Alvarus, Thomas
,
Liber de triplici motu
,
1509
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211 - 240
241 - 270
271 - 290
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De motu rarefactionis et condenſationis.
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ante inſtans medium totius temporis. </
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>
<
s
xml:id
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N21519
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xml:space
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">incipiet tale
<
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/>
corpus rarefieri poſt̄ condēſabit̄̄: igitur inſtans
<
lb
/>
mediū illius temporis non eſt inſtans in quo tale
<
lb
/>
corpus incipit rarefieri poſt̄ antea condenſabat̄̄.
<
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/>
</
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>
<
s
xml:id
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N21523
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xml:space
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preserve
">Conſequētia pꝫ et arguit̄̄ añs et volo / illa medie-
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/>
tas denſior deperdat vniformiter duos gradꝰ den
<
lb
/>
ſitatis et illos acq̇rat medietas minus denſa / et ma
<
lb
/>
nifeſtum eſt / medietas denſior efficitur in ſexqui
<
lb
/>
quinto minus denſa et ſic acquirit ſupra ſe vnam
<
lb
/>
quintam pedalis: et alia medietas efficitur in quī-
<
lb
/>
tuplo denſior ꝙ̄ erat antea et ſic deꝑdit q̈tuor quin
<
lb
/>
tas ſui et manet p̄ciſe vna quīta pedalis: volo dein
<
lb
/>
de medietas dēſior ꝑdat medietatem vnius gra-
<
lb
/>
dus et tm̄ acq̇rat medietas minꝰ denſa eq̄ velociter:
<
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/>
</
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<
s
xml:id
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N21539
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xml:space
="
preserve
">Et argr̄ ſic / in tꝑe illo in q̊ pars denſior deperdit me
<
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/>
dietate vnius gradus et pars minꝰ denſa tm̄ acq̇rit
<
lb
/>
iã totū rarefit. </
s
>
<
s
xml:id
="
N21540
"
xml:space
="
preserve
">et illud tp̄s eſt añ inſtans medium vt
<
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/>
pꝫ ex ſe: igr̄ añ inſtãs mediū totiꝰ tꝑis īcipit tale cor
<
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/>
pus rarefieri poſt̄ cõdēſabat̄̄. </
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>
<
s
xml:id
="
N21547
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xml:space
="
preserve
">pꝫ ↄ̨ña et argr̄ ma
<
lb
/>
ior / q2 in tp̄e illo pars dēſior q̄ ē maior pedali deꝑ-
<
lb
/>
dit ꝓportionē ſexquidecimã nonnã in dēſitate et ſic
<
lb
/>
acq̇rit vnã decimã nonã vniꝰ pedalis et plus. </
s
>
<
s
xml:id
="
N21550
"
xml:space
="
preserve
">Pars
<
lb
/>
vero minus denſa efficit̄̄ in ſexquiquīto denſior, et
<
lb
/>
ꝑ ↄ̨ñs in ſexq̇quinto minor et ſic perdit vnã ſextã ſui
<
lb
/>
et ipſa eſt vna quinta pedalis. </
s
>
<
s
xml:id
="
N21559
"
xml:space
="
preserve
">g̊ perdit vnã ſextam
<
lb
/>
quinte pedalis: et ſexta vnius quīte pedalis eſt vna
<
lb
/>
trigeſima pedalis / vt pꝫ intuenti: igr̄ illḋ totale cor
<
lb
/>
pus ꝑdit vnã trigeſimã vniꝰ pedalis et acq̇rit pluſ̄
<
lb
/>
vnã decimã nona in tp̄e illo añ inſtãs mediū: igitur
<
lb
/>
plus acq̇rit de quãtitate ꝙ̄ deperdit et per cõſeq̄ns
<
lb
/>
rarefit / quod fuit probandum.</
s
>
</
p
>
<
p
xml:id
="
N21572
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<
s
xml:id
="
N21573
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xml:space
="
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">Quīto prīcipaliṫ argr̄ ſic </
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>
<
s
xml:id
="
N21576
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xml:space
="
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">Si raritas
<
lb
/>
et denſitas eēnt poſſibiles. </
s
>
<
s
xml:id
="
N2157B
"
xml:space
="
preserve
">Seq̄ret̄̄ / datis duobꝰ
<
lb
/>
corporibꝰ inequalibus maiore plus continente de
<
lb
/>
materia ꝙ̄ minus ſemꝑ maius eſſet dēſius minore.
