138 quã certam velocitatē et ponere ī equali parte ſicut
fit in reductione qualitatis vniformiter difformis
vel capiendo ab aliq̈ parte et ponēdo in minori vel
a mīori et ponēdo in maiori. Nõ tertiū / q2 tūc facile
reducēdo ad vniformitatē ꝓbaret̄̄ / velocitas illiꝰ
rote ſit īfinita q2 caperet̄̄ a prima parte ꝓportiõali
vnꝰ g̈dus, et a ſcḋa tm̄, et a tertia tm̄: et poneret̄̄ per
totã rotã: et ſic eſſet īfinita velocitas. Nec ſcḋm / quia
tūc ſeq̄ret̄̄ / tota velocitas eſſet minor quã vt q̈tu-
or vt ſi velocitas totiꝰ rote poneret̄̄ īmedietate eiꝰ
et ibi eſſet vniformis vt quatuor: deinde accipiendo
medietatē illiꝰ latitudinis motꝰ reducta ad vnifor-
mitatē puta duos g̈dus. et ponēdo eos in alia me-
dietate et ſic tota velocitas maneret vt duo: Nec eſt
dicendū primū / q2 diuiſa illa rota in duas partes
cõcentricas quaꝝ vna ſit quarta pars totiꝰ rote, et
reſidua ſus circūferentiã ſit tres quarte / vt pone-
batur in p̄cedēti capite in ſcḋa cõfirmatiõe puta vl
tima primi argumēti. Deinde volo / ille tres q̈rte
reducant̄̄ ad vniformitatē / et ptꝫ / erūt vniformis
in motu g̈du ſexto cū totalis motꝰ illiꝰ partis q̄ cõ-
ponit̄̄ ex illis tribꝰ quartis ſit vniformiter diffor-
mis a quarto vſ ad octauū: et volo etiã / reducat̄̄
alia pars ꝓpe centū ad vniformitatē: et manifeſtū
eſt / erit vt duo motꝰ eiꝰ: cū ſit vniformiter diffor-
mis a non gtadū vſ ad quartū. Deinde volo / a
q̄libet triū quartaꝝ magis intēſaꝝ remoueat̄̄ vnꝰ
g̈dusꝰ / et ponat̄̄ in quarta minꝰ intēſēſa / q̄ eſt vt duo /
et manifeſtū eſt / oēs quarte manebūt vt quī vni-
formes: et ꝑ ↄ̨ñs tota illa velocitas talis motꝰ vni-
formiter difformis reducendo ad vniformitatē re-
mouēdo a parte equali et ponēdo ſibi in equali erit
vt quin / quod eſt falſum: quia eſt vt quatuor cum
eſt a non gradu vſ ad octauū: igr̄ velocitas mo-
tus vniformiter difformis quo ad ſubiectū nõ de-
bet cõmenſari penes reductionē ad vniformitatē.
11Dicitur. ¶ Dices forte cõcedēdo / motꝰ circularis nõ poteſt
reduci ad vniformitatē ipſo manēte in ſubiecto cir
culariter moto q2 hoc repugnat et ītellige ſicut ītel
ligendum eſt: ſed bene talis velocitas reduceret̄̄ ad
vniformitatē qua tale mobile moueat̄̄ vniformiter
motu recto quolibet pūcto deſcribente tantã lineã
quantã deſcribit pūctꝰ mediꝰ. Et hoc loquendo de
motu circulari / vt loquūtur terminiſte. Si autē lo-
quimur / vt reales credo / dicendū eſſet ſcḋm eoruꝫ
viã / motꝰ circularis eſſentialiter eſſet circularis
ita talis motꝰ nõ põt eſſe quin ſit motꝰ circularis
q2 differt ſpecie eſſentiali a motu recto. Et ideo / vt
modꝰ reſpõdendi huic argumēto et etiã cognoſcē-
di velocitatem motus difformis quo ad ſubiectum
ſit vtri vie communis.
