Alvarus, Thomas
,
Liber de triplici motu
,
1509
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<
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De motu augmentationis.
"
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0210
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n
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210
"/>
falſum: igr̄ ex illud quo ſequit̄̄. </
s
>
<
s
xml:id
="
N24AD9
"
xml:space
="
preserve
">Seq̄la ptꝫ / q2 tantã
<
lb
/>
quãtitatē ſupra totã p̄habitã acq̇rit medietas: ſic
<
lb
/>
totū: igr̄ medietas, et totū eq̄ velociṫ augent̄̄. </
s
>
<
s
xml:id
="
N24AE0
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xml:space
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">Ptꝫ
<
lb
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ↄ̨ña expoſitiõe. </
s
>
<
s
xml:id
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N24AE5
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xml:space
="
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">Sed ꝓbo falſitatē ↄ̨ñtis. </
s
>
<
s
xml:id
="
N24AE8
"
xml:space
="
preserve
">Tū ṗmo
<
lb
/>
q2 tūc ſeq̄ret̄̄ / eq̄ velociṫ augeret̄̄ totū ſicut in īfi-
<
lb
/>
nitū modica eiꝰ pars. </
s
>
<
s
xml:id
="
N24AEF
"
xml:space
="
preserve
">Sꝫ hoc vr̄ abſurdū: igr̄ illud
<
lb
/>
ex q̊ ſequit̄̄. </
s
>
<
s
xml:id
="
N24AF4
"
xml:space
="
preserve
">Seq̄la ptꝫ / q2 qñ totū acq̇rit vnū ſemipe
<
lb
/>
dale, medietas eiꝰ acq̇rit tm̄, et octaua et ſexdecima
<
lb
/>
termīata ad illã quantitatē acq̇ſitã, et ſic ↄ̨ñter: igr̄.
<
lb
/>
</
s
>
<
s
xml:id
="
N24AFC
"
xml:space
="
preserve
">Tū ſcḋo q2 ſtat / medietas alicuiꝰ intēdat̄̄ aliq̈liṫ
<
lb
/>
velociṫ acq̇rēdo aliquã intēſionē: tñ totū nõ acq̇rit
<
lb
/>
tantã. </
s
>
<
s
xml:id
="
N24B03
"
xml:space
="
preserve
">ergo eodē mõ ſtat in motu augmētatiõis
<
lb
/>
medietas aliqualiṫ velociṫ augeat̄̄, et totū nõ: et ꝑ
<
lb
/>
ↄ̨ñs illatū flm̄. </
s
>
<
s
xml:id
="
N24B0A
"
xml:space
="
preserve
">¶ Dices et bene ↄ̨cedēdo illatū in ta
<
lb
/>
li caſu: et ad ꝓbationē falſitatꝪ eiꝰ ↄ̨cedēdo illḋ ↄ̨ñs
<
lb
/>
vcꝫ / ita velociter auget̄̄ totū ſicut īfinite modica
<
lb
/>
eiꝰ pars ſignãter ſi hoc fiat ꝑ additionē quãtitatis
<
lb
/>
alicui medietati: ſicut ſit qñ aliq̇d addit̄̄ parti aīaĺ:
<
lb
/>
et augmētat̄̄ aīal. </
s
>
<
s
xml:id
="
N24B17
"
xml:space
="
preserve
">¶ Ad ſcḋam īprobationē cõcedo
<
lb
/>
<
gap
/>
q2 ſtat medietas
<
lb
/>
alicꝰ ītēdat̄̄ et nõ totū: et ſtat totū ītēdat̄̄ et vna eiꝰ
<
lb
/>
medietas nõ intēdat̄̄. </
s
>
<
s
xml:id
="
N24B21
"
xml:space
="
preserve
