Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Tertii tractatus
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oīno eodē modo ſicut diminuebat̄̄ acq̇rendo vnifor
<
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miter quãtitatē ſicut eam deperdebat. </
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<
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xml:space
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">quo poſito
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arguit̄̄ ſic .a. in inſtanti initiatiuo alterius hore ſe-
<
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quentis incipit vniformiter acq̇rere quãtitatē quia
<
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vniformiter deperdit in hora priori cum poſitis in
<
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caſu: et tamen incipit in infinitū velociter augeri / vt
<
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patet ex principio huiꝰ ſecūdi argumēti: igit̄̄ ꝓpo
<
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/>
ſitum.
<
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note
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<
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xml:space
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">¶ Dices et bene cõcedēdo quod infertur: et ne
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gando illud repugnet. </
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<
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ſeq̇tur ex hac poſitiõe.</
s
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<
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">Sꝫ contra q2 tūc ſequeretur / quoti-
<
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/>
enſcun hora diuidit̄̄ ꝓportiõe dupla et aliq̇d inci
<
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/>
pit augeri a non quãto in qualibet parte ꝓportio-
<
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/>
nali acq̇rēdo vniformiter vnam ſui partē propor-
<
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/>
tionalē ꝓportione dupla: ip̄m incipit vniformiter
<
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acq̇rere quãtitatē: et cõtinuo vniformiter aquirit.
<
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<
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">Patet hoc / q2 in equalibꝰ partibꝰ tēporis equaleꝫ
<
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quãtitatē oīno acquirit: ſꝫ cõſequēs eſt falſum: igit̄̄
<
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/>
illud ex quo ſequit̄̄. </
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<
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xml:space
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">Falſitas ↄ̨ſequētꝪ arguitur: q2
<
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tunc ſeq̄retur / ſi duo inciperēt augeri a nõ quãto:
<
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/>
et vnū illorū in qualibet parte ꝓportionli tempo
<
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/>
ris ꝓportõe dupla iucipiēdo a minoribus acq̇reret
<
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/>
vniformiter vnã partē ꝓportionalē ſui ꝓportione
<
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/>
dupla ita in qualibet ꝑte ꝓportionali acq̇reret
<
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/>
proportionē duplã: et aliud in certa ꝓportione cõ-
<
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/>
tinuo velocius augeretur puta in qualibet parte ꝓ
<
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/>
portionali talis tēporis acquirēdo ꝓportionē qua
<
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/>
druplam vel octuplam cõtinuo: tunc illud quod in
<
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/>
certa proportiõe cõtinuo velocius augetur incipit
<
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/>
infinitū tarde acq̇rere de quãtitate: ſed ↄ̨ſequēs eſt
<
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/>
falſum: quia tūc ſequeret̄̄ / omne qḋ a nõ quãto in
<
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/>
cipit augeri: et in qualibet parte tēporis ꝓportio-
<
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/>
nali ꝓportione dupla maiorē ꝓportionē acquirit
<
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/>
quã dupla: ī īfinitū tarde acq̇reret de ̄titate quod
<
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/>
videt̄̄ oīno extraneū. </
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">Sequela tamē ꝓbat̄̄: et volo /
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/>
a. ſic incipiat augeri a nõ quãto: et ī qualibet ꝑte
<
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/>
ꝓportiõali tēporis ꝓportiõe dupla acq̇rat pro
<
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/>
portionē duplã acq̇rendo vniformiter de quãtitate
<
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/>
et .b. in omni ↄ̨ſimili parte tēporis acquirat maio
<
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/>
rem proportionē dupla puta triplã vel quadruplã
<
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/>
vel octuplã, in idē redit, quo poſito arguitur ſic .a.
<
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/>
et .b. incipiūt augeri a nõ quãto: et .b. in certa ꝓpor-
<
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/>
tione cõtinuo velocius augebitur ꝙ̄ a. / ergo ſeq̇tur /
<
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/>
a. incipit in infinitū eē maius ip̄o .b. / et ꝑ ↄ̨ſequēs
<
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/>
incipit in infinitū maiorē quãtitatē acq̇rere ipſo .b. /
<
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/>
vt patet ex vltima replica ſecundi argumēti: et vltra
<
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/>
ſequitur / in infinitū maiorē quãtitatē acquirit .a.
<
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/>
̄ .b. in eodē tempore: et a. cõtinuo vniformiter et eq̄
<
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/>
velociter acquirit quãtitatē: ergo .b. incipit in infi-
<
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/>
nitū tarde acq̇rere de quãtitate / quod fuit ꝓbandū.</
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">Cõfir° .2.</
note
>
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<
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">Confirmatur ſecundo / quia ſi poſitio
<
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eſſet vera ſequeret̄̄ / ſi a nõ quãto aliquid inciperet
<
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/>
augeri in qualibet parte ꝓportionali temporis ꝓ-
<
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/>
portiõe dupla diuiſi acquirēdo minorē ꝓportionē
<
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/>
̄ duplã: ip̄m inciperet in infinitū velociter acq̇rere
<
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de quãtitate: ſꝫ cõſequēs eſt falſum: igitur illud ex
<
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quo ſeq̇tur. </
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">Seq̄la ꝓbat̄̄ et capio .a. et .b. et volo / .a.