fit in reductione qualitatis vniformiter difformis
vel capiendo ab aliq̈ parte et ponēdo in minori vel
a mīori et ponēdo in maiori. Nõ tertiū / q2 tūc facile
reducēdo ad vniformitatē ꝓbaret̄̄ / velocitas illiꝰ
rote ſit īfinita q2 caperet̄̄ a prima parte ꝓportiõali
vnꝰ g̈dus, et a ſcḋa tm̄, et a tertia tm̄: et poneret̄̄ per
totã rotã: et ſic eſſet īfinita velocitas. Nec ſcḋm / quia
tūc ſeq̄ret̄̄ / tota velocitas eſſet minor quã vt q̈tu-
or vt ſi velocitas totiꝰ rote poneret̄̄ īmedietate eiꝰ
et ibi eſſet vniformis vt quatuor: deinde accipiendo
medietatē illiꝰ latitudinis motꝰ reducta ad vnifor-
mitatē puta duos g̈dus. et ponēdo eos in alia me-
dietate et ſic tota velocitas maneret vt duo: Nec eſt
dicendū primū / q2 diuiſa illa rota in duas partes
cõcentricas quaꝝ vna ſit quarta pars totiꝰ rote, et
reſidua ſus circūferentiã ſit tres quarte / vt pone-
batur in p̄cedēti capite in ſcḋa cõfirmatiõe puta vl
tima primi argumēti. Deinde volo / ille tres q̈rte
reducant̄̄ ad vniformitatē / et ptꝫ / erūt vniformis
in motu g̈du ſexto cū totalis motꝰ illiꝰ partis q̄ cõ-
ponit̄̄ ex illis tribꝰ quartis ſit vniformiter diffor-
mis a quarto vſ ad octauū: et volo etiã / reducat̄̄
alia pars ꝓpe centū ad vniformitatē: et manifeſtū
eſt / erit vt duo motꝰ eiꝰ: cū ſit vniformiter diffor-
mis a non gtadū vſ ad quartū. Deinde volo / a
q̄libet triū quartaꝝ magis intēſaꝝ remoueat̄̄ vnꝰ
g̈dusꝰ / et ponat̄̄ in quarta minꝰ intēſēſa / q̄ eſt vt duo /
et manifeſtū eſt / oēs quarte manebūt vt quī vni-
formes: et ꝑ ↄ̨ñs tota illa velocitas talis motꝰ vni-
formiter difformis reducendo ad vniformitatē re-
mouēdo a parte equali et ponēdo ſibi in equali erit
vt quin / quod eſt falſum: quia eſt vt quatuor cum
eſt a non gradu vſ ad octauū: igr̄ velocitas mo-
tus vniformiter difformis quo ad ſubiectū nõ de-
bet cõmenſari penes reductionē ad vniformitatē.
11Dicitur. ¶ Dices forte cõcedēdo / motꝰ circularis nõ poteſt
reduci ad vniformitatē ipſo manēte in ſubiecto cir
culariter moto q2 hoc repugnat et ītellige ſicut ītel
ligendum eſt: ſed bene talis velocitas reduceret̄̄ ad
vniformitatē qua tale mobile moueat̄̄ vniformiter
motu recto quolibet pūcto deſcribente tantã lineã
quantã deſcribit pūctꝰ mediꝰ. Et hoc loquendo de
motu circulari / vt loquūtur terminiſte. Si autē lo-
quimur / vt reales credo / dicendū eſſet ſcḋm eoruꝫ
viã / motꝰ circularis eſſentialiter eſſet circularis
ita talis motꝰ nõ põt eſſe quin ſit motꝰ circularis
q2 differt ſpecie eſſentiali a motu recto. Et ideo / vt
modꝰ reſpõdendi huic argumēto et etiã cognoſcē-
di velocitatem motus difformis quo ad ſubiectum
ſit vtri vie communis.
