Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Secundi tractatus
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mīore velocitate quã in ſecūda / et ſic cõſequēter: tūc
<
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ſpaciū ꝑtranſitū in totali hora ſe habet ad ſpaciū
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ꝑtranſitū in prima parte ꝓportionali in ꝓportiõe
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ſuꝑtripartiente quartas, qualis eſt .7. ad .4. </
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<
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xml:space
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batur / q2 ſpaciū ꝑtranſitū in prima parte ꝓporti-
<
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/>
onali ſe habet ad ſpaciū ꝑtranſitū in ſecunda in ꝓ
<
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/>
portiõe dupla ſexquitertia, et in eadē ꝓportione ſe
<
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/>
habet ſpaciū ꝑtranſitū in ſeeunda ad ſpaciū ꝑtrã
<
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/>
ſitum in tertia, et ſic cõſequenter: igitur totale ſpa-
<
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/>
ciū ſe habet ad ſpaciū ꝑtranſitū in prima parte ꝓ
<
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portiõali in ꝓportione ſupratripartiēte quartas
<
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</
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<
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xml:space
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">Patet hec cõſequentia ex priori cõcluſione: hoc ad
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dito / quodlibet corpus diuiſū per partes ꝓpor-
<
lb
/>
tionales ꝓportiõe dupla ſexquitertia ſe habet ad
<
lb
/>
primã partē ꝓportionalē in ꝓportione ſuꝑtripar
<
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tiente quartas: vt facile eſt intueri ex prima parte
<
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/>
huiꝰ operis. </
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<
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<
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xml:space
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portio prime partis tēporis ad ſecundã eſt ſuꝑbi-
<
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partiens tertias, et velocitatis prime partis ad ve
<
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/>
locitatē ſecunde eſt ꝓportio ſuꝑbipartiens quītas /
<
lb
/>
igitur totius ſpacii ꝑtranſiti in prima parte ꝓpor
<
lb
/>
tionali que eſt maius tēpus ad ſpaciū ꝑtranſitū in
<
lb
/>
ſecunda parte ꝓportionali eſt ꝓportio dupla ſex-
<
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/>
q̇tertia: et ſic ꝓbabis de ſpaciis ꝑtranſitis in aliis
<
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/>
partibꝰ quibuſcū īmediatis. </
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>
<
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xml:space
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preserve
">Cõſequentia ꝓbat̄̄ /
<
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ꝑ tertiã ꝓpoſitionē ſecūdi notabilis huiꝰ q̄ſtionis
<
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/>
hoc addito / proportio dupla ſexq̇tertia cõponit̄̄
<
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/>
adequate ex ꝓportione ſuꝑbipartiente tertias, et
<
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/>
ſuꝑbipartiente quintas: vt ptꝫ in his terminis .7.
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/>
.5.3. / et ſic ptꝫ correlariū
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xml:space
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">2. correĺ.</
note
>
</
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<
s
xml:id
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xml:space
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preserve
">¶ Sequitur ſecundo / diui
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ſa hora ꝑ partes ꝓportionales ꝓportione dupla
<
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mobili cõtinuo in duplo tardius mouente in parte
<
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/>
ſequēti minori quã in parte maiori īmediate prece
<
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/>
denti illã: ſpaciū ꝑtranſitū in totali hora ſe habet
<
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/>
ad ſpaciū ꝑtranſitū in prima parte proportionali
<
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/>
hore in ꝓportione ſexquitertia. </
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>
<
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xml:space
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">Probatio / q2 pro
<
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portio cõpoſita ex ꝓportione tēporis maioris ad
<
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/>
tēpus minꝰ dupla, et velocitatis temporis maioris
<
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/>
ad velocitatē tēporis minoris ſimiliter dupla eſt
<
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/>
quadrupla, vt ſatis ↄ̨ſtat: et quodlibet totū diuiſū
<
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/>
ꝑ partes ꝓportionales ꝓportione quadrupla ſe
<
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/>
habet ad primã partē ꝓportionalē in proportione
<
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/>
ſexquitertia, vt ptꝫ ex prima parte: igr̄ totale ſpa-
<
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/>
ciū ꝑtranſitū in illa hora in caſu correlarii ſe ha-
<
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/>
bet ad ſpaciū ꝑtranſitū in prima parte ꝓportiõali
