Alvarus, Thomas
,
Liber de triplici motu
,
1509
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<
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De motu locali quo ad effectū ſcḋm ſubiectū difformi.
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0138
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138
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quã certam velocitatē et ponere ī equali parte ſicut
<
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fit in reductione qualitatis vniformiter difformis
<
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vel capiendo ab aliq̈ parte et ponēdo in minori vel
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a mīori et ponēdo in maiori. </
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>
<
s
xml:id
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N1D6B8
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xml:space
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">Nõ tertiū / q2 tūc facile
<
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reducēdo ad vniformitatē ꝓbaret̄̄ / velocitas illiꝰ
<
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rote ſit īfinita q2 caperet̄̄ a prima parte ꝓportiõali
<
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vnꝰ g̈dus, et a ſcḋa tm̄, et a tertia tm̄: et poneret̄̄ per
<
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totã rotã: et ſic eſſet īfinita velocitas. </
s
>
<
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xml:space
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">Nec ſcḋm / quia
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tūc ſeq̄ret̄̄ / tota velocitas eſſet minor quã vt q̈tu-
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or vt ſi velocitas totiꝰ rote poneret̄̄ īmedietate eiꝰ
<
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et ibi eſſet vniformis vt quatuor: deinde accipiendo
<
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medietatē illiꝰ latitudinis motꝰ reducta ad vnifor-
<
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mitatē puta duos g̈dus. </
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<
s
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xml:space
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">et ponēdo eos in alia me-
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dietate et ſic tota velocitas maneret vt duo: </
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<
s
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xml:space
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">Nec eſt
<
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dicendū primū / q2 diuiſa illa rota in duas partes
<
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cõcentricas quaꝝ vna ſit quarta pars totiꝰ rote, et
<
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reſidua ſus circūferentiã ſit tres quarte / vt pone-
<
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batur in p̄cedēti capite in ſcḋa cõfirmatiõe puta vl
<
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tima primi argumēti. </
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>
<
s
xml:id
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xml:space
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">Deinde volo / ille tres q̈rte
<
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reducant̄̄ ad vniformitatē / et ptꝫ / erūt vniformis
<
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in motu g̈du ſexto cū totalis motꝰ illiꝰ partis q̄ cõ-
<
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ponit̄̄ ex illis tribꝰ quartis ſit vniformiter diffor-
<
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mis a quarto vſ ad octauū: et volo etiã / reducat̄̄
<
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alia pars ꝓpe centū ad vniformitatē: et manifeſtū
<
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eſt / erit vt duo motꝰ eiꝰ: cū ſit vniformiter diffor-
<
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/>
mis a non gtadū vſ ad quartū. </
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>
<
s
xml:id
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N1D6F3
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xml:space
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">Deinde volo / a
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q̄libet triū quartaꝝ magis intēſaꝝ remoueat̄̄ vnꝰ
<
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g̈dusꝰ / et ponat̄̄ in quarta minꝰ intēſēſa / q̄ eſt vt duo /
<
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et manifeſtū eſt / oēs quarte manebūt vt quī vni-
<
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formes: et ꝑ ↄ̨ñs tota illa velocitas talis motꝰ vni-
<
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formiter difformis reducendo ad vniformitatē re-
<
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mouēdo a parte equali et ponēdo ſibi in equali erit
<
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vt quin / quod eſt falſum: quia eſt vt quatuor cum
<
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eſt a non gradu vſ ad octauū: igr̄ velocitas mo-
<
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tus vniformiter difformis quo ad ſubiectū nõ de-
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bet cõmenſari penes reductionē ad vniformitatē.