Reſpõdeo alter de facto motꝰ diffor
mis quo ad ſubiectū velocitas nequā cõmēſura-
ri debet ꝑ reductionē ad vniformitatē: ſed cõmēſu-
randa eſt penes denoīationē partiū nõ ̄tū ad ma
gnitudinē: ſed ̄tū ad lõgitudinē Uolo dicere / nõ
in ea ꝓportionē qua pars eſt maior altera in ea ꝓ-
porõe velocitas motꝰ exiſtēs in ea plus facit ad de-
noīationē totiꝰ velocitatis. Sꝫ volo dicere / in ea
ꝓportiõe in qua eſt lõgior ceteris paribꝰ in ea plus
facit ad denoīationē totiꝰ ita tm̄ adequate mo-
uet̄̄ vna rota ̄tū vna linea ꝓcedēs a cētro illiꝰ ro-
te vſ ad circūferentiã. Et ſi talis linea moueat̄̄ a
nõ g̈du vſ ad octauū etiã tota rota. Et põt vena-
ri velocitas motꝰ illiꝰ linee penes denoīationē iſto
mõ medietas huiꝰ linee q̄ velociua mouet̄̄, mouet̄̄ vt
ſex: igr̄ denoīat totū moueri vt tria: et alia medietas
totius vt vnū: et ſic tota linea mouetur vt quatuor.
mis quo ad ſubiectū velocitas nequā cõmēſura-
ri debet ꝑ reductionē ad vniformitatē: ſed cõmēſu-
randa eſt penes denoīationē partiū nõ ̄tū ad ma
gnitudinē: ſed ̄tū ad lõgitudinē Uolo dicere / nõ
in ea ꝓportionē qua pars eſt maior altera in ea ꝓ-
porõe velocitas motꝰ exiſtēs in ea plus facit ad de-
noīationē totiꝰ velocitatis. Sꝫ volo dicere / in ea
ꝓportiõe in qua eſt lõgior ceteris paribꝰ in ea plus
facit ad denoīationē totiꝰ ita tm̄ adequate mo-
uet̄̄ vna rota ̄tū vna linea ꝓcedēs a cētro illiꝰ ro-
te vſ ad circūferentiã. Et ſi talis linea moueat̄̄ a
nõ g̈du vſ ad octauū etiã tota rota. Et põt vena-
ri velocitas motꝰ illiꝰ linee penes denoīationē iſto
mõ medietas huiꝰ linee q̄ velociua mouet̄̄, mouet̄̄ vt
ſex: igr̄ denoīat totū moueri vt tria: et alia medietas
totius vt vnū: et ſic tota linea mouetur vt quatuor.
Sed ↄ̨̨tra.
Q2 ſi talis modꝰ cognoſcē-
di velocitatē motꝰ difformis q̊ ab ſubiectū eſſet vĺr
validꝰ ſeq̄ret̄̄ / dabilis eēt vna ꝑs rote vniformiter
difformiṫ mote q̄ nõ vniformiṫ difformiṫ moueret̄̄
īmo nõ eēt dabilis g̈dꝰ q̊ adeq̈te moueret̄̄: ſꝫ q̊libet
īadeq̈te citra ſūmū / et ↄ̨ñs oī opiniõi aduerſat̄̄: igr̄
illud ex q̊ ſequit̄̄. Seq̄la ꝓbat̄̄ / et capio vnã rotã que
moueat̄̄ vniformiṫ difformiṫ a nõ g̈du vſ ad octa-
uū, et ſigno in ea vnã colūnã cuiꝰ vnū extremū tãgat
cētrū et aliud circūferētiã. Deīde educo lineã girati
uã ꝓcedentē a cētro talis rote et girantē oēs partes
ꝓportiõales taĺ colūne (et loquor de linea giratiua
ſicut loquūtur noīales ̄uis idē eſſet ſi loq̄rer ſcḋm
reales) / q̊ poſito ſic arguitur talis linea eſt. ꝑs illius
colūne: et hꝫ īfinitas ꝑtes eq̈les quaꝝ q̄libet mouet̄̄
maiori et velociori g̈du quã q̈tuor, et hꝫ īfinitas eq̈-
les quaꝝ q̄libet mouet̄̄ velociꝰ quã quī, et ſic ↄ̨ñter
vſ ad octauū g̈dū excluſiue: et reſidue partes ſolū
ſūt finite vt facile eſt ītueri: igr̄ talis linea mouetur
