Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Tertii tractatus
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175
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tionabiliter ſicut raritas augetur ita et dēſitas di
<
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minuit̄̄ / g̊ raritas et denſitas nõ ſunt poſitiua. </
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>
<
s
xml:id
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N2101A
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xml:space
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preserve
">Con
<
lb
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ſequētia eſt nota cū minori, et argr̄ maior / q2 ſi illḋ
<
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eſſet poſſibile de aliquibꝰ poſitiuis: hoc maxīe eſſet
<
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qñ maiꝰ diminuit̄̄ et minꝰ auget̄̄ ſicut dictū eſt in ſo-
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lutione: ſed hoc nõ: igr̄. </
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>
<
s
xml:id
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N21025
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xml:space
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preserve
">Probat̄̄ minor / q2 vel illud
<
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minꝰ qḋ augetur ſemꝑ in augmentatione manebit
<
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minꝰ altero, vel aliqñ deueniet ad equalitatē: ſi cõ-
<
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tinuo illud qḋ augetur erit minꝰ illo qḋ diminuitur
<
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/>
et ita velociter diminuit̄̄ maiꝰ ſicut augetur minus
<
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/>
ſequit̄̄ / cõtinuo in toto illo tꝑe in quo erit minus
<
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/>
ipſum velociꝰ ꝓportiõabiliter augebit̄̄ ꝙ̄ aliud di-
<
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/>
minuitur volo dicere in quolibet inſtãti intrinſeco
<
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illiꝰ tēporis: ptꝫ hec ↄ̨ña regulã geometricã. </
s
>
<
s
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N21038
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xml:space
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">Qñcū
<
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aliqua latitudo demit̄̄ a maiori et addit̄̄ minori
<
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ipſo manēte minori ꝙ̄ illud ad quo demit̄̄ illa latitu
<
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/>
do cõtinuo maiorē ꝓportionē acquirit illud minꝰ
<
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̄ deꝑdat illud maiꝰ. </
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>
<
s
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N21043
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xml:space
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preserve
">Quod ptꝫ / q2 ſi poſt̄ illa la
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titudo eſt addita minori addat̄̄ tanta latitudo illi
<
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/>
maiori a quo fuit dēpta, minorē ꝓportionē acq̇ret
<
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/>
illud maiꝰ ꝙ̄ deꝑdet illud minꝰ: g̊ qñ maius deꝑdat
<
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/>
illã latitudinē et minꝰ acq̇rit eandē maiorē ꝓporti-
<
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/>
onē acq̇rit minꝰ ꝙ̄ deꝑdat maiꝰ, cū nõ deꝑdat niſi
<
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/>
illã quã acq̇ſiuit: igr̄ illa regula eſt vera. </
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>
<
s
xml:id
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N21052
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xml:space
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preserve
">Si aūt illa
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ꝑueniant ad equalitatē, iã nõ eque velociter et eque
<
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ꝓbationabiliter vnū illoꝝ augebitur ſicut aliud di
<
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/>
minuitur / vt ꝓbatū eſt in argumento
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xml:space
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matio</
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<
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xml:space
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">¶ Cõfirmatur
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</
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<
s
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xml:space
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">Quia raritas et denſitas inter ſe nõ differūt cū idē
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ſit ꝓpinquitas punctoꝝ et diſtantia eorūdē: igr̄ ille
<
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nõ ſunt qualitates poſitiue.
<
note
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xml:id
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N210E8
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xml:space
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matio</
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</
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<
s
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N21070
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xml:space
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">¶ Cõfirmat̄̄ ſcḋo. </
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>
<
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="
N21073
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xml:space
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">Q2
<
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ſi eſſent qualitates eſſent cõtrarie: ſed hoc eſt falſū /
<
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/>
q2 tūc nullū rarū eſſet denſum et eocõtra et aliquid
<
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/>
eſſet qḋ nõ eſſet rarū ne dēſum : q2 rarū et denſum
<
lb
/>
eſſent termini cõtrarii.