<
lb
/>
</
s
>
<
s
xml:id
="
N21583
"
xml:space
="
preserve
">ↄ̨ñs eſt falſū. </
s
>
<
s
xml:id
="
N21586
"
xml:space
="
preserve
">igr̄ et añs </
s
>
<
s
xml:id
="
N21589
"
xml:space
="
preserve
">Seq̄la ſuadet̄̄ q2 capto cor-
<
lb
/>
pore bipedali vniformiter qḋ habeat tres gradus
<
lb
/>
materie. </
s
>
<
s
xml:id
="
N21590
"
xml:space
="
preserve
">et pedali habeat vnum gradū materie
<
lb
/>
dūtaxat manifeſtū eſt maius eſt dēſius mīore q2
<
lb
/>
ſi manente eadem quãtitate maius ꝑderet vnū gra
<
lb
/>
dū materie. </
s
>
<
s
xml:id
="
N21599
"
xml:space
="
preserve
">ipſū rarefieret: et in fine maneret vnifor
<
lb
/>
miter eq̄ denſū cū pedali. </
s
>
<
s
xml:id
="
N2159E
"
xml:space
="
preserve
">igr̄ mõ eſt denſius illo pe
<
lb
/>
dali / qḋ fuit ꝓbãdū </
s
>
<
s
xml:id
="
N215A3
"
xml:space
="
preserve
">Falſitas tñ ↄ̨ñtis ꝓbat̄̄ et capio
<
lb
/>
vnū pedale qḋ habeat duos gradus materie: et vnū
<
lb
/>
bipedale vniforme qḋ habeat tres / et argr̄ ſic / illud
<
lb
/>
pedale ē dēſius illo bipedali maiori continēte plus
<
lb
/>
de materia: igr̄ nõ ſi aliq̇d eſt maiꝰ plꝰ ↄ̨tinēs de ma
<
lb
/>
teria ꝙ̄ aliud minꝰ eo ipſū ē eo: dēſiꝰ. </
s
>
<
s
xml:id
="
N215B0
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xml:space
="
preserve
">Probat̄̄ añs
<
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/>
et volo / ſtãte quãtitate ipſius pedalis perdat me-
<
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/>
dietatē vniꝰ gradꝰ materie. </
s
>
<
s
xml:id
="
N215B7
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xml:space
="
preserve
">q̊ poſito illḋ pedale ra
<
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/>
refit vt notū eſt et in fine manebit eq̄ dēſū cū bipeda
<
lb
/>
li: igr̄ antea erat dēſius. </
s
>
<
s
xml:id
="
N215BE
"
xml:space
="
preserve
">Coña pꝫ cū maiore et argr̄
<
lb
/>
minor / q2 illud pedale in fine manebit eq̄ dēſū ſicut
<
lb
/>
medietas illius bipedalis q2 cõtinebit tm̄ de mate
<
lb
/>
ria adeq̈te ſicut medietas illius bipedalis: et bipe-
<
lb
/>
dale eſt vniforme vt ponit̄̄: g̊ illud pedale eſt ita dē
<
lb
/>
ſū ſicut bipedale / qḋ fnit ꝓbãdū.
<
note
position
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left
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xlink:href
="
note-0178-01a
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xlink:label
="
note-0178-01
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xml:id
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N215DB
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xml:space
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preserve
">Dicitur.</
note
>
</
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>
<
s
xml:id
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N215D0
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xml:space
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preserve
">¶ Dices et bñ negã
<
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do ſeq̄lã īmo aliqñ minꝰ ē dēſius maiore: et eↄ̈: et ali
<
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/>
qñ eq̄ denſum vt apparere poteſt ex argumento.</
s
>
</
p
>
<
p
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<
s
xml:id
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xml:space
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">Sꝫ ↄ̨̨tra </
s
>
<
s
xml:id
="
N215E5
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xml:space
="
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">Q2 tūc ſeq̄ret̄̄ / nõ poſſet da
<
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ri certa regula ad ſciēdū qñ vnū e denſius altero: et
<
lb
/>
qñ maius eſt dēſius minore vel econtra: quod ſi ne-
<
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/>
ges des illam. </
s
>
<
s
xml:id
="
N215EE
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xml:space
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">ſed cõſequēs eſt falſum: igitur illud
<
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ex quo ſequitur.</
s
>
</
p
>
<
p
xml:id
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<
s
xml:id
="
N215F4
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xml:space
="
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">Sexto prīcipaliṫ argr̄ ſic hoc tãgen
<
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do rara difformia. </
s
>
<
s
xml:id
="
N215F9
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xml:space
="
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">Q2 ſi raritas et denſitas eſſent
<
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poſſibiles ſeq̄ret̄̄ / dabile eēt raꝝ vniformiter dif
<
lb
/>
forme ab aliquo gradu vſ ad non gradū: et eiꝰ ra
<
cb
chead
="
De motu rarefactionis et condenſationis.
