Alvarus, Thomas
,
Liber de triplici motu
,
1509
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De motu locali mixto difformi tꝑe ſubiecto quo ad effectū
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<
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xml:space
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">Sed cõtra / q2 tūc ſequeretur / ſtaret
<
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ī caſu ſortē valde fatigari nitendo moueri nullo im
<
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/>
pedimēto poſito imo ipſo ſorte habēte optimã diſ
<
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poſitionē. </
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<
s
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N207EC
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xml:space
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">ad currenduꝫ et ad mouēdū: et tñ nullo pa
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cto moueri: ſed hoc ē falſuꝫ igitur. </
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<
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<
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q2 ſi nullū ē īpedimentū: et ſortes nitit̄̄ moueri: ſeq̇t̄̄ /
<
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ipſe ſortes mouetur. </
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>
<
s
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xml:space
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">Itē ſortes fatigat̄̄: et nõ niſi
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q2 mouetur: igr̄ ſortes mouetur </
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<
s
xml:id
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xml:space
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">Seq̄la tñ ꝓbatur et
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pono caſu / ſortes ſit in naui q̄ moueat̄̄ ſus oriē-
<
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tē: et ſortes nitatur moueri ſus occidentē. </
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<
s
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xml:space
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<
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tes deſcribat aliquod ſpaciū in ipſa naui ita velo
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citer ſicut nauis mouetur adequate: et moueat̄̄ na-
<
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uis ita velociter ſortes fatigetur plurimū. </
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<
s
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xml:space
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<
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poſito arguitur ſic / ſortes fatigatur nitendo moue
<
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ri nullo īpedimēto poſito et tñ nõ mouetur igr̄. </
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<
s
xml:id
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N20814
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xml:space
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">Mi-
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nor ꝓbatur / q2 ſortes ſemꝑ eſt in eodē loco reſpectu
<
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ſpacii fixi ex quo debet ſumi idētitas loci et īmobili
<
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tas. </
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>
<
s
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xml:space
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">vt patet ꝑ phm̄ quarto phiſicoꝝ dicentē locū eē
<
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terminū cõtinētis īmobilē ṗmū: igitur ſortes ī tali
<
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/>
caſu nõ mouet̄̄ (nullū eī ſpaciū fixū deſcribit) / igitur</
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</
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<
p
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<
s
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xml:space
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">Tertio prīcipalit̄̄ ↄ̨̨tra eadē ꝑtē q̄ſtio
<
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nis arguitur ſic: q2 nullꝰ eſt motꝰ mixtus. </
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>
<
s
xml:id
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N2082A
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xml:space
="
preserve
">g̊ illa pars
<
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p̄ſupponit falſum et ꝑ ↄ̨ñs falſa. </
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<
s
xml:id
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xml:space
="
preserve
">Añs ꝓbatur / q2 ſi
<
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eſſet aliq̇s motus mixtus maxime eſſet motus cõpo
<
lb
/>
ſitus ex aſcenſu et deſcēſu: ſꝫ nullus eſt dabilis ta-
<
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/>
lis: igitur. </
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>
<
s
xml:id
="
N20838
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xml:space
="
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">Probat̄̄ minor / q2 ſi aliq̇s talis eēt dabi
<
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lis: ſeq̄retur / dabile eēt vnū corpꝰ finitū cuius vna
<
lb
/>
pars aſcenderet et alia deſcenderet: et relictum ſue
<
lb
/>
naturali diſpoſitione ſic ꝑpetuo moueretur ↄ̨tinuo
<
lb
/>
vna ꝑte eiꝰ aſcendente et alia deſcendēte: ſꝫ ↄ̨ñs ē fal
<
lb
/>
ſum: igr̄ illḋ ex quo ſeq̇t̄̄. </
s
>
<
s
xml:id
="
N20845
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xml:space
="
preserve
">Seq̄la ꝓbatur et pono caſū /
<
lb
/>
terra ſit ꝑforata ꝑ cētrū mūdi ab oriēte in occidē
<
lb
/>
tē: et capiat̄̄ globꝰ terre vniformis grauitatis vĺ ali
<
lb
/>
cuiꝰ alteriꝰ figure (ī idē reddit) descēdat illa terra
<
lb
/>
ꝑ illḋ foramē vſ. ad cētrū mūdi illo foramīe vacuo
<
lb
/>
exñte ꝑmittat deꝰ illã terrã moueri tãdiu ̄diu ha
<
lb
/>
buerit ꝓportionē maioris ineq̈litatis ad mouēdū.