maiori vtlocitate quã vt quatuor quã vt quī ꝙ̄ vt
ſex etc̈. vſ ad octauū g̈dū excluſiue / qḋ fuit ꝓbãdū
di velocitatē motꝰ difformis q̊ ab ſubiectū eſſet vĺr
validꝰ ſeq̄ret̄̄ / dabilis eēt vna ꝑs rote vniformiter
difformiṫ mote q̄ nõ vniformiṫ difformiṫ moueret̄̄
īmo nõ eēt dabilis g̈dꝰ q̊ adeq̈te moueret̄̄: ſꝫ q̊libet
īadeq̈te citra ſūmū / et ↄ̨ñs oī opiniõi aduerſat̄̄: igr̄
illud ex q̊ ſequit̄̄. Seq̄la ꝓbat̄̄ / et capio vnã rotã que
moueat̄̄ vniformiṫ difformiṫ a nõ g̈du vſ ad octa-
uū, et ſigno in ea vnã colūnã cuiꝰ vnū extremū tãgat
cētrū et aliud circūferētiã. Deīde educo lineã girati
uã ꝓcedentē a cētro talis rote et girantē oēs partes
ꝓportiõales taĺ colūne (et loquor de linea giratiua
ſicut loquūtur noīales ̄uis idē eſſet ſi loq̄rer ſcḋm
reales) / q̊ poſito ſic arguitur talis linea eſt. ꝑs illius
colūne: et hꝫ īfinitas ꝑtes eq̈les quaꝝ q̄libet mouet̄̄
maiori et velociori g̈du quã q̈tuor, et hꝫ īfinitas eq̈-
les quaꝝ q̄libet mouet̄̄ velociꝰ quã quī, et ſic ↄ̨ñter
vſ ad octauū g̈dū excluſiue: et reſidue partes ſolū
ſūt finite vt facile eſt ītueri: igr̄ talis linea mouetur
maiori vtlocitate quã vt quatuor quã vt quī ꝙ̄ vt
ſex etc̈. vſ ad octauū g̈dū excluſiue / qḋ fuit ꝓbãdū
In oppoſitū tamē eſt coīs ſchola aſſe
rens velocitatē motꝰ difformis quo ad ſubiectū ali
quo illorū modorū attendi debere ſiue cõmēſurari
rens velocitatē motꝰ difformis quo ad ſubiectū ali
quo illorū modorū attendi debere ſiue cõmēſurari
Pro deſciſioue huiꝰ q̄ſtionis ſupponē
da eſt diffinitio motus vniformiter difformis quo
ad ſubiectū. Et etiã diffinitio motꝰ difformiter dif-
formis quo ad ſubiectū q̄ ſuꝑiori capite poſite ſunt
¶ Item aduertendū eſt / in motu circulari duo cõ-
ſiderãda ſunt: puta ipſa circuitio: et ipſe motus cir-
cularis: quãuis eī idē ſit motꝰ circularis et circuitio
penes aliud tñ cõmenſurari habet velocitas circui
tionis: et velocitas motus circularis: ſicut idē eſt al
bedo et ſiĺitudo: et penes aliḋ cognoſci hꝫ intēſio al
bedinis: et ītenſio ſiĺitudinls qḋ facile ex dialecticis
ꝑcipi põt. In iſtis eī aſpicienda eſt appellatio ne in
ea fallamur: Uelocitas em̄ motꝰ circularis attendi
tur penes lineam deſcriptam a certo puncto vt infe
riꝰ declarabit̄̄. 22Penes
q̇d hꝫ at-
tēdi velo
citas cir
caitiõis. Sed velocitas circuitionis attēdi hꝫ
penes angulū deſcriptū in tãto vel tanto tp̄e circa
centrū: ita ſi in eq̈li tp̄e duo mobilia ſiue eq̈lia ſi-
ue ineq̈lia circulariter mota eq̈les angulos circa cē
trū deſcribūt ipſa eq̈liter circueūt et circūgyrãt: Si
vero in eodē tp̄e ineq̈les deſcribãt circa cētrū angu
los: notū euadet eorū circuitiones ineq̈les eē. 33paulꝰ ve
netꝰ ī ſū.
phiſi. ca.
35. Et hec
opinio eſt cõiter loq̄ntiū: et ſignãter Pauli veneti ī
ſua ſūma in libro phiſicoꝝ capitulo .35. vide eū ibi.