<
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/>
in ꝓportione ſexquitertia / quod fuit ꝓbandū. </
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>
<
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ſequentia ptꝫ ex cõcluſione octaua </
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<
s
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xml:space
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preserve
">¶ Sequit̄̄ tertio
<
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/ diuiſa hora in partes ꝓportionales ꝓportione
<
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/>
tripla, mobili cõtinuo in quadruplo tardiꝰ mo-
<
lb
/>
uēte in parte ſequenti minori ꝙ̄ in īmediate p̄ceden
<
lb
/>
ti eã: ſpaciū ꝑtranſitū in totali hora ſe habebit ad
<
lb
/>
ſpaciū ꝑtranſitū in prima parte ꝓportionali in ꝓ
<
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/>
portione ſexquivndecima: pertranſito pedali in
<
lb
/>
prima: duodecim vndecimas pedalis ī totali hora
<
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abſoluet. </
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<
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">Probatur / q2 ꝓportio cõpoſita ex ꝓpor
<
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tione tēporis maioris ad tēpus minꝰ tripla et velo-
<
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/>
citatis tēporis maioris ad velocitatē tēporis mi-
<
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/>
noris quadrupla eſt duodecupla, vt patet in his
<
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/>
terminis .12.4.1. et quodlibet totū diuiſuꝫ ꝑ partes
<
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/>
ꝓportionales ꝓportione duodecupla ſe habet ad
<
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primã ſui partē ꝓportionalē in ꝓportione ſexqui
<
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/>
vndecima, vt ptꝫ ex prima parte: igitur ſpaciū per
<
lb
/>
tranſitū a mobili in totali tēpore ſe habet ad ſpa
<
lb
/>
cium ꝑtranſitum in prima parte proportionali in
<
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/>
proportione ſexquivndecima. </
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>
<
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ex octaua concluſione.</
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">Nona concluſio. </
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<
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xml:space
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">Diuiſa hora per par
<
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tes ꝓportiõales q̈uis ꝓportione, et in certa ꝓpor-
<
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/>
tiõe ↄ̨tinuo mobile velociꝰ moueat̄̄ ī qualibet parte
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Capitulū tertiū.
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pari ſequenti quã in pari īmediate precedenti eaꝫ
<
lb
/>
et ſimiliter in certa proportione equali maiori, vel
<
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/>
minori, continuo in qualibet parte ſequente impa
<
lb
/>
ri velocius moueatur quã in impari īmediate pre-
<
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/>
cedenti: ſpaciū pertranſitū in totali hora erit infi-
<
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/>
nitū dūmodo ꝓportio velocitatū ſit equalis pro-
<
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/>
portioni tempoꝝ vel maior: et ſi ꝓportio velocita-
<
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/>
tum partiū pariuꝫ, et ꝓportio velocitatū partium
<
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/>
impariū fuerit minor ꝓportione tempoꝝ: tunc ſpa
<
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/>
cium pertranſitū in omnibus partibus paribus ſe
<
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/>
habet ad ſpaciū pertranſitū in prima illaꝝ pariū
<
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/>
in ꝓportione qua ſe habet aliquod totum diuiſuꝫ
<
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/>
per partes ꝓportionales ꝓportione per quã pro-
<
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/>
portio tempoꝝ excedit ꝓportionē velocitatum ad
<
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primã partē ꝓportionale eiuſdē totius. </
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<
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xml:space
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">Et ſimili-
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ter dicendū eſt de ſpacio ꝑtranſito in omnibꝰ par-
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tibus imparibus. </
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<
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">Declaratur hec cõcluſio iſto mo
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do: diuidatur hora per partes proportionales
<
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/>
proportione dupla, et capiantur ex vno latere oēs
<
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/>
ꝑtes pares: et ex alio oēs īpares, et in qualibet īpa
<
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/>
ri ſequente moueatur a. mobile in quadruplo velo
<
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/>
cius quã in impari īmediate precedenti eam: tunc
<
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/>
dicit prima pars concluſionis / illud mobile in
<
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/>
finitū ſpaciū ꝑtranſit et etiã infinitū ſpaciū tranſi-
<
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/>
ret ſi in qualibet ſequēti impari moueretur in quī-
<
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/>
