē reduci:
                    <note position="left" xlink:href="note-0177-02a" xlink:label="note-0177-02" xml:id="N213F9" xml:space="preserve">calcula.
                      <lb/>
                    ſuiſeth.</note>
                  ſed ſubtiliter dicit ſuiſeth calcula­
                    <lb/>
                  tor ad reducendū raritatē ad vniformitatē oportet
                    <lb/>
                  reducere denſitatem: ſicut ad reducendã remiſſiõeꝫ
                    <lb/>
                  oportet reducere intenſionē: q2 oē vniformiter den­
                    <lb/>
                  ſū ē vniformiter rarū: et ſic ſi dēſitas eſt vniformita­
                    <lb/>
                  ti reſtituta etiam raritas.</s>
                </p>
                <p xml:id="N21401">
                  <s xml:id="N21402" xml:space="preserve">Sꝫ ↄ̨̨tra / q2 tūc ſeq̇ret̄̄ /  denſum vni-
                    <lb/>
                  formiter difforme cuius vna medietas eſt dēſa vni-
                    <lb/>
                  formiter vt octo et alia medietas vt quatuor poſſet
                    <lb/>
                  reduci ad vniformitatem medietate denſiori tãtum
                    <lb/>
                  perdente adequate quantum medietas minus dē-
                    <lb/>
                  ſa acquirit: ipſo corpore contino manente eque
                    <lb/>
                  denſo: ſed conſequens ē falſum / igitur illud ex quo
                    <lb/>
                  ſequitur </s>
                  <s xml:id="N21413" xml:space="preserve">Falſitas cõſequenis probatur et pono / 
                    <lb/>
                  medietas vnius pedalis ſit denſa vt octo: et alia vt
                    <lb/>
                  quatuor; et ī vna medietate hore deꝑdat medietas
                    <lb/>
                  denſior vnum gradum denſitatis et tantum acqui-
                    <lb/>
                  rat medietas minus denſa. </s>
                  <s xml:id="N2141E" xml:space="preserve">Quo poſito ſic arguo
                    <lb/>
                  totale corpus in illa media hora cõdenſatur: ergo
                    <lb/>
                  ſequitur /  non valet ſic ad vniformitatem reduci ꝑ
                    <lb/>
                  te minus denſa tantum acquirente quantuꝫ magis
                    <lb/>
                  denſa deperdit: continuo ipſo manente eque den-
                    <lb/>
                  ſo. </s>
                  <s xml:id="N2142B" xml:space="preserve">Conſequentia patet: et arguitur antecedens / q2
                    <lb/>
                  ipſum efficitur minus quã antea et nullã materiam
                    <lb/>
                  deperdit: ergo ſequitur /  cõdenſatur: </s>
                  <s xml:id="N21432" xml:space="preserve">Patet cõſe-
                    <lb/>
                  quentia cum minore et arguitur maior videlicet 
                    <lb/>
                  efficitur minus: q2 medietas denſior perdit vnum
                    <lb/>
                  gradum denſitatis: et ſic efficitur in ſexquiſeptimo
                    <lb/>
                  minus denſa: igitur in ſexquiſeptimo magis rara.
                    <lb/>
                  </s>
                  <s xml:id="N2143E" xml:space="preserve">et maior et per ↄ̨ñs acq̇rit vnã ſeptimam ſui que eſt
                    <lb/>
                  quatuor decīa vnius pedalis: alia vero pars vel me­
                    <lb/>
                  dietas que eſt denſa vt quatuor acquirit vnuꝫ gra-
                    <lb/>
                  dum denſitatis. </s>
                  <s xml:id="N21447" xml:space="preserve">et ſic efficitur in ſexquiquarto den-
                    <lb/>
                  ſior et per ↄ̨ñs in ſexq̇quarto minor et ſic ꝑdit vnam
                    <cb chead="Capitulum primum"/>
                  quintã ſui q̄ eſt decima vniꝰ pedalis: igr̄ illud tota-
                    <lb/>
                  le corpus perdidit vnã decimã: et acq̇rit vnã quatuor
                    <lb/>
                  decimã ſui. </s>
                  <s xml:id="N21453" xml:space="preserve">magis igr̄ deꝑdit ꝙ̄ acq̇rit et ex ↄ̨ñti effi­
                    <lb/>
                  citur minus ꝙ̄ erat antea  fuit ꝓbãdū.