<
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</
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>
<
s
xml:id
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N20855
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xml:space
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">Quo poſito ſic argumētor. </
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>
<
s
xml:id
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N20858
"
xml:space
="
preserve
">illa terra ꝑpetuo moue
<
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/>
bit̄̄ ↄ̨tinuo vna ꝑte eiꝰ aſcēdēte et alṫa deſcēdēte: igr̄
<
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/>
ꝓpoſitū </
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<
s
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xml:space
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preserve
">Probat̄̄ añs / q2 īclinatio illiꝰ ṫre ē cētrū
<
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eiꝰ ſit cētrū mūdi: cū idē ſit locꝰ totiꝰ et ꝑtꝪ prīo celi.
<
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</
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<
s
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xml:space
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">igr̄ illa terra ſue naturali diſpoſitioni relicta cõti
<
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nuo mouebit̄̄ quovſ (ſi fieri p̄t) cētrū eiꝰ ſit cētrum
<
lb
/>
mundi: ſꝫ ſic mouēdo ꝑ infinitū tp̄s mouebit̄̄ ãteā
<
lb
/>
(ſi fieri p̄t) cētrū eiꝰ fiat cētrū mūdi: igr̄ illa terra ꝑ-
<
lb
/>
petuo mouebit̄̄ cõtinuo vna ꝑte eiꝰ aſcendēte et alia
<
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/>
deſcēdēte: qḋ fuit ꝓbandū </
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>
<
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xml:space
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">Sꝫ iam ꝓbo / talis terra ſic
<
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mouēdo ꝑ infinitū tp̄s mouebit̄̄ antea ꝙ̄ etc. cētrū eiꝰ
<
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/>
fiat cētrū mūdi. </
s
>
<
s
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N20879
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xml:space
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">Qḋ ſic ꝓbat̄̄ et volo / diuidat̄̄ illa
<
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terra in q̈tuor ꝑtes eq̈les: et vna illaꝝ ſit vltra cen
<
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/>
trū reliq̄ vero tres ſint citra centrū: et manifeſtū eſt
<
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/>
q̈rta vltra cētrū reſiſtit tribꝰ q̈rtis citra cētruꝫ ne
<
lb
/>
deſcēdãt vt ↄ̨ſtat: et deſcēdūt ſiue īcipiūt deſcendere
<
lb
/>
illi tres q̈rte a ꝓportione tripla mouēdo vel mīori:
<
lb
/>
vt patet ex caſu: diuido igr̄ medietatē exceſſus quo
<
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/>
pars citra cētrū excedit ꝑtē vltra cētrū q̄ q̇dē medie-
<
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/>
tas exceſſus eſt vna q̈rta īter cētrū illius globi et cē
<
lb
/>
trū mundi: et hoc ꝑ ꝑtes ꝓportionales ꝓportiõe du
<
lb
/>
pla maioribꝰ ſus cētrū mūdi terminatis quo poſi
<
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/>
to arguit̄̄ ſic q̄libet pars ꝓportionalis illius exceſ
<
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/>
ſus descēdet: et ꝑ tãtū tꝑis vel maiꝰ mouebit̄̄ ſiue de
<
lb
/>
ſcēdet q̄libet ſicut īmediate p̄cedens eã: et ſūt infini-
<
lb
/>
te: igr̄ ꝑ infinitꝫ tp̄s mouebitur talis terra / qḋ fuit ꝓ
<
lb
/>
bãdū </
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>
<
s
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xml:space
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">Probat̄̄ minor / q2 ṗma illaꝝ ꝑtiū deſcendet
<
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a ꝓportione tripla vel minori. </
s
>
<
s
xml:id
="
N2089F
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xml:space
="
preserve
">et ſcḋa deſcendet a ꝓ
<
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portione ſuprabiꝑtiēs tertias vel minori q̄ ē minor
<
lb
/>
̄ ſubdupla ad triplã vt ↄ̨ſtat intuenti: et tertia a ꝓ
<
lb
/>