<
note
position
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left
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xlink:href
="
note-0175-03a
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note-0175-03
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xml:id
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N210F0
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xml:space
="
preserve
">3. confir-
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matio</
note
>
</
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<
s
xml:id
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xml:space
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">¶ Cõfirmatur tertio. </
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>
<
s
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N21086
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xml:space
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">Quia
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tūc ſeq̇tur / poſſibile eſt dare rarū vniformiter dif
<
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forme a certo gradu vſ ad nõ gradū, vt ab octa-
<
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/>
uo vſ ad nõ gradū: ſed ↄ̨ñs eſt falſū: g̊ et illud ex q̊
<
lb
/>
ſeq̇tur. </
s
>
<
s
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N21091
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xml:space
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">Cõſequētia ꝓbatur: q2 oīs qualitas corpo-
<
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rea poteſt eſſe vniformiter difformis a certo gradu
<
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/>
vſ ad nõ gradū: ſed raritas eſt huiuſmodi per te
<
lb
/>
igr̄. </
s
>
<
s
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N2109A
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xml:space
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">Maior ptꝫ / q2 vbicū eſt qualitas vniformis:
<
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ibi eſt vna medietas intenſiua vniformiter diffor-
<
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mis a maximo gradu quē hꝫ illa qualitas vſ ad
<
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/>
nõ gradū: vt ptꝫ iutuenti. </
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<
s
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N210A3
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xml:space
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">Sed iam argr̄ falſitas cõ
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ſequentis / q2 ſit illud a. / et arguo ſic / illud eſt vniformi
<
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ter difformiter rarū ab octauo vſ ad nõ gradū: g̊
<
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prima pars ꝓportionalis eiꝰ eſt aliqualiter rara et
<
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ſcḋa in duplo minꝰ rara, et tertia in duplo minꝰ ra-
<
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ra ꝙ̄ ſcḋa, et ſic ↄ̨ñter / vt ptꝫ de albedine vniformiter
<
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/>
difformi ab octauo vſ ad nõ g̈dū, et ꝑ ↄ̨ñs ṗma ꝑs
<
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ꝓportiõalis eſt aliq̈liṫ denſa, et ſcḋa in duplo den
<
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ſior, et tertia in duplo denſior ꝙ̄ ſcḋa. etc̈. / igr̄ a. eſt
<
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infinite denſū q2 infinitã materiã cõtinet ſub finita
<
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quãtitate, nã q̄libet pars ꝓportionalis cõtinet tan
<
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tam materiã ſicut prima: q2 in quacū ꝓportione
<
lb
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aliqua pars ꝓportiõalis eſt minor prima in eadē
<
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eſt denſior prima, et vltra a. eſt īfinite denſum: g̊ nõ
<
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eſt rarū, et ſic nõ eſt vniformiter difformiter rarum /
<
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quod eſt oppoſitū cõceſſi.
<
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xml:id
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xml:space
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preserve
">4. confir
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matio.</
note
>
</
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<
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N210C9
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xml:space
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">¶ Cõfirmatur quarto / q2
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rarū eſt qḋ ſub magna quãtitate cõtinet parum de
<
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materia, denſum vero eſt / ſub parua quãtitate cõ
<
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tinet multū de materia: et hoc deſcribendo rarū et
<
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denſum: g̊ dato a. nullã qualititatē haberet et ſub
<
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finita quantitate finitam materiam contineret ad
<
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huc illud eſſet rarum et denſum, vt facile deducitur
<
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ex deſcriptione rari et denſi: igitur raritas et den-
<
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ſitas nõ ſunt qualitates nec poſitiue ſe habent.</
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>
</
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<
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">Scḋo prīcipaliter. </
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>
<
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">Tangēdo penes
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quid maioritas raritatis et dēſitatis attēdat̄̄ argr̄
<
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="
Capitulū primū.
