91 tem equalē vel maiorē magis reſiſtentiã quã potē-
tia vt .10. / et per cõſequēs ↄ̨tinuo potentia illa vt .16.
maiorē proportionē deperdit per acquiſitionē re-
ſiſtentie quã potentia vt .10. Patet hec conſequētia
ex ſecūda ſuppoſitione octaui capitis huiꝰ. Quã-
uis em̄ hec potentia varietur: nichilominus ex par
te acquiſitionis reſiſtentie tantã ꝓportionē vel ma
iorem deperdit ac ſi maneret cõtinuo īuariata: igi
tur cõtinuo maiorē ꝓportionē deperdit / quod fuit
probandum.
tia vt .10. / et per cõſequēs ↄ̨tinuo potentia illa vt .16.
maiorē proportionē deperdit per acquiſitionē re-
ſiſtentie quã potentia vt .10. Patet hec conſequētia
ex ſecūda ſuppoſitione octaui capitis huiꝰ. Quã-
uis em̄ hec potentia varietur: nichilominus ex par
te acquiſitionis reſiſtentie tantã ꝓportionē vel ma
iorem deperdit ac ſi maneret cõtinuo īuariata: igi
tur cõtinuo maiorē ꝓportionē deperdit / quod fuit
probandum.
Reſpondeo negãdo antecedens: ad
ꝓbationē admiſſo caſu nego maiorē: et ad ꝓbatio-
nem nego antecedens videlicet / continue maiorē
ꝓpõrtionē deperdit: et cum ꝓbatur concedo antece
cedens / et nego cõſequentiã: ſed bene ſequitur / ma
iorē reſiſtentiã ꝓportiõabiliter acquirit. Quãuis
em̄ deperdat cõtinue ꝓportionē maiorē per acqui-
ſitionē reſiſtentie tamen ſemper aliquã ꝓportionē
acquirit per intenſionē potentie. Et ſic argumentū
bene ꝓbaret ꝓpropoſitū ſi potentia non intenderetur
ꝓbationē admiſſo caſu nego maiorē: et ad ꝓbatio-
nem nego antecedens videlicet / continue maiorē
ꝓpõrtionē deperdit: et cum ꝓbatur concedo antece
cedens / et nego cõſequentiã: ſed bene ſequitur / ma
iorē reſiſtentiã ꝓportiõabiliter acquirit. Quãuis
em̄ deperdat cõtinue ꝓportionē maiorē per acqui-
ſitionē reſiſtentie tamen ſemper aliquã ꝓportionē
acquirit per intenſionē potentie. Et ſic argumentū
bene ꝓbaret ꝓpropoſitū ſi potentia non intenderetur
Sed contra / quia tunc ſequeretur /
ſi potentia illa remitteretur cõtinuo ipſa nõ poſſet
vniformiter remittere motū ſuū illud mediū tran-
ſeundo: ſed cõſequens eſt contra correlariū ſecūde
ↄ̨cluſionis octaui capitis huiꝰ / igitur ſolutio nulla
Probatur ſequela / q2 tūc talis potentia continuo
moueretur velocius alia potentia maiore nõ varia
ta difformiter remittente motū ſuū idem medium
tranſeundo verſus extremū intenſius: igitur con-
tinuo maiorē ꝓportionē deperderet: et per conſe-
quens velocius continuo remitteret motū ſuū quã
potentia maior vt .10. nõ variata: et ſic nõ vniformi
ter. Cõſequentia tamen ptꝫ ex ſecūda ſuppoſitione
octaui capitis preallegata. Sed ãtecedens arguit̄̄
videlicet / potentia illa vt .16. cõtinuo velociꝰ mo-
ueretur: et pono potentiã vt .16. ſimul cum potentia
vt .10. ad principiū vltime quarte puta ad punctum
vt .4. / et pono potentiã vt .8. q̄ nõ variata ꝑtrãſeūdo
c. mediū īuariatū cõtinuo vniformiter remittit mo-
tū ſuū ad punctū ītrīſecū eiuſdē vltime q̈te / ad qḋ ha
bet ꝓportionē irrationalē ſubduplã duple: et mo-
ueantur ſic oēs ille potentie ſimul ab eodē inſtanti /
quo poſito ptꝫ / maior potentia variata puta vt
16. cõtinuo velocius mouebitur quã potentia vt .10.
qm̄ potentia vt .16. incipit moueri a multo maiori
proportione: igitur propoſitum. Hec em̄ a dupla
ſexquialtera: illa autem a quadrupla ſuum motum
inchoat / vt patet ex caſu.
