Alvarus, Thomas
,
Liber de triplici motu
,
1509
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<
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Tertii tractatus
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177
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ad vniformitatē reduci medietate rariori tãtum de
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perdente quantū minus rara medietas acquirit ip
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ſo difformi manēte cõtinuo ſub eodē gradu rarita
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tis: ſed bene p̄t fieri reducat̄̄ ad vniformitatē ſub
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eodē gradu ſub quo eſt puta ſub gradu medio in to
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to tꝑe: ̄uis in tp̄e medio ſit magis raruꝫ. </
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<
s
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xml:space
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">hoc eſt in
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quolibet inſtanti intrīſeco. </
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<
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xml:space
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">Uolo dicere / poſt̄
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pars minꝰ rara acq̇ſiuerit medietatē exeſſꝰ ꝑ queꝫ
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medietas magis rara excedit eã tunc totum mane-
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bit eq̄ rarum ſicut erat in principio qñ erat difformi-
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ter difforme cuiꝰ vtra medietas erat vniformis.</
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<
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xml:space
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">Sꝫ ↄ̨̨tra </
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>
<
s
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N2139B
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xml:space
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">Q2 volo / in hora illa medie
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/>
tas q̄ eſt vt octo deꝑdat duos gradꝰ et tm̄ acq̇rat me
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dietas minus rara puta vt quatuor quo poſito in fi
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ne pars minꝰ rara acq̇ſiuit medietatē exeeſſus per
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quē exceſſū pars magis rara excedebat eã: et totum
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manet vniforme ſub gradu medio inter octauum et
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/>
quartū q̇ ē vt ſex et tūc totale corpꝰ eſt rarius ꝙ̄ erat
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in principio qñ erat difformiter difforme cuiꝰ vtra
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medietas eſt vniformis. </
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>
<
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xml:space
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">igr̄ antea erat minus ra
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rū ꝙ̄ vt ſex. / et ꝑ ↄ̨ñs ſolutio nulla: </
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xml:space
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">Coña pꝫ cū maio-
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re: et argr̄ minor v3 tale corpꝰ rarefit. </
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<
s
xml:id
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N213B8
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xml:space
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preserve
">q2 in fine ē
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maius ꝙ̄ erat antea et nullã materiã acq̇ſiuit: igr̄ ra
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refit: </
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<
s
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N213BF
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xml:space
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">Argr̄ maior / q2 medietas eiꝰ puta rarior effe-
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cta eſt in ꝓportione ſexq̇tertia minus rara: et ꝑ ↄ̨ñs
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in eadē ꝓportione minor: et ſic ip̄a deꝑdit vnã quar
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/>
tã ſui q̄ ē vna octaua pedalis: medietas vero minꝰ
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/>
rara effecta eſt in ſexq̇altero rarior / vt pꝫ ex caſu igr̄
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effecta ē ī ſexquialtero maior: et ſic ipſa acq̇ſiuit medie
<
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/>
tatē ſui ſupra ſe q̄ medietas eiꝰ eſt vna quarta peda
<
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lis: igr̄ totū illud corpꝰ in duplo maiorē quãtitatē
<
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/>
acq̇ſiuit ꝙ̄ deꝑdit: igr̄ eſt maiꝰ: qḋ fuit probandum.
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<
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xml:id
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">Dicitur.</
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<
s
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N213D9
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xml:space
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">¶ Dices forte et bene / nõ p̄t ſic / rarū vniformiṫ dif
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forme cuiꝰ vtra medietas eſt vniformis ad vnifor
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mitatē reduci:
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xml:space
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">calcula.
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ſuiſeth.</
note
>
ſed ſubtiliter dicit ſuiſeth calcula
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tor ad reducendū raritatē ad vniformitatē oportet
<
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/>
reducere denſitatem: ſicut ad reducendã remiſſiõeꝫ
<
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/>
oportet reducere intenſionē: q2 oē vniformiter den
<
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/>
ſū ē vniformiter rarū: et ſic ſi dēſitas eſt vniformita
<
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ti reſtituta etiam raritas.</
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<
s
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xml:space
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">Sꝫ ↄ̨̨tra / q2 tūc ſeq̇ret̄̄ / denſum vni-
<
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formiter difforme cuius vna medietas eſt dēſa vni-
<
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/>
formiter vt octo et alia medietas vt quatuor poſſet
<
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/>
reduci ad vniformitatem medietate denſiori tãtum
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/>
perdente adequate quantum medietas minus dē-
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ſa acquirit: ipſo corpore contino manente eque
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denſo: ſed conſequens ē falſum / igitur illud ex quo
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ſequitur </
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">Falſitas cõſequenis probatur et pono /
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medietas vnius pedalis ſit denſa vt octo: et alia vt
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quatuor; et ī vna medietate hore deꝑdat medietas
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denſior vnum gradum denſitatis et tantum acqui-
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rat medietas minus denſa. </
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">Quo poſito ſic arguo
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totale corpus in illa media hora cõdenſatur: ergo
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ſequitur / non valet ſic ad vniformitatem reduci ꝑ
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te minus denſa tantum acquirente quantuꝫ magis
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denſa deperdit: continuo ipſo manente eque den-
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ſo. </
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">Conſequentia patet: et arguitur antecedens / q2
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ipſum efficitur minus quã antea et nullã materiam
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deperdit: ergo ſequitur / cõdenſatur: </
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">Patet cõſe-
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quentia cum minore et arguitur maior videlicet
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efficitur minus: q2 medietas denſior perdit vnum
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gradum denſitatis: et ſic efficitur in ſexquiſeptimo
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minus denſa: igitur in ſexquiſeptimo magis rara.