"/>
ritas correſponderat gradui medio: ſed ↄ̨ñs eſt fal
<
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ſum: igitur et antecedēs. </
s
>
<
s
xml:id
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xml:space
="
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">Sequela ꝓbatur / quia da
<
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/>
bile eſt rarum vniformiter difforme a certo gradu
<
lb
/>
vſ ad nõ gradū: g̊ etiã pari forma dabile eſt rarū
<
lb
/>
vniformiter difforme a certo gradu vſ ad nõ gra
<
lb
/>
dū. </
s
>
<
s
xml:id
="
N21610
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xml:space
="
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">Sed falſitas conſequentis ꝓbatur / q2 ex illo ſe-
<
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/>
quitur aliquid eē rarū et idē non eē rarum / quod eſt
<
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/>
impoſſibile: </
s
>
<
s
xml:id
="
N21617
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xml:space
="
preserve
">Sequela ꝓbatur / q2 capto tali corpo-
<
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/>
re vniformiter difformiter raro a gradu quarto vſ
<
lb
/>
ad non gradū: tale corpus eſt raꝝ vt duo ꝑ te cū
<
lb
/>
eius raritas correſpondeat ſuo gradui medio: et eſt
<
lb
/>
nõ rarū cū ſit infinite dēſum: igr̄ intentū: minor pro
<
lb
/>
batur / q2 prīa ꝑs ꝓportionalis illiꝰ corporis ꝓpor
<
lb
/>
tione dupla eſt aliq̈liter denſa. </
s
>
<
s
xml:id
="
N21626
"
xml:space
="
preserve
">et ſecunda in duplo
<
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/>
denſior et tertia in quadruplo et ſic in infinitū: igit̄̄
<
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/>
illud corpus eſt infinite dēſum: et per ↄ̨ñs non rarum.
<
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/>
</
s
>
<
s
xml:id
="
N2162E
"
xml:space
="
preserve
">Q, ſecunda pars ꝓportiõalis ſit in duplo den-
<
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/>
ſior prīa patet / q2 eſt in ſubduplo rarior;: g̊ in duplo
<
lb
/>
denſior: pꝫ ↄ̨ña qm̄ ī quacū ꝓportione raritas ē
<
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/>
minor: in eadem denſitas ē maior. </
s
>
<
s
xml:id
="
N21637
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xml:space
="
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">vt ſatis facile ꝓ
<
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/>
bari p̄t ex diffinitionibꝰ magis rari et magis denſi
<
lb
/>
et añs pꝫ / q2 prīa ꝑs ꝓportionalis eſt rara vt tria,
<
lb
/>
cū eius raritas ſit vniformiter difformis a quatuor
<
lb
/>
vſ ad duo: et ſcḋa pars proportionalis eſt rara vt
<
lb
/>
vnū cū dimidio: ſꝫ vnū cū dimidio eſt ſubdupluꝫ ad
<
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/>
tria. </
s
>
<
s
xml:id
="
N21646
"
xml:space
="
preserve
">igr̄ ſcḋa pars ꝓportionalis eſt in ſubduplo ra
<
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/>
rior ꝙ̄ prima / qḋ fuit ꝓbãdū. </
s
>
<
s
xml:id
="
N2164B
"
xml:space
="
preserve
">Et ſic ꝓbabis / tertia
<
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/>
eſt in duplo denſior ꝙ̄ ſcḋa et quarta in duplo den-
<
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/>
ſior ꝙ̄ tertia: et ſic in infinitū. </
s
>
<
s
xml:id
="
N21652
"
xml:space
="
preserve
">igit̄̄ totū cõtinet infini
<
lb
/>
tã materiã ſub finita quantitate: et ꝑ ↄ̨ñs non eſt ra-
<
lb
/>
rū. </
s
>
<
s
xml:id
="
N21659
"
xml:space
="
preserve
">Oīs em̄ pars illius ꝓportionalis tantū cõtinet
<
lb
/>
de materia ſicut prīa / vt pꝫ calculatanti igit̄̄.