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incipiat augeri a nõ quãto in qualibet parte ꝓpor
<
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/>
tionali tēporis ꝓportiõe dupla diuiſi acq̇rendo vni
<
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formiter ↄ̨ſimilem partē ꝓportionalē ſui ꝓportio
<
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/>
ne dupla ita in qualibet tali parte tēporis acq̇-
<
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/>
rat vnã ꝓportionē duplã: et .b. in qualibet conſimili
<
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/>
parte tēporis acquirat vnã partē ꝓportionalē ſui
<
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ꝓportione minori dupla puta ſexquitertia vel ſex
<
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quialtera. </
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<
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xml:space
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">Quo poſito arguit̄̄ ſic .a. et .b. incipiunt
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augeri a nõ quãto: et b. ī certa ꝓportiõe cõtinuo tar
<
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/>
dius ip̄o .a. / igit̄̄ incipit eē in infinitū maius ipſio .a. /
<
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et per ↄ̨ſequens incipit in infinitū velociter maiorē
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Capi. ſecundum
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quãtitatē acq̇rere ꝙ̄ a. in eodem tēpore. </
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quentia vt prius: et a. cõtinuo certe velociter acq̇rit
<
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quãtitatē vt poſitū eſt: igit̄̄ .b. in infinitū velociter ac
<
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quirit quãtitatē / quod fuit ꝓbadū. </
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<
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">Sꝫ iam probo
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falſitatē cõſequētis: q2 tūc ſequeretur / ſi a. et b. in
<
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/>
ciperet a nõ quãto augeri: et a. in qualibet parte
<
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/>
ꝓportionali tēporis proportiõe dupla acquereret
<
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proportionē ſexquialterã: et b. in cõſimili parte cõ-
<
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/>
tinuo acq̇reret ꝓportiõeꝫ ſexquitertiã: tunc vtrun
<
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illorū inciperet infinite velociter acquirere de quã
<
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titate: et ꝑ cõſequēs .b. nõ īciperet velocius acq̇rere
<
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de quãtitate ꝙ̄ a. et ſic nõ inciperet in īfinitū eē maiꝰ
<
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/>
ipſo a. / quod eſt ↄ̨tra cõcluſionē ꝓbatã in vltima re
<
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plica ſecundi argumēti. </
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<
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quia nõ videt̄̄ poſſibile vtrū illorū inciperet in
<
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finite velociter acquirere de quãtitate: et tamē vnuꝫ
<
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illorum inciperet in infinitū velocius altero acqui-
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rere. </
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pit augeri a nõ quãto continuo in qualibet parte ꝓ-
<
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portionali tēporis ꝓportiõe dupla acquirēdo mi-
<
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norē ꝓportionem dupla: igitur.</
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">Cõfir° .3.</
note
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<
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">Confirmatur tertio / quia ſi poſitio eēt
<
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vera ſeq̄retur / quãtuncun magnū corpus ſit di
<
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/>
uiſum per partes ꝓportionales aliquã proportio
<
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ne: et aliud quãtuncū parū diuiſum per partes
<
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ꝓportionales aliqua proportione minori: in infini
<
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tū maior eſt aliqua pars proportionalis minoris
<
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parte proportionali correſpõdente maioris: ſꝫ cõ-
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ſequens apparet falſum: igitur illud ex quo ſequit̄̄
<
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</
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<
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">Sequela probatur / q2 ſi non detur vnū cētupedale
<
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diuiſum ꝑ partes proportionales proportiõe qua
<
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durupla: et vnū ſemipedale vel quãtūcū paruum
<
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/>
volueris diuiſum ꝑ partes portionales proportio
<
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/>
ne ſexquitertia ſeu quauis alia proportiõe minori
<
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quadrupla: et diminuãtur illa duo vſ ad nõ ̄tuꝫ
<
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/>
ita maius cõtinuo in qualibet parte proportio-
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nali tēporis proportiõe dupla vnã ſui partiē pro-
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portionalē perdat ꝑdēdo proportionē quadruplã
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et ſemipedale in qualibet parte cõſimili perdat ꝓ-
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portionē ſexquitertiã ꝑdendo vnam partē propor-
<
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/>
tionalē ſui proportiõe ſextertia quouſ veniãt ad
<
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/>
nõ quãtū: tūc volo / īcipiãt oīno eodē modo acqui
<
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/>
rere quãtitates deperditas et oīno eodē modo au-
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geri ſicut diminuebant̄̄. </
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<
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xml:space
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">Quo poſito arguitur ſic
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illud / qḋ fuit cētupedale: et illḋ quod fuit ſemipe
<
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dale incipit in certa portiõe tardius cõtinuo auge-
<
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ri ꝙ̄ centupedale: igit̄̄ illud qḋ fuit ſemipedale inci
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pit in infinitū eē maius illo altero quod fuit centi-
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pedale: et illud qḋ fuit centipedale incipit acquire-
<
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re partes proportionales proportiõe quadrupla
<
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quas antea ṗdidit: et illḋ qḋ fuit ſemipedale īcipit
<
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acq̇rere partes proportionales proportione ſexq̇-
<
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tertia quas antea deꝑdit: igit̄̄ incipit in infinitum
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maiores partes acquirere illud quod fuit ſemipe-
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dale ꝙ̄ illud qḋ fuit centipedale. </
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<
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">Patet cõſequētia /
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q2 immediate poſt illud qḋ fuit ſemipedale in infi-
<
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nitū erit maius illo qḋ fuit centipedale. </
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<
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xml:space
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">igit̄̄ imme-
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diate poſt hoc in infinitū maiores erunt partes pro
<
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portiõales illius proportiõe ſexquitertia partibꝰ
<
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proportionalibꝰ alterius proportiõe quadrupla:
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et tales partes īcipit acq̇rere: et ſemꝑ acq̇runt par-
<
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tes correſpõdētes ſicut deperdebãt: igit̄̄ in infinitū
<
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maior eſt aliqua pars proportionalis minoris ꝑ-
<
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te proportionali correſpõdente maioris quod fuit
<
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probandum.</
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<
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ſic. </
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<
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">Si illa poſitio eſſet vera ſeq̄retur hec cõcluſio </
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