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</
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<
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xml:space
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">et maior et per ↄ̨ñs acq̇rit vnã ſeptimam ſui que eſt
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quatuor decīa vnius pedalis: alia vero pars vel me
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dietas que eſt denſa vt quatuor acquirit vnuꝫ gra-
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dum denſitatis. </
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<
s
xml:id
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xml:space
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">et ſic efficitur in ſexquiquarto den-
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ſior et per ↄ̨ñs in ſexq̇quarto minor et ſic ꝑdit vnam
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quintã ſui q̄ eſt decima vniꝰ pedalis: igr̄ illud tota-
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le corpus perdidit vnã decimã: et acq̇rit vnã quatuor
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decimã ſui. </
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<
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">magis igr̄ deꝑdit ꝙ̄ acq̇rit et ex ↄ̨ñti effi
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citur minus ꝙ̄ erat antea fuit ꝓbãdū.
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">Dicitur.</
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<
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xml:space
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">¶ Dices et
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bñ / argumentū bñ ꝓbat talia difformia in dēſitate
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poſſe ſic ad vniformitatē reduci ip̄is manētibꝰ con-
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tinuo ſub eodē gradu dēſitatꝪ: q2 neceſſe ē qñ ſic vna
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medietas tm̄ acquirit quãtum: alia deperdit de dē
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ſitate: ipſa difformia per aliquod tempus condēſa
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ri: et ꝑdere quantitatē: ſed tunc per tempus ſequens
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tantum rarefient ̄tum antea fuerunt condenſata,
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et ſic in totali tempore ipſa nec rarefiunt nec condē
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ſantur vt ſi medietas vt octo in hora perdat duos
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gradus adequate: et tantum medietas vt quatuor
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adequate acquirat: tunc in fine quantū vna medie-
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tas acquiſiuit tantum alia deperdit et manebit ade
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quate illud pedale in fine tante quantitatis quante
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erat antea. </
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">Quod patet ſic /q2 illa medietas vt octo
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perdit proportionem ſexquitertiam denſitatis: et
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per conſequens ipſa efficitur in ſexquitertio maior /
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igitur ipſa acquiſiuit vnam tertiam ſui que eſt vna
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ſexta pedalis: altera vero medietas effecta eſt in ſex
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quialtero denſior: igitur in ſexquialtero minor: et ꝑ
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conſequens ipſa deperdit vnam tertiam ſui que eſt
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ſexta vnius pedalis: igitur quantū illud corpus ac
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quiſiuit de quantitate tãtum deperdit: et in fine ma
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nebit vniforme ſub gradu medio qui eſt ſextus: igr̄
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nunc illi gradui ſua denſitas correſpondet. </
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<
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fuit inducendum.</
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<
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">Sed contra hanc ſolutionē arguitur
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ſic / q2 tale pedale per totam illam horam rarefit:
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igitur per nullam partem illius hore condenſatur
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et etiam in fine manebit rarius ꝙ̄ antea: et ſic nõ ma
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nebit ita denſum ſicut antea: nec eidē gradui correſ
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pondebit et per conſequens ſolutio nulla. </
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<
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ãtecedēs / quia continuo in illa hora per maioreꝫ ꝑ
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tem erit deperditio denſitatis ꝙ̄ acquiſitio eiuſdē
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eodē gradus / vt patet ex caſu: ergo illḋ pedale remit
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titur in denſitate et per conſequens ipſum rarefit ꝑ
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totum illud tempus / quod fuit probandum. </
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<
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N214BD
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">Antece
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dens patet / quia continuo pars que remittitur ī dē
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ſitate erit maior ꝙ̄ pars que intenditur in denſita-
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te / vt patet intuenti. </
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>
<
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">Conſequentia patet a ſimili / q2
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ſi continuo aliquod corpus per maiorem parteꝫ ac
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quirit albedinem ꝙ̄ nigredine eodem gradu ma-
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nifeſtum eſt / tale corpus remittitur in nigridine:
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dato ipſum antea fuerit nigrū vt facile eſt inſpi-
<
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cere: igr̄ a ſimili ſi per maiorē partē ē remiſſio den
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ſitatis ꝙ̄ intenſio eiuſdem eodeꝫ gradu ſequitur to
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tum remitti in denſitate.
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">cõfirma.</
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">Q2 non
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eſt dabile inſtans in toto illo tempore in quo tale
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corpus incipit rarefieri poſt̄ condenſabatur: igi-
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tur falſum eſt dicere ſemper quando aliquod cor
<
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pus ſic ad vniformitatem denſitatis reducit̄̄ tp̄m
<
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per aliquod tempus primo condenſatur et deiñ ꝑ
<
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tempus ſequens rarefit acquirendo quantitatem
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quam perdiderat </
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<
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">Probatur antecedens / q2 maxīe
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tale inſtans eſſet inſtans medium illius temporis
<
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in quo videlicet medietas denſitatis deperdende a
<
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medietate denſiori eſt deperdita et reliqua medie-
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tas incipit deperdi: ſed hoc eſt falſum / igitur illḋ ex
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quo ſequitur </
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<
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N214FD
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xml:space
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">Sequela patet / q2 non videtur qḋ in-
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ſtans ſit illud niſi fuerit medium inſtans. </
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<
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">Falſitas
<
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tamen conſequentis arguitur: et capio vnum bipe-
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dale cuius vna medietas ſit denſa vt duodecim et
<
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alia vt dimidium: et volo / per horam vniformiter
<
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/>
medietas denſior deperdat quin gradus cum tri
<
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bus quartis et tm̄ acq̇rat medietas minus dēſa ita
<
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totum in fiue maneat vniforme. </
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>
<
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xml:id
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N21511
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xml:space
="
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">et arguitur ſic </
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