">Nõ tñ ſtat pars augmētet̄̄
<
lb
/>
ſine diminutiõe aliq̈ quī totū augmētet̄̄. </
s
>
<
s
xml:id
="
N24B26
"
xml:space
="
preserve
">Cõtra tūc
<
lb
/>
ſeq̄ret̄̄ / ſēꝑ eq̄ velociter augmētaret̄̄ aliqua pars
<
lb
/>
ſicut totū. </
s
>
<
s
xml:id
="
N24B2D
"
xml:space
="
preserve
">Sed ↄ̨ñs eſt flm̄: igr̄ illud ex q̊ ſequit̄̄. </
s
>
<
s
xml:id
="
N24B30
"
xml:space
="
preserve
">Fal
<
lb
/>
ſitas ↄ̨ñtis ꝓbat̄̄. </
s
>
<
s
xml:id
="
N24B35
"
xml:space
="
preserve
">Et volo / vtri medietati vnius
<
lb
/>
pedalis addat̄̄ ſemipedale in extremis oppoſitis:
<
lb
/>
tūc manifeſtū eſt totū acq̇rit pedalē quãtitatem
<
lb
/>
et nulla ꝑs eiꝰ acq̇rit pedalē quãtitatē: igr̄ nulla ꝑs
<
lb
/>
ibi auget̄̄ ita velociṫ ſicut totū: et ꝑ ↄ̨ñs nõ ſēꝑ eque
<
lb
/>
velociṫ etc̈. </
s
>
<
s
xml:id
="
N24B42
"
xml:space
="
preserve
">Seq̄la tñ ꝓbat̄̄: q2 ſi nõ ſēꝑ augmētaret̄̄
<
lb
/>
aliq̈ pars ita velociṫ ſicut totū: maxīe eſſet in caſu
<
lb
/>
in q̊ ꝓbat̄̄ falſitas ↄ̨ñtis: ſed in illo caſu eque velo-
<
lb
/>
citer augetur aliqua pars ſicut totum puta pars
<
lb
/>
que cõponitur ex duabꝰ quartis extremis cū parti-
<
lb
/>
bus extremalibꝰ q̄ ꝑtes extreme circūferētiales cõ-
<
lb
/>
ſtituūt vnū quadratū inṫ qḋ manet aliud vt ptꝫ in
<
lb
/>
<
figure
xlink:href
="
fig-0210-01a
"
xlink:label
="
fig-0210-01
"
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N24B9E
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number
="
12
">
<
image
file
="
0210-01
"
xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0210-01
"/>
</
figure
>
figura iã ſequenti: igr̄. </
s
>
<
s
xml:id
="
N24B58
"
xml:space
="
preserve
">¶ Dices et bñ
<
lb
/>
negãdo ſeq̄lã: et ad punctū ꝓbatiõis
<
lb
/>
dr̄ etiã in illo caſu eq̄ velociṫ au-
<
lb
/>
get̄̄ aliq̈ ꝑs ſicut totū / vt ꝓbat argu-
<
lb
/>
mētū: et ſic negat̄̄ / maxīe eſſet ī illo
<
lb
/>
caſu: ſed dico / eſt in caſu vbi totuꝫ
<
lb
/>
ꝑ totū rarefit: tūc em̄ nulla ꝑs ita velociṫ auget̄̄ ſi-
<
lb
/>
cut totū / vt ſatꝪ ptꝫ / quī ſi totū aliqḋ qḋ ꝑ totū rare-
<
lb
/>
fit rarefiat ad duplū: ipſū totū acq̇rit tantã quãti-
<
lb
/>
tatē ſicut ipſū eſt: et nulla ꝑs acq̇rit quãtitatē
<
lb
/>
ſicut illud totū eſt. </
s
>
<
s
xml:id
="
N24B6F
"
xml:space
="
preserve
">¶ Sed ↄ̈: q2 tūc ſeq̄ret̄̄ / qñ ali-
<
lb
/>
quid augmētaret̄̄ ꝑ rarefactionē q̄ rarefactio eſt ꝑ
<
lb
/>
totū ſubiectū quãtitas quã adeq̈te acq̇rit totū eſſet
<
lb
/>
mīma quã nõ acq̇rit aliq̄ ꝑs. </
s
>
<
s
xml:id
="
N24B78
"
xml:space
="
preserve
">Sed hoc vr̄ flm̄: igr̄ il-
<
lb
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lud ex quo ſequit̄̄. </