ſi potentia illa remitteretur cõtinuo ipſa nõ poſſet
vniformiter remittere motū ſuū illud mediū tran-
ſeundo: ſed cõſequens eſt contra correlariū ſecūde
ↄ̨cluſionis octaui capitis huiꝰ / igitur ſolutio nulla
Probatur ſequela / q2 tūc talis potentia continuo
moueretur velocius alia potentia maiore nõ varia
ta difformiter remittente motū ſuū idem medium
tranſeundo verſus extremū intenſius: igitur con-
tinuo maiorē ꝓportionē deperderet: et per conſe-
quens velocius continuo remitteret motū ſuū quã
potentia maior vt .10. nõ variata: et ſic nõ vniformi
ter. Cõſequentia tamen ptꝫ ex ſecūda ſuppoſitione
octaui capitis preallegata. Sed ãtecedens arguit̄̄
videlicet / potentia illa vt .16. cõtinuo velociꝰ mo-
ueretur: et pono potentiã vt .16. ſimul cum potentia
vt .10. ad principiū vltime quarte puta ad punctum
vt .4. / et pono potentiã vt .8. q̄ nõ variata ꝑtrãſeūdo
c. mediū īuariatū cõtinuo vniformiter remittit mo-
tū ſuū ad punctū ītrīſecū eiuſdē vltime q̈te / ad qḋ ha
bet ꝓportionē irrationalē ſubduplã duple: et mo-
ueantur ſic oēs ille potentie ſimul ab eodē inſtanti /
quo poſito ptꝫ / maior potentia variata puta vt
16. cõtinuo velocius mouebitur quã potentia vt .10.
qm̄ potentia vt .16. incipit moueri a multo maiori
proportione: igitur propoſitum. Hec em̄ a dupla
ſexquialtera: illa autem a quadrupla ſuum motum
inchoat / vt patet ex caſu.
Reſpõdeo negando ſequelã / ad pro-
bationē nego / potentia vt .16. continuo velocius
mouebitur quã potentia vt .10. maior nõ variata / et
cū ꝓbatur admiſſo caſu nego antecedens. Dico em̄ /
illa potentia maior vt .16. variata antea quã de-
euniat ad finē ab in infinitū parua ꝓportione mo-
uebitur qm̄ ipſa ſic cõtinue remittente cū altera re
mittente motū ſuū ad nõ gradū: neceſſe eſt ipſã ad
nõ gradū remittere ſimiliter motū ſuū: et ſic ab in
īfinitū parua ꝓportiõe moueri / vt ſepiꝰ ſupra argu
gutū eſt. 111. correĺ. ¶ Ex quo ſequit̄̄ / ſi aliqua potētia varia
ta moueretur vniformiter cõtinuo remittēs motuꝫ
ſuū ad nõ gradū cū alia nõ variata: et moueret̄̄ cõ-
tinuo a ꝓportiõe in cētuplo vel millecuplo vel quã-
tūcun volueris maiori: ipſã ab in infinitū parua
ꝓportiõe mouebit̄̄ antea quã deueniat ad finē quã
quecū potētia quãtacū parua nõ remittēte mo
tum ſuū ad nõ gradū idē mediū trãſeūdo. Hoc ptꝫ
ex ꝓbatione concluſionum precedentis capitis.