Poſſet tñ facile attēdi velocitas circuitiõis penes
velocitatē motꝰ alicuiꝰ pūcti equaliter diſtãtis a cē
tro: hoc eſt dicere / ſi in duobus mobilibꝰ circulari
ter ſiue eq̈lia ſint ſiue īequalia duo pūcta eq̈liter di
ſtãtia a cētro equaliter moueant̄̄: talia mobilia eq̈
liter circueūt. Nõ tñ arbitreris quãto pūctū ē pro
pinquiꝰ cētro tãto velociꝰ circuit: qm̄ qḋlibet eq̄ve-
lociter circuit cū altero dūmõ corꝑis motꝰ ſit vnifor
miter difformis quo ad ſubiectū Quare ꝑſpicuū ē
videre diſtãtiã pūctorū nullo pacto conferre ad ve
locitatē circuitiõis (loquor de diſtãtia a cētro) quã
uis plurimū ad velocitatē motꝰ circularis vt ſupe-
rius tactū eſt in quodã argumēto: et inferius tange
tur. His ſuppoſitis ſit.
da eſt diffinitio motus vniformiter difformis quo
ad ſubiectū. Et etiã diffinitio motꝰ difformiter dif-
formis quo ad ſubiectū q̄ ſuꝑiori capite poſite ſunt
¶ Item aduertendū eſt / in motu circulari duo cõ-
ſiderãda ſunt: puta ipſa circuitio: et ipſe motus cir-
cularis: quãuis eī idē ſit motꝰ circularis et circuitio
penes aliud tñ cõmenſurari habet velocitas circui
tionis: et velocitas motus circularis: ſicut idē eſt al
bedo et ſiĺitudo: et penes aliḋ cognoſci hꝫ intēſio al
bedinis: et ītenſio ſiĺitudinls qḋ facile ex dialecticis
ꝑcipi põt. In iſtis eī aſpicienda eſt appellatio ne in
ea fallamur: Uelocitas em̄ motꝰ circularis attendi
tur penes lineam deſcriptam a certo puncto vt infe
riꝰ declarabit̄̄. 22Penes
q̇d hꝫ at-
tēdi velo
citas cir
caitiõis. Sed velocitas circuitionis attēdi hꝫ
penes angulū deſcriptū in tãto vel tanto tp̄e circa
centrū: ita ſi in eq̈li tp̄e duo mobilia ſiue eq̈lia ſi-
ue ineq̈lia circulariter mota eq̈les angulos circa cē
trū deſcribūt ipſa eq̈liter circueūt et circūgyrãt: Si
vero in eodē tp̄e ineq̈les deſcribãt circa cētrū angu
los: notū euadet eorū circuitiones ineq̈les eē. 33paulꝰ ve
netꝰ ī ſū.
phiſi. ca.
35. Et hec
opinio eſt cõiter loq̄ntiū: et ſignãter Pauli veneti ī
ſua ſūma in libro phiſicoꝝ capitulo .35. vide eū ibi.
Poſſet tñ facile attēdi velocitas circuitiõis penes
velocitatē motꝰ alicuiꝰ pūcti equaliter diſtãtis a cē
tro: hoc eſt dicere / ſi in duobus mobilibꝰ circulari
ter ſiue eq̈lia ſint ſiue īequalia duo pūcta eq̈liter di
ſtãtia a cētro equaliter moueant̄̄: talia mobilia eq̈
liter circueūt. Nõ tñ arbitreris quãto pūctū ē pro
pinquiꝰ cētro tãto velociꝰ circuit: qm̄ qḋlibet eq̄ve-
lociter circuit cū altero dūmõ corꝑis motꝰ ſit vnifor
miter difformis quo ad ſubiectū Quare ꝑſpicuū ē
videre diſtãtiã pūctorū nullo pacto conferre ad ve
locitatē circuitiõis (loquor de diſtãtia a cētro) quã
uis plurimū ad velocitatē motꝰ circularis vt ſupe-
rius tactū eſt in quodã argumēto: et inferius tange
tur. His ſuppoſitis ſit.