portione ſuprabipartiente ſeptimas vel minori q̄
<
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/>
eſt minor ꝙ̄ ſubdupla ad ꝓportionē ſuprabipartiē
<
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chead
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De motu locali mixto difformi tꝑe ſubiecto quo ad effectū
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tē tertias / vt patet aſpiciēti: et quarta deſcendet a ꝓ
<
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portione ſuprabipartiente quīdecimas vel minori
<
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/>
q̄ eſt minor ꝙ̄ ſubdupla ad ꝓportioneꝫ ſuprabipar
<
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/>
tientē ſeptimas / et ſic ↄ̨̨ñter repperies q̄libet pars
<
lb
/>
ꝓportionalis medietatis illius exceſſus ſequēs de
<
lb
/>
ſcendit a ꝓportione ſubdupla vel minor ad ꝓpor-
<
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/>
tionē a qua īcipit deſcendere pars īmediate prece-
<
lb
/>
dens: et ille ꝑtes ꝓportionales cõtinuo ſe hñt in pro
<
lb
/>
portione dupla: igr̄ ꝑ tãtū tꝑis vel maius mouebit̄̄
<
lb
/>
ſiue descēdet q̄libet pars ꝓportionalis ſicut īmedi
<
lb
/>
ate p̄cedēs eã: vel ſaltē ſequitur ꝑ infinitum tp̄s mo
<
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/>
uebitur talis terra / qḋ ꝓbare intendimus.</
s
>
</
p
>
<
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<
s
xml:id
="
N208C4
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xml:space
="
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">In oppoſitū tñ arguit̄̄ ſic / q2 penes ali
<
lb
/>
quid menſnrãda ē tã̄ penes effectū velocitas motꝰ
<
lb
/>
difformis ſcḋm tp̄s et ſubiectum ſimul et ēt motꝰ mix
<
lb
/>
ti: et nõ niſi penes id qḋ dr̄ ī titulo q̄ſtiõis: igr̄ qõ a</
s
>
</
p
>
<
p
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<
s
xml:id
="
N208CE
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xml:space
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">Pro enucleatione huius parue q̄ſtio-
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nis notãdū eſt primo: ī oī motu difformi quo ad
<
lb
/>
tp̄s et ſubiectū ſimul velocitas mēſurãda ē penes re
<
lb
/>
ductionē ad vniformitatē ſaltē denoīationis vt ſu
<
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perius dicebat̄̄ ī ſecūdo capite huiꝰ tractatꝰ </
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<
s
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xml:space
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">¶ Hoc
<
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tñ vnū aduertendū eſt motus difformis quo ad tē
<
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/>
pus et ſubiectū ſimul aliqñ fit ſecluſo alio motu ſub
<
lb
/>
iecti puta rarefactionis aut ↄ̨dēſatiõis etc / vt cuꝫ ro
<
lb
/>
ta nõ rarefacta aut cõdēſata cõtinuo circulariṫ ve-
<
lb
/>
locius et velocius mouet̄̄ aut tardius et tardius. </
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>
<
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xml:id
="
N208E6
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xml:space
="
preserve
">Ali
<
lb
/>
quando vero fit talis motus cõcomitante rarefacti
<
lb
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one aut condēſatione ſiue augmentatione etc. </
s
>
<
s
xml:id
="
N208ED
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xml:space
="
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">Pri-
<
lb
/>
mo mõ debet mēſurari talis motꝰ velocitas penes
<
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/>
velocitatem qua mouet̄̄ pūctꝰ medius aut velociſ-
<
lb
/>
ſime motꝰ ſcḋm diuerſitatē opinionuū eo mõ quo ſu
<
lb
/>
perius dicebatur de motu difformi quo ad ſubiectū
<
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/>
tm̄ </
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>
<
s
xml:id
="
N208FA
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xml:space
="
preserve
">Et ēt mēſurãda ē velocitas illiꝰ motus penes li-
<
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neã deſcriptã a pūcto medio talis corꝑis vel velo-
<
lb
/>
ciſſime moto: ſed tale pūctū duplici motu mouetur
<
lb
/>
motu vcꝫ locali et rarefactionis ſiue cõdēſatiõis etc.