"/>
ſic. </
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<
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xml:space
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">Si raritas et denſitas eſſent poſſibiles vel ī qua
<
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cun ꝓportione raritas efficitur maior: ꝓportio
<
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quãtitatis ad materiã efficiret̄̄ maior, et nõ quãti-
<
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tas in illa ꝓportione, vel in quacū ꝓportione ra
<
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ritas efficit̄̄ maior: quãtitas efficit̄̄ maior. </
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>
<
s
xml:id
="
N21117
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xml:space
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">Sed neu
<
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trū iſtoꝝ eſt dicendū: igr̄ raritas et denſitas nõ ſūt
<
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/>
poſſibiles. </
s
>
<
s
xml:id
="
N2111E
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xml:space
="
preserve
">Minor ptꝫ / q2 iſte due ſunt famate opi-
<
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niones quas maior tangit de maioritate et minori
<
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tate raritatis et nõ plures ꝓ nūc practicantur. </
s
>
<
s
xml:id
="
N21125
"
xml:space
="
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">Sed
<
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/>
iam ꝓbatur minor: et primo nõ in quacū ꝓpor
<
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tione raritas efficitur maior proportio quãtitatis
<
lb
/>
ad materiã efficitur maior: q2 tūc ſeq̄retur / ad du
<
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/>
plationē raritatis nõ ſeq̄retur duplatio quãtita-
<
lb
/>
tis q2 aliqñ ſequitur magis ꝙ̄ duplatio quantita-
<
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tes, et aliqñ minꝰ, et aliqñ adequata duplatio: igr̄.
<
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/>
</
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>
<
s
xml:id
="
N21135
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xml:space
="
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">ſed ↄ̨ñs eſt falſū: igr̄. </
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>
<
s
xml:id
="
N21138
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xml:space
="
preserve
">Falſitas ↄ̨ñtis argr̄ / q2 rarum
<
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eſt qḋ ſub magna quãtitate cõtinet modicū de ma-
<
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teria, ergo illud erit in duplo magis rarum quod
<
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/>
ſubdupla maiori quantitate ↄ̨tinet equale de ma-
<
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/>
teria, et ſic ſemꝑ ad duplationē raritatis ſequitur
<
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/>
duplatio quãtitatꝪ. </
s
>
<
s
xml:id
="
N21145
"
xml:space
="
preserve
">Sed iam ꝓbo ſequelã: et capio
<
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/>
vnū pedale cuiꝰ quãtitatis ad materiã ſit ꝓportio
<
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/>
ſexq̇altera et volo / dupletur eiꝰ raritas quo po-
<
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/>
ſito argr̄ ſic / quãtitas illiꝰ pedalis nõ efficitur in du
<
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/>
plo maior: ſed p̄ciſe in ſexq̇altero maior: igr̄ ꝓpoſi
<
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tum. </
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>
<
s
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="
N21152
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xml:space
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">Probat̄̄ añs, q2 in fine ꝓportio quantitatis
<
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ad materiã erit dupla ad ſexquialterã puta dupla
<
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ſexquiq̈rta: g̊ ſeq̇tur, p̄ciſe quãtitas acq̇ſiuit pro
<
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portionē ſexq̇alterã et nõ duplã. </
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>
<
s
xml:id
="
N2115B
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xml:space
="