bationē nego / potentia vt .16. continuo velocius
mouebitur quã potentia vt .10. maior nõ variata / et
cū ꝓbatur admiſſo caſu nego antecedens. Dico em̄ /
illa potentia maior vt .16. variata antea quã de-
euniat ad finē ab in infinitū parua ꝓportione mo-
uebitur qm̄ ipſa ſic cõtinue remittente cū altera re
mittente motū ſuū ad nõ gradū: neceſſe eſt ipſã ad
nõ gradū remittere ſimiliter motū ſuū: et ſic ab in
īfinitū parua ꝓportiõe moueri / vt ſepiꝰ ſupra argu
gutū eſt. 111. correĺ. ¶ Ex quo ſequit̄̄ / ſi aliqua potētia varia
ta moueretur vniformiter cõtinuo remittēs motuꝫ
ſuū ad nõ gradū cū alia nõ variata: et moueret̄̄ cõ-
tinuo a ꝓportiõe in cētuplo vel millecuplo vel quã-
tūcun volueris maiori: ipſã ab in infinitū parua
ꝓportiõe mouebit̄̄ antea quã deueniat ad finē quã
quecū potētia quãtacū parua nõ remittēte mo
tum ſuū ad nõ gradū idē mediū trãſeūdo. Hoc ptꝫ
ex ꝓbatione concluſionum precedentis capitis.
Tertio principaliter cõtra eandē cõ-
cluſione arguit̄̄ ſic / q2 ſi illa eſſet vera / ſeq̄ret̄̄ a. potē
tiã maiorē variatã in īfinitū intēdi: ſed ↄ̨ſequēs eſt
falſū: igit̄̄ illud ex quo ſequit̄̄: falſitas cõſequentis
apparet manifeſte: qm̄ tūc nõ cõtinuo remittet mo
tum ſuū. Plus em̄ aliquãdo accreſceret ſibi de pro
portiõe ꝑ intēſionē ſue potentie quã deꝑderet̄̄ ꝑ re-
ſiſtentie acquiſitionē. Seq̄la tamē ꝓbat̄̄ / qm̄ in īfi-
nitū vetociter intendit̄̄ ipſa a. potētia: igit̄̄ ipſa in
īfinitū ītendit̄̄. Aneecedēs ꝓbat̄̄: qm̄ in īfinitū velo-
citer ꝓportiõabiliter accreſcet ſibi reſiſtētia / vt ptꝫ
ex ꝓbatiõe quīte cõcluſiõis ſeptimi capitis huiꝰ: et
ipſa cõtinuo vniformiter remittit motū ſuū: igit̄̄ in
īfinitū velociter accreſcit ſibi potentia. Minor eſt
nota ex cõcluſiõe: et ꝓbat̄̄ ↄ̨ña / qm̄ ſi ſolū finite velo-
citer accreſceret ſibi potētia: et reſiſtētia in īfinitum
velociter ei accreſceret ſequeret̄̄ / nõ ſemꝑ eque ve
lociter deꝑderet ꝓportionē: et ꝑ ↄ̨ñs nõ vniformiter
remitteret motū ſuū: igit̄̄ ſi cõtinuo vniformiter re
mittit motū ſuū: et in īfinitū velociter ꝓportiõabi-
liter acquirit̄̄ ſibi reſiſtētia: ſequit̄̄ / potētia eiꝰ in
īfinitū velociter intēdit̄̄. Patet hec ↄ̨ña / qm̄ oppo-
ſitū cõſcqrētis cū altera parte ãtecedētis īfert op-
poſitū alteriꝰ partis eiuſdē ãtecedētis. Sed iã ꝓbo
ãtecedēs / q̄ eſt vna cõditiõalis videlicet / ſi ſolū fini
te velociter creſceret ſibi potētia et reſiſtētia in īfini
tū velociter ei accreſceret / tã ſeq̄ret̄̄ / nõ ſemꝑ eque
velociter deꝑderet ꝓportionē: et ſic nõ vniformiter
cõtinuo remitteret motū ſuū: q2 ſi ſolū finite veloci-
ter accreſceret ſibi potētia: et reſiſtētia in īfinitū ve-
lociter ei accreſceret: tã ſeq̄ret̄̄ / in īfinitū velocius
ꝓportiõabiliter accreſceret ei reſiſtētia quã poten-
tia: et ꝑ ↄ̨ñs in īfinitū maiorē ꝓportionē deꝑderet ꝑ
acquiſitionē reſiſtētie quã acquireret ꝑ acquiſitio-