s
>
<
s
xml:id
="
N24B7D
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xml:space
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preserve
">Seq̄la pꝫ. </
s
>
<
s
xml:id
="
N24B80
"
xml:space
="
preserve
">q2 dato / totū acq̇rat
<
lb
/>
pedalē quãtitatē: manifeſtū eſt / vna medietas eiꝰ
<
lb
/>
acq̇ſiuit aliquã partē illiꝰ: et aggregatū ex illa me-
<
lb
/>
dietate et ṗma ꝑte ꝓportiõali alteriꝰ medietatꝪ acq̇
<
lb
/>
ſiuit maiorē: et aggregatū ex illa et duabus primis
<
lb
/>
ꝑtibꝰ ꝓportiõabilibꝰ alteriꝰ adhuc acq̇ſiuit maiorē /
<
lb
/>
et ſic ↄ̨ñter calculando. </
s
>
<
s
xml:id
="
N24B8F
"
xml:space
="
preserve
">Ptꝫ / quãtitas acq̇ſita ipſi
<
lb
/>
toti eſt minima quã nõ acquiſiuit aliqua pars.</
s
>
</
p
>
<
p
xml:id
="
N24BA4
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<
s
xml:id
="
N24BA5
"
xml:space
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">Octauo contra eandē partē q̄ſtionis
<
lb
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argr̄ ſic. </
s
>
<
s
xml:id
="
N24BAA
"
xml:space
="
preserve
">Qm̄ ſi velocitas augmētatiõis attēderet̄̄
<
lb
/>
penes abſolutã acq̇ſitionē quãtitatꝪ: ſeq̄ret̄̄ / qḋlꝫ
<
lb
/>
iſtoꝝ īciperet īfinite velociṫ augeri: et tñ īciperet in-
<
lb
/>
finitū tarde augeri aliqḋ iſtoꝝ: ſed ↄ̨ñs videt̄̄ re-
<
lb
/>
pugnare: igr̄ illud ex quo ſequit̄̄. </
s
>
<
s
xml:id
="
N24BB5
"
xml:space
="
preserve
">Seq̄la ptꝫ et volo /
<
lb
/>
ſint īfinita ↄ̨tinuo ſe habētia in ꝓportiõe ſubdu
<
lb
/>
pla: ita primū ſit pedale, ſcḋ3 ſemipedale, tertiū
<
lb
/>
q̈rta pedalis / et ſic ↄ̨ñter: et diuidat̄̄ hora ꝑ ꝑtes ꝓ-
<
lb
/>
portiõales ꝓportione dupla qḋlibet o illoꝝ diu
<
cb
chead
="
De motu augmentationis.
"/>
dat̄̄ ꝑ partes ꝓportiõales ꝓportiõe ſexquialtera: et
<
lb
/>
qḋlꝫ illoꝝ in q̈libet ꝑte ꝓportiõali hore ꝑdat vnaꝫ
<
lb
/>
partē ꝓportionalē ſui ꝓportiõe ſexq̇altera quouſ
<
lb
/>
in fine hore deueniat ad nõ quantū: deinde īcipiant
<
lb
/>
illa a nõ quãto augeri oīno ſicut diminuebant̄̄ pu-
<
lb
/>
ta in q̈libet ꝑte ꝓportiõali hore ꝓportiõe dupla ac
<
lb
/>
quirēdo vna ꝑte ꝓportiõalē ſui ꝓportiõe ſexq̇alte-
<
lb
/>
ra q̊ poſito argr̄ ſic: qḋlꝫ illoꝝ īmediate poſt illud
<
lb
/>
inſtãs augmētatiõis a nõ quãto in īfinitū velociter
<
lb
/>
augmētabit̄̄: et īmediate poſt tale inſtãs in infinitū
<
lb
/>
tarde augebit̄̄ aliqḋ illoꝝ: et mõ nullum illoꝝ aug-
<
lb
/>
mentat̄̄ igr̄ ꝓpoſitū. </
s
>
<
s
xml:id
="
N24BD9
"
xml:space
="
preserve
">Probat̄̄ maior: q2 qḋlꝫ illoꝝ
<
lb
/>
īcipit a nõ quãto in qualꝫ ꝑte ꝓportiõali ꝓportiõe
<
lb
/>
dupla acq̇rere ꝓportionē ſexq̇alterã: g̊ qḋlꝫ illoꝝ in