<
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</
s
>
<
s
xml:id
="
N20904
"
xml:space
="
preserve
">Et ideo tale pūctū tantã lineã deſcribit ac ſi moue-
<
lb
/>
retur ṗmo mõ: et in ſuꝑ deſcribit illã lineã ꝑ quã plꝰ
<
lb
/>
diſtat ſi rarefiat: aut minus ſi condenſetur: a cētro
<
lb
/>
talis motꝰ ꝙ̄ antea diſtabat a principio motꝰ. </
s
>
<
s
xml:id
="
N2090D
"
xml:space
="
preserve
">vt ſi
<
lb
/>
rota moueat̄̄ ī hora cõtinuo rarefiēdo: ita ꝑ rare
<
lb
/>
factionē acq̇rat pūctus penes cuiꝰ motū debet attē
<
lb
/>
di velocitas rote pedalē diſtãtiã a cētro ſupra diſtã
<
lb
/>
tiã iã habitã: et moueat̄̄ talis pūctus motu circula-
<
lb
/>
ri cõtinuo velociꝰ et velociꝰ: tūc dico / velocitas ta-
<
lb
/>
lis motus mēſurãda eſt penes lineã quã deſcriberet
<
lb
/>
motu illo circulari ſi non rarefieret: et penes illã li-
<
lb
/>
neã pedalē quã motu rarefactionis deſcribit</
s
>
</
p
>
<
p
xml:id
="
N20920
">
<
s
xml:id
="
N20921
"
xml:space
="
preserve
">Hic tñ tu aduerte / nõnū̄ mouet̄̄ aliqḋ mobile et
<
lb
/>
motu recto er circulari et rarefactionis ſimul: ita
<
lb
/>
cõtinuo cētrū illiꝰ corꝑis moueatur: quēadmodū
<
lb
/>
contingit ſi pila vel aliqḋ aliud corpꝰ ſpericū vel al
<
lb
/>
teriꝰ figure moueat̄̄ motu recto et circulari continuo
<
lb
/>
rotando continuo rarefiendo et ī hoc et ſimili caſu
<
lb
/>
velocitas talis mobilis iudicãda eſt penes velocita
<
lb
/>
tē cētri mobilis. </
s
>
<
s
xml:id
="
N20932
"
xml:space
="
preserve
">Nõ eī video quo° certiꝰ et cõmodius
<
lb
/>
talis motꝰ velocitas ↄ̨mēſurari dēat. </
s
>
<
s
xml:id
="
N20937
"
xml:space
="
preserve
">¶ Ex his faci
<
lb
/>
le pꝫ ↄ̨ſiderãti tot modꝪ tīgit corpꝰ moueri motu
<
lb
/>
difformi quo ad tp̄s et ſubiectū ſimul quot ↄ̨tīgit ip
<
lb
/>
ſū moueri motu difformi quo ad tp̄s dūtaxat. </
s
>
<
s
xml:id
="
N20940
"
xml:space
="
preserve
">Põt
<
lb
/>
eī pūctꝰ penes cuiꝰ velocitatē attendi d3 talis motꝰ
<
lb
/>
velocitas in q̊libet illoꝝ triū modoꝝ moueri ī prīa
<
lb
/>
ꝑte ꝓportionali hore ̄uis ꝓportione ꝑtite aliquã
<
lb
/>
tula velocitate. </
s
>
<
s
xml:id
="
N2094B
"
xml:space
="
preserve
">et in ſcḋa in duplo velociꝰ: et ī tertia
<
lb
/>
ī triplo velociꝰ ꝙ̄ ī ṗma: et ſic ↄ̨ñter. </
s
>
<
s
xml:id
="
N20950
"
xml:space
="
preserve
">vel quouis alio°
<
lb
/>
et tūc ī iſto et ſiĺibꝰ caſibus velocitas et ſpaciū ꝑtran
<
lb
/>
ſitū mediãte tali velocitate ex his q̄ dcã ſūt p̄ceden-
<
lb
/>
tibus captis cõmode menſuratur inſpectis theore-
<
lb
/>
matibus ibidem demonſtratis</
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>
</
p
>
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>
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