                    <note position="right" xlink:href="note-0177-03a" xlink:label="note-0177-03" xml:id="N2149C" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N2145D" xml:space="preserve">¶ Dices et
                    <lb/>
                  bñ /  argumentū bñ ꝓbat talia difformia in dēſitate
                    <lb/>
                  poſſe ſic ad vniformitatē reduci ip̄is manētibꝰ con-
                    <lb/>
                  tinuo ſub eodē gradu dēſitatꝪ: q2 neceſſe ē qñ ſic vna
                    <lb/>
                  medietas tm̄ acquirit quãtum: alia deperdit de dē­
                    <lb/>
                  ſitate: ipſa difformia per aliquod tempus condēſa­
                    <lb/>
                  ri: et ꝑdere quantitatē: ſed tunc per tempus ſequens
                    <lb/>
                  tantum rarefient ̄tum antea fuerunt condenſata,
                    <lb/>
                  et ſic in totali tempore ipſa nec rarefiunt nec condē­
                    <lb/>
                  ſantur vt ſi medietas vt octo in hora perdat duos
                    <lb/>
                  gradus adequate: et tantum medietas vt quatuor
                    <lb/>
                  adequate acquirat: tunc in fine quantū vna medie-
                    <lb/>
                  tas acquiſiuit tantum alia deperdit et manebit ade­
                    <lb/>
                  quate illud pedale in fine tante quantitatis quante
                    <lb/>
                  erat antea. </s>
                  <s xml:id="N2147C" xml:space="preserve">Quod patet ſic /q2 illa medietas vt octo
                    <lb/>
                  perdit proportionem ſexquitertiam denſitatis: et
                    <lb/>
                  per conſequens ipſa efficitur in ſexquitertio maior /
                    <lb/>
                  igitur ipſa acquiſiuit vnam tertiam ſui que eſt vna
                    <lb/>
                  ſexta pedalis: altera vero medietas effecta eſt in ſex­
                    <lb/>
                  quialtero denſior: igitur in ſexquialtero minor: et ꝑ
                    <lb/>
                  conſequens ipſa deperdit vnam tertiam ſui que eſt
                    <lb/>
                  ſexta vnius pedalis: igitur quantū illud corpus ac­
                    <lb/>
                  quiſiuit de quantitate tãtum deperdit: et in fine ma­
                    <lb/>
                  nebit vniforme ſub gradu medio qui eſt ſextus: igr̄
                    <lb/>
                  nunc illi gradui ſua denſitas correſpondet. </s>
                  <s xml:id="N21493" xml:space="preserve">quod
                    <lb/>
                  fuit inducendum.</s>
                </p>
                <p xml:id="N214A2">
                  <s xml:id="N214A3" xml:space="preserve">Sed contra hanc ſolutionē arguitur
                    <lb/>
                  ſic / q2 tale pedale per totam illam horam rarefit:
                    <lb/>
                  igitur per nullam partem illius hore condenſatur
                    <lb/>
                  et etiam in fine manebit rarius ꝙ̄ antea: et ſic nõ ma­
                    <lb/>
                  nebit ita denſum ſicut antea: nec eidē gradui correſ­
                    <lb/>
                  pondebit et per conſequens ſolutio nulla. </s>
                  <s xml:id="N214B0" xml:space="preserve">Arguitur
                    <lb/>
                  ãtecedēs / quia continuo in illa hora per maioreꝫ ꝑ­
                    <lb/>
                  tem erit deperditio denſitatis ꝙ̄ acquiſitio eiuſdē
                    <lb/>
                  eodē gradus / vt patet ex caſu: ergo illḋ pedale remit­
                    <lb/>
                  titur in denſitate et per conſequens ipſum rarefit ꝑ
                    <lb/>
                  totum illud tempus / quod fuit probandum. </s>
                  <s xml:id="N214BD" xml:space="preserve">Antece­
                    <lb/>
                  dens patet / quia continuo pars que remittitur ī dē­
                    <lb/>
                  ſitate erit maior ꝙ̄ pars que intenditur in denſita-
                    <lb/>
                  te / vt patet intuenti. </s>
                  <s xml:id="N214C6" xml:space="preserve">Conſequentia patet a ſimili / q2
                    <lb/>
                  ſi continuo aliquod corpus per maiorem parteꝫ ac­
                    <lb/>
                  quirit albedinem ꝙ̄ nigredine eodem gradu ma-
                    <lb/>
                  nifeſtum eſt /  tale corpus remittitur in nigridine:
                    <lb/>
                  dato  ipſum antea fuerit nigrū vt facile eſt inſpi-
                    <lb/>
                  cere: igr̄ a ſimili ſi per maiorē partē ē remiſſio den­
                    <lb/>
                  ſitatis ꝙ̄ intenſio eiuſdem eodeꝫ gradu ſequitur to­
                    <lb/>
                  tum remitti in denſitate.
                    <note position="right" xlink:href="note-0177-04a" xlink:label="note-0177-04" xml:id="N2156C" xml:space="preserve">cõfirma.</note>
                  </s>
                  <s xml:id="N214DC" xml:space="preserve">¶ Et confirmatur </s>
                  <s xml:id="N214DF" xml:space="preserve">Q2 non
                    <lb/>
                  eſt dabile inſtans in toto illo tempore in quo tale
                    <lb/>
                  corpus incipit rarefieri poſt̄ condenſabatur: igi-
                    <lb/>
                  tur falſum eſt dicere  ſemper quando aliquod cor­
                    <lb/>
                  pus ſic ad vniformitatem denſitatis reducit̄̄  tp̄m
                    <lb/>
                  per aliquod tempus primo condenſatur et deiñ ꝑ
                    <lb/>
                  tempus ſequens rarefit acquirendo quantitatem
                    <lb/>
                  quam perdiderat </s>
                  <s xml:id="N214F0" xml:space="preserve">Probatur antecedens / q2 maxīe
                    <lb/>
                  tale inſtans eſſet inſtans medium illius temporis
                    <lb/>
                  in quo videlicet medietas denſitatis deperdende a
                    <lb/>
                  medietate denſiori eſt deperdita et reliqua medie-
                    <lb/>
                  tas incipit deperdi: ſed hoc eſt falſum / igitur illḋ ex
                    <lb/>
                  quo ſequitur </s>
                  <s xml:id="N214FD" xml:space="preserve">Sequela patet / q2 non videtur qḋ in-
                    <lb/>
                  ſtans ſit illud niſi fuerit medium inſtans. </s>
                  <s xml:id="N21502" xml:space="preserve">Falſitas
                    <lb/>
                  tamen conſequentis arguitur: et capio vnum bipe-
                    <lb/>
                  dale cuius vna medietas ſit denſa vt duodecim et
                    <lb/>
                  alia vt dimidium: et volo /  per horam vniformiter
                    <lb/>
                  medietas denſior deperdat quin gradus cum tri­
                    <lb/>
                  bus quartis et tm̄ acq̇rat medietas minus dēſa ita
                    <lb/>
                   totum in fiue maneat vniforme. </s>
                  <s xml:id="N21511" xml:space="preserve">et arguitur ſic </s>
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