<
lb
/>
cipit in īfinitū velociṫ acq̇rere de quãtitate / vt ptꝫ ex
<
lb
/>
ſcḋa ↄ̨firmatiõe ſcḋi argumēti huiꝰ q̄ſtiõis et ꝑ ↄ̨ñs
<
lb
/>
qḋlꝫ illoꝝ īcipit in īfinitū velociṫ augeri qñ in īfini
<
lb
/>
tū velox augmētatio eſt in īfinitū velox acq̇ſitio quã
<
lb
/>
titatꝪ / vt ptꝫ ex hac poſitionē. </
s
>
<
s
xml:id
="
N24BEA
"
xml:space
="
preserve
">Probat̄̄ minor vcꝫ /
<
lb
/>
īmediate poſt hoc in īfinitū tarde acq̇ret aliqḋ iſto
<
lb
/>
rū de quãtitate q2 ↄ̨tinuo in īfinitū minꝰ primo erit
<
lb
/>
aliqḋ illoꝝ: ſicut fuit in via diminutiõis: et incipiunt
<
lb
/>
oīa illa a nõ quãto in eodē inſtãti augeri: g̊ quocū
<
lb
/>
inſtãti dato poſt hoc īter hoc et illud īfinite modicū
<
lb
/>
quãtitatē acq̇ſiuit aliqḋ illoꝝ: et ꝑ ↄ̨ñs īfinite tarde
<
lb
/>
auget̄̄ aliqḋ illoꝝ. </
s
>
<
s
xml:id
="
N24BFB
"
xml:space
="
preserve
">¶ Dices et bñ ↄ̨cedēdo illatū nec
<
lb
/>
illud eſt incõueniēs: ſed ſequēs / vt ꝓbat argumentū.
<
lb
/>
</
s
>
<
s
xml:id
="
N24C01
"
xml:space
="
preserve
">Sed ↄ̈ / q2 pari rõne ↄ̨cedendū eſſet / qḋ vnū et idem a
<
lb
/>
nõ quãto īciperet in īfinitū velociṫ augmētari: et il-
<
lb
/>
lud idē īciperet a nõ quãto in īfinitū tarde augmē-
<
lb
/>
tari. </
s
>
<
s
xml:id
="
N24C0A
"
xml:space
="
preserve
">ſed ↄ̨ñs eſt flm̄: igr̄ illud ex quo ſequit̄̄. </
s
>
<
s
xml:id
="
N24C0D
"
xml:space
="
preserve
">Falſi-
<
lb
/>
tas ↄ̨ñtis ptꝫ / q2 detur illud et ſit a. / et argr̄ ſic / a. inci
<
lb
/>
pit in īfinitū velociṫ augmētari: g̊ īcipit in infinitū
<
lb
/>
velociter acq̇rere de quãtitate: et ꝑ ↄ̨ñs nõ īcipit in
<
lb
/>
infinitū velociṫ acq̇rere de quãtitate: et ſic habet̄̄
<
lb
/>
īcipit ī īfinitū velociṫ acq̇rere de quantitate: et nõ
<
lb
/>
īcipit ī īfinitū velociṫ acq̇rē de quãtitate / qḋ īplicat
<
lb
/>
</
s
>
<
s
xml:id
="
N24C1D
"
xml:space
="
preserve
">Seq̄la tū ꝓbat̄̄ et volo / a. īcipiat augeri a nõ quã
<
lb
/>
to in aliqua hora diuiſa ꝑ partes ꝓportiõales ꝓ-
<
lb
/>
portiõe dupla ſiĺr vna medietas eiꝰ in qualꝫ ꝑte
<
lb
/>
ꝓportiõali pari acq̇rat ꝓportionē ſexq̇alterã: et al
<
lb
/>
tera medietas in q̈libet īpari acq̇rat octuplã quo
<
lb
/>
poſito argr̄ ſic / illud in tali caſu īcipit in īfinitū ve-
<
lb
/>
lociter augeri et etiã īcipit in īfinitū tarde augeri et
<
lb
/>
hoc a nõ quãto: igr̄ ꝓpoſitū. </
s
>
<
s
xml:id
="
N24C2E
"
xml:space
="
preserve
">Argr̄ maior / q2 incipit
<
lb
/>
in ꝑtibꝰ ꝓportiõalibꝰ paribꝰ īfinite velociṫ acq̇rere
<
lb
/>
de quãtitate / vt ptꝫ ex ſcḋa ↄ̨firmatiõe ſcḋi argumē
<
lb
/>
ti p̄allegati: igr̄ incipit in īfinitū velociter augeri.