<
note
position
="
right
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xlink:href
="
note-0178-02a
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xlink:label
="
note-0178-02
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xml:id
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N2167B
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xml:space
="
preserve
">Dicitur</
note
>
</
s
>
<
s
xml:id
="
N21663
"
xml:space
="
preserve
">¶ Dices
<
lb
/>
et bñ negando ſequelã et ad ꝓbationē conceſſo añte
<
lb
/>
negãdo ↄ̨ñam / q2 ad raꝝ vniformiter difformi a cer
<
lb
/>
to gradu vſ ad non gradū ſeq̇tur ipſum eſſe rarū
<
lb
/>
et non rarum vt bene ꝓbat argumentum. </
s
>
<
s
xml:id
="
N2166E
"
xml:space
="
preserve
">Ad rarū
<
lb
/>
vero vniformiṫ difforme a gradu vſ certū gradū
<
lb
/>
illḋ nõ ſeq̇tur: nec aliud etiam incõueniens iõ negã-
<
lb
/>
da eſt ſimilitudo.</
s
>
</
p
>
<
p
xml:id
="
N21681
">
<
s
xml:id
="
N21682
"
xml:space
="
preserve
">Sꝫ ↄ̨̨tra </
s
>
<
s
xml:id
="
N21685
"
xml:space
="
preserve
">Q2 eadē rõe ſeq̄ret̄̄ / nõ poſ
<
lb
/>
ſet dari denſū vniformiter difforme a certo gradu
<
lb
/>
vſ ad non gradū: ſed ↄ̨ñs ē falſū: igr̄ et añs. </
s
>
<
s
xml:id
="
N2168C
"
xml:space
="
preserve
">Seq̄
<
lb
/>
la pꝫ / q2 non eſt maior ratio de raritate vniformiṫ
<
lb
/>
difformi a gradu vſ ad nõ gradū quã de dēſitate
<
lb
/>
vniformiter difformi a gradu vſ ad nõ graduꝫ: g̊
<
lb
/>
ſi vnū nõ eſt dabile: nec aliud cõcedēdū erit. </
s
>
<
s
xml:id
="
N21697
"
xml:space
="
preserve
">Sꝫ iã ꝓ
<
lb
/>
bat̄̄ falſitas conſequentis / q2 ad denſum vniformi-
<
lb
/>
ter difforme a certo gradu vſ ad nõ gradū nulluꝫ
<
lb
/>
ſeq̇tur incõueniens: igr̄ denſū vniformiter difforme
<
lb
/>
a certo gradu vſ ad nõ gradū ē poſſiblle. </
s
>
<
s
xml:id
="
N216A2
"
xml:space
="
preserve
">Et ſi ne
<
lb
/>
gas ad illud nullū ſequat̄̄ īcõueuiēs des illud / igr̄
<
lb
/>
inconueniēs / qḋ ſeq̇tur. </
s
>
<
s
xml:id
="
N216A9
"
xml:space
="
preserve
">et nõ poteris. </
s
>
<
s
xml:id
="
N216AC
"
xml:space
="
preserve
">q2 nõ ſequitur
<
lb
/>
illud quod ſequitur ad rarum vniformiter diffor-
<
lb
/>
me a certo gradu vſ ad non gradum: nec aliquod
<
lb
/>
aliud: igitur. </
s
>
<
s
xml:id
="
N216B5
"
xml:space
="
preserve
">Antecedens probatur / quia licet talis
<
lb
/>
vniformiter difformiter denſi etc. ſecunda pars pro
<
lb
/>
portionalis ꝓportione dupla ſit in ſubduplo den
<
lb
/>
ſior et per conſequens duplo rarior ꝙ̄ prima et ter-
<
lb
/>
tia in duplo rarior ꝙ̄ ſecunda: et quarta ꝙ̄ tertia et
<
lb
/>
ſic in infinitum: non tamen eo illud denſum vnifor-
<
lb
/>
miter difformiter etc. eſt infinite rarum. </
s
>
<
s
xml:id
="
N216C4
"
xml:space
="
preserve
">Continet
<
lb
/>
enim ſub finita quantitate aliquam materiam: vt
<
lb
/>
patet. </
s
>
<
s
xml:id
="
N216CB
"
xml:space
="
preserve
">igitur non ſequitur tale inconueniens / quod
<
lb
/>
fuit probandum.
<
note
position
="
right
"
xlink:href
="
note-0178-03a
"
xlink:label
="
note-0178-03
"
xml:id
="
N21727
"
xml:space
="
preserve
">.1. confir.</
note
>
</
s
>
<
s
xml:id
="
N216D5
"
xml:space
="
preserve
">¶ Et confirmatur </
s
>
<
s
xml:id
="
N216D8
"
xml:space
="
preserve
">Quia
<
lb
/>
ſi raritas et denſitas eſſent poſſibiles ſequeretur /
<
lb
/>
poſſet dari infinite denſum / ſed conſequens eſt fal-
<
lb
/>
ſum. </
s
>
<
s
xml:id
="
N216E1
"
xml:space
="
preserve
">igitur illud ex quo ſequitur falſitas conſequē
<
lb
/>
tio oſtenditur / q2 illud denſum īfinite eēt aliq̈liṫ ma
<
lb
/>
gnū. </
s
>
<
s
xml:id
="
N216E8
"
xml:space
="
preserve
">et poſſet eiꝰ pūcta adhuc mag approxīari et ad </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>