Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Tertii tractatus
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in fine eſt tripla. </
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<
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xml:space
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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.</
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<
s
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xml:space
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">¶ 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. </
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>
<
s
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N238CE
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xml:space
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preserve
">Si vero eque velociter deperdant de
<
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denſitate: tunc denſius minorem quantitatem ac-
<
lb
/>
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. </
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>
<
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xml:space
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">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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</
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<
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xml:space
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portionem ſuperbipartientem tertias que eſt pro-
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portio denſitatum in fine. </
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>
<
s
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N238EE
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xml:space
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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.
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xml:space
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">3. nöbile</
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<
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xml:space
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bile. </
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<
s
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xml:space
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">Si ſint duo inequalia et inequaliter denſa. </
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<
s
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N2390A
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xml:space
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">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. </
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>
<
s
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N23923
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xml:space
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">Si vero illa talia eque velociter de-
<
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/>
perdant de dēſitate: et proportio denſitatū in fine
<
lb
/>
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. </
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>
<
s
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xml:space
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">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. </
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>
<
s
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xml:space
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">Si autem proportio den-
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ſitatum in fine ſit maior proportione quantitatuꝫ
<
lb
/>
in principio: tunc minus denſum maiorem quanti
<
lb
/>
tatem acquirit in ea proportione per quam pro-
<
lb
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portio denſitatū in fine excedit proportionē quan-
<
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titatum in principio. </
s
>
<
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xml:space
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">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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</
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<
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xml:space
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">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
<
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Capitulū primum.
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proportionē denſitatum in fine que eſt ſexquialte-
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ra / vt patet. </
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<
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xml:space
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">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. </
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>
<
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">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
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<
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xml:space
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">¶ Quartum nota
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bile. </
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>
<
s
xml:id
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N2398C
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xml:space
="
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">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. </
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>
<
s
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xml:space
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">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
<
lb
/>
fine excedit proportioneꝫ que eſt inter quantitates
<
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/>
in principio talis acquiſitionis ipſius denſitatis.
<
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</
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>
<
s
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xml:space
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">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
="
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xml:space
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preserve
">Si autem proportio denſitatum in fine exce-
<
lb
/>
dit proportionem quantitatum in principio: tunc
<
lb
/>
magis denſum maiorem quantitatē deperdit quã
<
lb
/>
minus denſum in ea proportione per quam pro-
<
lb
/>
portio quantitatis in principio excedit proporti-
<
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/>
onem denſitatum in fine. </
s
>
<
s
xml:id
="
N239C7
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xml:space
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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
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xml:space
="
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">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
<
lb
/>
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
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N239ED
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xml:space
="
preserve
">Ideo minus den-
<
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ſum maiorem quantitatem acquiret in proporti-
<
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one ſexquiquarta. </
s
>
<
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xml:id
="
N239F4
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xml:space
="
preserve
">Exemplum tertii / vt in eodem ca
<
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ſu. </
s
>
<
s
xml:id
="
N239F9
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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
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xml:space
="
preserve
">Exem-
<
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plum quarti / vt in eodem exemplo. </
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>
<
s
xml:id
="
N23A07
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xml:space
="
preserve
">ſi vtrum il-
<
lb
/>
lorum corporū acquirat quī gradus denſitatis
<
lb
/>
tunc magis denſum maiorem quantitatem deper-
<
lb
/>
dit in proportione ſexquitridecimo quoniam pro-
<
lb
/>
portio quantitatum in principio que eſt dupla pro
<
lb
/>
portionem denſitatum exuperat que eſt proportio
<
lb
/>
ſuperſextipartiens ſeptimas ꝑ proportionē ſex-
<
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quitridecimam: vt ſatis conſtat. </
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<
s
xml:id
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N23A18
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xml:space
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preserve
">Hec notabilia que
<
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numero quaternario abſoluūtur tanta ſubtilita- </
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