<
lb
/>
</
s
>
<
s
xml:id
="
N24C38
"
xml:space
="
preserve
">Probat̄̄ mīor: q2 illud īcipit in īfinitū tarde acq̇re
<
lb
/>
re de quantitate in partibꝰ īparibꝰ / vt ptꝫ ex dedu-
<
lb
/>
ctione ṗme ↄ̨firmatiõis ſcḋi argumēti preallegati:
<
lb
/>
igr̄ īcipit illud īfinite tarde augeri in ꝑtibꝰ īparibꝰ
<
lb
/>
<
note
position
="
right
"
xlink:href
="
note-0210-01a
"
xlink:label
="
note-0210-01
"
xml:id
="
N24C7B
"
xml:space
="
preserve
">Confir-
<
lb
/>
matio.</
note
>
</
s
>
<
s
xml:id
="
N24C48
"
xml:space
="
preserve
">¶ Confirmat̄̄. </
s
>
<
s
xml:id
="
N24C4B
"
xml:space
="
preserve
">Q2 ſi illn poſito eſſet vera ſeq̇ret̄̄ /
<
lb
/>
nullū quadratū ꝑfectū poſſet vniformiṫ diminui
<
lb
/>
ad nõ quãtū qñ trina eiꝰ dimēſio puta lõgitudo la
<
lb
/>
titudo et ꝓfūditas vniformiṫ a nõ quãto diminuūt̄̄ /
<
lb
/>
ſed ↄ̨ñs eſt flm̄ / q2 nõ videt̄̄ repugnare tale quadra
<
lb
/>
tū vniformiter ſic diminui ad nõ quantū: igit̄̄ illud
<
lb
/>
ex quo ſequit̄̄. </
s
>
<
s
xml:id
="
N24C5A
"
xml:space
="
preserve
">Sequela tñ ꝓbatur: quia ſi aliquod
<
lb
/>
ſic poteſt diminui detur aliquod quadratū pedalr̄
<
lb
/>
lõgū, pedaliṫ latū, pedaliṫ ꝓfūdū, qḋ ſit a. </
s
>
<
s
xml:id
="
N24C61
"
xml:space
="
preserve
">Tūc ar̄
<
lb
/>
ſic / ↄ̨tinuo lõgitudo latitudo et ēt ꝓfūditas huiꝰ q̈-
<
lb
/>
drati a. vniformiṫ ī hora diminuit̄̄ vſ ad nõ ̄tū:
<
lb
/>
igr̄ in ṗma ꝑte ꝓportiõali hore ꝓportiõe dupla il-
<
lb
/>
lud q̈dratū efficit̄̄ in duplo minꝰ logū ī duplo minꝰ
<
lb
/>
latū. </
s
>
<
s
xml:id
="
N24C6E
"
xml:space
="
preserve
">in duplo minꝰ ꝓfundū: et ſic ꝑ ↄ̨ñs efficit̄̄ ī octu
<
lb
/>
plo minꝰ: et ꝑ ↄ̨ñs in ṗma medietate ꝑdit ſeptē octa
<
lb
/>
uas: et in ſcḋa medietate vnã tm̄: et ꝑ ↄ̨ñs in illa hõ
<
lb
/>
cõtinuo diminuit̄̄ vniformiṫ / qḋ fuit probandū</
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>