tuplo velocius quã in impari īmediate precedenti
<
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/>
eam quia ꝓportio velocitatū eſt ibi maior vel equa
<
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/>
lis ꝓportioni tempoꝝ. </
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>
<
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">Tēpora em̄ illa continuo ſe
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habent in ꝓportione quadrupla. </
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>
<
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xml:space
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preserve
">Si vero mobile
<
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/>
in qualibet parte ſequeti impari moueretur in du-
<
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/>
plo velociꝰ preciſe ꝙ̄ in parte īmediate precedenti
<
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/>
impari, diuiſione ſic facta in partes ꝓportionales
<
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/>
ꝓportione dupla: tunc ſpaciū ꝑtranſitū in omnibꝰ
<
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/>
partibus paribus ſe habet ad ſpaciū ꝑtrauſitū
<
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/>
in prima pari in ꝓportione dupla: et ſpaciū ꝑtran
<
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/>
ſitum in omnibus partibus imparibus etiã ſe ha-
<
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/>
bet ad ſpaciū pertranſitū in prima impari in pro-
<
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/>
portione dupla: quia proportio tempoꝝ quadru-
<
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/>
pla excedit ꝓportionem velocitatū duplam ꝑ du-
<
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/>
plam: et corpus diuiſum per partes ꝓportionales
<
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/>
ꝓportione dupla ſe habet ad primã partē propor
<
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/>
tionalem etiam in ꝓportione dupla, et etiã veloci-
<
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/>
tas maior eſt coextenſa tempori minori. </
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>
<
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xml:space
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preserve
">Ideo to-
<
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/>
tum ſpaciū pertranſitū in omnibus partibus im-
<
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/>
paribus eſt duplū ad ſpaciū ꝑtranſitū in prima
<
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illarū impariū. </
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>
<
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xml:space
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preserve
">Et conſimiliter dicendum eſt de pa
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ribus. </
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>
<
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xml:space
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">Probatur hec concluſio ex predictis, et hoc
<
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generaliter: et primo patet prima pars ex ſexta
<
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/>
concluſione: et ſecunda ex ſeptima.
<
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note-0161-02
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xml:id
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xml:space
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">1. correĺ.</
note
>
</
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<
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xml:space
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preserve
">¶ Ex hac conclu
<
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ſione ſequitur primo / partita hora per partes ꝓ
<
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/>
portionales ꝓportione dupla: et in prima illarum
<
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/>
mobile moueatur aliquanta velocitate vuiformi-
<
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/>
ter, et in ſecūda moueat̄̄ vniformiter intēdendo mo
<
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/>
tū ſuū a gradu quo mouetur in prima vſ ad gra-
<
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/>
dum duplū: et in tertia moueatur illo gradu duplo
<
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/>
vniformiter: et in quarta intendat vniformiter mo-
<
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/>
tum ſuū ab illo gradu duplo vſ ad gradū duplū
<
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/>
illius, ita in omnibus partibus imparibus mo-
<
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/>
ueatur vniformiter continuo in duplo velocius in
<
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/>
ſequente impari ꝙ̄ īmediate precedenti impari, et
<
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/>
in qualibet parte pari moueatur intendendo mo-
<
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/>
tum ſuum vniformiter a gradu partis imparis im
<
lb
/>
mediate precedentis vſ ad gradum partis paris
<
lb
/>
īmediate ſequentis: ita velocitates partium im-
<
lb
/>
parium reducte ad vniformieatem etiam ſi habe-
<
lb
/>
ant continuo in proportione dupla: tunc ſpacium
<
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/>
totale pertranſitum in hora ſe habebit in propor-
<
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/>
tione tripla ſexquialtera ad ſpacium pertranſi-
<
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/>
tum in prima parte proportionali impari. </
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