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<
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xml:id
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">Dicitur.</
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</
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<
s
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xml:space
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">¶ Dices forte cõcedēdo / motꝰ circularis nõ poteſt
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reduci ad vniformitatē ipſo manēte in ſubiecto cir
<
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culariter moto q2 hoc repugnat et ītellige ſicut ītel
<
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ligendum eſt: ſed bene talis velocitas reduceret̄̄ ad
<
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vniformitatē qua tale mobile moueat̄̄ vniformiter
<
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motu recto quolibet pūcto deſcribente tantã lineã
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quantã deſcribit pūctꝰ mediꝰ. </
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<
s
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xml:space
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">Et hoc loquendo de
<
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motu circulari / vt loquūtur terminiſte. </
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>
<
s
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xml:space
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">Si autē lo-
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quimur / vt reales credo / dicendū eſſet ſcḋm eoruꝫ
<
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viã / motꝰ circularis eſſentialiter eſſet circularis
<
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ita talis motꝰ nõ põt eſſe quin ſit motꝰ circularis
<
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q2 differt ſpecie eſſentiali a motu recto. </
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<
s
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xml:space
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">Et ideo / vt
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modꝰ reſpõdendi huic argumēto et etiã cognoſcē-
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di velocitatem motus difformis quo ad ſubiectum
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ſit vtri vie communis.</
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</
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<
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<
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xml:space
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">Reſpõdeo alter de facto motꝰ diffor
<
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mis quo ad ſubiectū velocitas nequā cõmēſura-
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ri debet ꝑ reductionē ad vniformitatē: ſed cõmēſu-
<
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randa eſt penes denoīationē partiū nõ ̄tū ad ma
<
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gnitudinē: ſed ̄tū ad lõgitudinē </
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<
s
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xml:space
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">Uolo dicere / nõ
<
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in ea ꝓportionē qua pars eſt maior altera in ea ꝓ-
<
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porõe velocitas motꝰ exiſtēs in ea plus facit ad de-
<
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noīationē totiꝰ velocitatis. </
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>
<
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">Sꝫ volo dicere / in ea
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ꝓportiõe in qua eſt lõgior ceteris paribꝰ in ea plus
<
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facit ad denoīationē totiꝰ ita tm̄ adequate mo-
<
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uet̄̄ vna rota ̄tū vna linea ꝓcedēs a cētro illiꝰ ro-
<
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te vſ ad circūferentiã. </
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>
<
s
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xml:space
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">Et ſi talis linea moueat̄̄ a
<
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nõ g̈du vſ ad octauū etiã tota rota. </
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<
s
xml:id
="
N1D770
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xml:space
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">Et põt vena-
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ri velocitas motꝰ illiꝰ linee penes denoīationē iſto
<
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mõ medietas huiꝰ linee q̄ velociua mouet̄̄, mouet̄̄ vt
<
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ſex: igr̄ denoīat totū moueri vt tria: et alia medietas
<
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totius vt vnū: et ſic tota linea mouetur vt quatuor.</
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</
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<
cb
chead
="
De motu locali quo ad effectū ſcḋm ſubiectū difformi.
"/>
<
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="
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<
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xml:space
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">Sed ↄ̨̨tra. </
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<
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="
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xml:space
="
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">Q2 ſi talis modꝰ cognoſcē-
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di velocitatē motꝰ difformis q̊ ab ſubiectū eſſet vĺr
<
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validꝰ ſeq̄ret̄̄ / dabilis eēt vna ꝑs rote vniformiter
<
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difformiṫ mote q̄ nõ vniformiṫ difformiṫ moueret̄̄
<
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īmo nõ eēt dabilis g̈dꝰ q̊ adeq̈te moueret̄̄: ſꝫ q̊libet
<
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īadeq̈te citra ſūmū / et ↄ̨ñs oī opiniõi aduerſat̄̄: igr̄
<
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illud ex q̊ ſequit̄̄. </
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<
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xml:space
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">Seq̄la ꝓbat̄̄ / et capio vnã rotã que
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moueat̄̄ vniformiṫ difformiṫ a nõ g̈du vſ ad octa-
<
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uū, et ſigno in ea vnã colūnã cuiꝰ vnū extremū tãgat
<
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cētrū et aliud circūferētiã. </
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>
<
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="
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xml:space
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">Deīde educo lineã girati
<
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uã ꝓcedentē a cētro talis rote et girantē oēs partes
<
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ꝓportiõales taĺ colūne (et loquor de linea giratiua
<
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ſicut loquūtur noīales ̄uis idē eſſet ſi loq̄rer ſcḋm
<
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reales) / q̊ poſito ſic arguitur talis linea eſt. ꝑs illius
<
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colūne: et hꝫ īfinitas ꝑtes eq̈les quaꝝ q̄libet mouet̄̄
<
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maiori et velociori g̈du quã q̈tuor, et hꝫ īfinitas eq̈-
<
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les quaꝝ q̄libet mouet̄̄ velociꝰ quã quī, et ſic ↄ̨ñter
<
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vſ ad octauū g̈dū excluſiue: et reſidue partes ſolū
<
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ſūt finite vt facile eſt ītueri: igr̄ talis linea mouetur
<
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maiori vtlocitate quã vt quatuor quã vt quī ꝙ̄ vt
<
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ſex etc̈. vſ ad octauū g̈dū excluſiue / qḋ fuit ꝓbãdū</
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</
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<
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<
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xml:space
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">In oppoſitū tamē eſt coīs ſchola aſſe
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rens velocitatē motꝰ difformis quo ad ſubiectū ali
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quo illorū modorū attendi debere ſiue cõmēſurari</
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>
</
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<
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<
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xml:space
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">Pro deſciſioue huiꝰ q̄ſtionis ſupponē
<
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da eſt diffinitio motus vniformiter difformis quo
<
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ad ſubiectū. </
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<
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="
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xml:space
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">Et etiã diffinitio motꝰ difformiter dif-
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formis quo ad ſubiectū q̄ ſuꝑiori capite poſite ſunt
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</
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<
s
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">¶ Item aduertendū eſt / in motu circulari duo cõ-
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ſiderãda ſunt: puta ipſa circuitio: et ipſe motus cir-
<
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cularis: quãuis eī idē ſit motꝰ circularis et circuitio
<
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penes aliud tñ cõmenſurari habet velocitas circui
<
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tionis: et velocitas motus circularis: ſicut idē eſt al
<
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bedo et ſiĺitudo: et penes aliḋ cognoſci hꝫ intēſio al
<
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bedinis: et ītenſio ſiĺitudinls qḋ facile ex dialecticis
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ꝑcipi põt. </
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<
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xml:space
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">In iſtis eī aſpicienda eſt appellatio ne in
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ea fallamur: </
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<
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xml:space
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">Uelocitas em̄ motꝰ circularis attendi
<
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tur penes lineam deſcriptam a certo puncto vt infe
<
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riꝰ declarabit̄̄.