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">Ptꝫ ↄ̨ña / q2 ꝓpor-
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tio quãtitatis ad materiã in fine cõponitur ex dua
<
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bus ſexq̇alteris: et iã quãtitas ad materiã habebat
<
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ꝓportionē ſexquialterã: g̊ modo p̄ciſe acq̇ſiuit ſexq̇al
<
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terã ſupra ſe. </
s
>
<
s
xml:id
="
N21166
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xml:space
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">Probat̄̄ ſcḋa / q2 ſi acq̇ſiuiſſet duplaꝫ
<
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/>
ꝓportionē ſupra ſe in fine ꝓportio quantitatis ad
<
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/>
materiã fuiſſet tripla q̄ ex dupla et ſexq̇altera cõpo
<
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/>
nitur et ſic nõ ad duplationē raritatis fuiſſet ſequu
<
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/>
ta duplatio ꝓportionis cū tripla ſit maior ꝙ̄ du-
<
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/>
pla ad ſexq̇alterã / vt pꝫ ex ſecūda parte huiꝰ operꝪ
<
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/>
et ſic ſeq̇tur / ad duplationē raritatis aliqñ ſeq̇tur
<
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minꝰ ꝙ̄ duplatio quãtitatis. </
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>
<
s
xml:id
="
N21177
"
xml:space
="
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">Q, vero aliqñ
<
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ſeq̈tur p̄ciſe duplatio quãtitatis ꝓbatur ponendo
<
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/>
ꝓportio quãtitatis ad materiã ſit dupla, et du
<
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/>
pletur raritas, et ſic habebitur intentū. </
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>
<
s
xml:id
="
N21180
"
xml:space
="
preserve
">Nã tūc ꝓ-
<
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portio quãtitatis ad materiã efficeretur quadru-
<
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pla q̄ eſt dupla ad duplã, et iã antea ꝓportio ̄tita
<
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/>
tis ad materiã fuit dupla adequate: g̊ modo acq̇ſi-
<
lb
/>
uit aliquã ꝓportionē duplã, et ſic ſeq̇tur / quãtitas
<
lb
/>
acq̇ſiuit duplã ꝓportionē ſupra ſe: qm̄ tantã acq̇ſi-
<
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/>
uit ſupra ſe quantam ſupra ſuam materiam. </
s
>
<
s
xml:id
="
N2118F
"
xml:space
="
preserve
">Sed
<
lb
/>
iam ꝓbo / nõ in quacū ꝓportione raritas effici
<
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/>
tur maior quãtitas efficitur maior: q2 alias ſeq̄ret̄̄ /
<
lb
/>
poſſet dari infinite rarū: ſed ↄ̨ñs eſt falſum: igr̄ et
<
lb
/>
illud ex quo ſeq̇tur. </
s
>
<
s
xml:id
="
N2119A
"
xml:space
="
preserve
">Seq̄la ꝓbatur et capio vnū pe-
<
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/>
dale vniforme ꝑ totū et volo / rarefiat in īfinitum
<
lb
/>
quo poſito illud erit īfinite raꝝ qm̄ ad duplationē
<
lb
/>
eiꝰ ſeq̇tur duplatio raritatis et ad triplationē quã
<
lb
/>
tatis ſeq̇tur triplatio raritatis / et ſic cõſequenter:
<
lb
/>
et acquiret̄̄ quãtitas īfinita: g̊ raritas īfinita. </
s
>
<
s
xml:id
="
N211A7
"
xml:space
="
preserve
">Sed
<
lb
/>
falſitas ↄ̨ñtis argr̄ et ſi illud eſt infinite rarū: ſequit̄̄ /
<
lb
/>
nullã materiã cõtinet, et vltra nullã materiã cõti
<
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/>
net. </
s
>
<
s
xml:id
="
N211B0
"
xml:space
="
preserve
">g̊ nec eſt rarū nec eſt dēſum. </
s
>
<
s
xml:id
="
N211B3
"
xml:space
="
preserve
">Conſequētia ptꝫ et
<
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/>
argr̄ ſeq̄la qm̄ vt ſuppono ipſum eſt vniforme, et
<
lb
/>
vniformiter rarefactū: ſi igr̄ hꝫ aliquã materiaꝫ in
<
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/>
aliqua parte ſui cū ipſum ſit vniforme: ſeq̇tur / in
<
lb
/>
qualibet tanta ſui parte hꝫ tantaꝫ ſicut ipſa eſt: et
<
lb
/>
ſunt infinite partes illi parti equales: g̊ ſeq̇tur /
<
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/>
hꝫ īfinitã materiã, et ſic eſt īfinite raꝝ / qḋ fuit ꝓbandū</
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>
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