<
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position
="
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xlink:href
="
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="
note-0138-02
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xml:id
="
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xml:space
="
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">Penes
<
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q̇d hꝫ at-
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tēdi velo
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citas cir
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caitiõis.</
note
>
</
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<
s
xml:id
="
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xml:space
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">Sed velocitas circuitionis attēdi hꝫ
<
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penes angulū deſcriptū in tãto vel tanto tp̄e circa
<
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centrū: ita ſi in eq̈li tp̄e duo mobilia ſiue eq̈lia ſi-
<
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ue ineq̈lia circulariter mota eq̈les angulos circa cē
<
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trū deſcribūt ipſa eq̈liter circueūt et circūgyrãt: </
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>
<
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="
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xml:space
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">Si
<
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vero in eodē tp̄e ineq̈les deſcribãt circa cētrū angu
<
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los: notū euadet eorū circuitiones ineq̈les eē.
<
note
position
="
right
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xlink:href
="
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="
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xml:id
="
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xml:space
="
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">paulꝰ ve
<
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netꝰ ī ſū.
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phiſi. ca.
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35.</
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<
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xml:space
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">Et hec
<
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opinio eſt cõiter loq̄ntiū: et ſignãter Pauli veneti ī
<
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ſua ſūma in libro phiſicoꝝ capitulo .35. vide eū ibi.
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</
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>
<
s
xml:id
="
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xml:space
="
preserve
">Poſſet tñ facile attēdi velocitas circuitiõis penes
<
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velocitatē motꝰ alicuiꝰ pūcti equaliter diſtãtis a cē
<
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/>
tro: hoc eſt dicere / ſi in duobus mobilibꝰ circulari
<
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/>
ter ſiue eq̈lia ſint ſiue īequalia duo pūcta eq̈liter di
<
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/>
ſtãtia a cētro equaliter moueant̄̄: talia mobilia eq̈
<
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liter circueūt. </
s
>
<
s
xml:id
="
N1D816
"
xml:space
="
preserve
">Nõ tñ arbitreris quãto pūctū ē pro
<
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/>
pinquiꝰ cētro tãto velociꝰ circuit: qm̄ qḋlibet eq̄ve-
<
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lociter circuit cū altero dūmõ corꝑis motꝰ ſit vnifor
<
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/>
miter difformis quo ad ſubiectū </
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>
<
s
xml:id
="
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xml:space
="
preserve
">Quare ꝑſpicuū ē
<
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videre diſtãtiã pūctorū nullo pacto conferre ad ve
<
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/>
locitatē circuitiõis (loquor de diſtãtia a cētro) quã
<
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/>
uis plurimū ad velocitatē motꝰ circularis vt ſupe-
<
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rius tactū eſt in quodã argumēto: et inferius tange
<
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tur. </
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>
<
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xml:id
="
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xml:space
="
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">His ſuppoſitis ſit.</
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>
</
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>
<
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<
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xml:id
="
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xml:space
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">Prīa ↄ̨̨cluſio. </
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>
<
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xml:id
="
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"
xml:space
="
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">Uelocitas motꝰ vnifor-
<
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/>
miṫ difformis quo ad ſubiectū nõ d3 attēdi aut cõ-
<
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/>
menſurari penes velocitatē pūcti exiſtētis in medio
<
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/>
corporis quãtū ad magnitudinē vt bene probat ter
<
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/>
tium argumentum huius capitis</
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>
</
p
>
<
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="
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<
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xml:space
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">Scḋa ↄ̨̨cluſio. </
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>
<
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="
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xml:space
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">Uelocitas motus vni- </
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>
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