nē potētie: et ex cõſequēti in īfinitū velociter deper-
deret ꝓportionē: et ſic nõ ſemꝑ eque velociter deper
deret ꝓportionē nec continuo vniformiter remitte
ret motū ſuū: et ſic de primo ad vltimū ptꝫ illa ↄ̨ña
ꝓbanda. Cõſequētia ptꝫ videlicet / ſi ſolū finite ve
lociter accreſceret ſibi potētia: reſiſtētia in īfinitū
velociter ei accreſceret ſequeret̄̄ / in īfinitū velociꝰ
ꝓportionabiliter accreſceret ei reſiſtentia quã po-
tentia: qm̄ ſi cõtinuo eque velociter accreſceret ſibi
reſiſtētia ſicut potētia: velocius ꝓportiõabiliter ac
creſceret quã potētia / vt ptꝫ ex octaua ſuppõe q̈rta
capitꝪ ſcḋe partꝪ: hoc addito / ↄ̨tinuo potētia ma
net maior: ſꝫ modo ī īfinitū velociꝰ accreſcit ſibi re
ſiſtētia quã potētia: g̊ in īfinitū velociꝰ ꝓportiõabi
liṫ accreſcit ſibi reſtētia quã potētia / qḋ fuit ꝓbãdū
cluſione arguit̄̄ ſic / q2 ſi illa eſſet vera / ſeq̄ret̄̄ a. potē
tiã maiorē variatã in īfinitū intēdi: ſed ↄ̨ſequēs eſt
falſū: igit̄̄ illud ex quo ſequit̄̄: falſitas cõſequentis
apparet manifeſte: qm̄ tūc nõ cõtinuo remittet mo
tum ſuū. Plus em̄ aliquãdo accreſceret ſibi de pro
portiõe ꝑ intēſionē ſue potentie quã deꝑderet̄̄ ꝑ re-
ſiſtentie acquiſitionē. Seq̄la tamē ꝓbat̄̄ / qm̄ in īfi-
nitū vetociter intendit̄̄ ipſa a. potētia: igit̄̄ ipſa in
īfinitū ītendit̄̄. Aneecedēs ꝓbat̄̄: qm̄ in īfinitū velo-
citer ꝓportiõabiliter accreſcet ſibi reſiſtētia / vt ptꝫ
ex ꝓbatiõe quīte cõcluſiõis ſeptimi capitis huiꝰ: et
ipſa cõtinuo vniformiter remittit motū ſuū: igit̄̄ in
īfinitū velociter accreſcit ſibi potentia. Minor eſt
nota ex cõcluſiõe: et ꝓbat̄̄ ↄ̨ña / qm̄ ſi ſolū finite velo-
citer accreſceret ſibi potētia: et reſiſtētia in īfinitum
velociter ei accreſceret ſequeret̄̄ / nõ ſemꝑ eque ve
lociter deꝑderet ꝓportionē: et ꝑ ↄ̨ñs nõ vniformiter
remitteret motū ſuū: igit̄̄ ſi cõtinuo vniformiter re
mittit motū ſuū: et in īfinitū velociter ꝓportiõabi-
liter acquirit̄̄ ſibi reſiſtētia: ſequit̄̄ / potētia eiꝰ in
īfinitū velociter intēdit̄̄. Patet hec ↄ̨ña / qm̄ oppo-
ſitū cõſcqrētis cū altera parte ãtecedētis īfert op-
poſitū alteriꝰ partis eiuſdē ãtecedētis. Sed iã ꝓbo
ãtecedēs / q̄ eſt vna cõditiõalis videlicet / ſi ſolū fini
te velociter creſceret ſibi potētia et reſiſtētia in īfini
tū velociter ei accreſceret / tã ſeq̄ret̄̄ / nõ ſemꝑ eque
velociter deꝑderet ꝓportionē: et ſic nõ vniformiter
cõtinuo remitteret motū ſuū: q2 ſi ſolū finite veloci-
ter accreſceret ſibi potētia: et reſiſtētia in īfinitū ve-
lociter ei accreſceret: tã ſeq̄ret̄̄ / in īfinitū velocius
ꝓportiõabiliter accreſceret ei reſiſtētia quã poten-
tia: et ꝑ ↄ̨ñs in īfinitū maiorē ꝓportionē deꝑderet ꝑ
acquiſitionē reſiſtētie quã acquireret ꝑ acquiſitio-
nē potētie: et ex cõſequēti in īfinitū velociter deper-
deret ꝓportionē: et ſic nõ ſemꝑ eque velociter deper
deret ꝓportionē nec continuo vniformiter remitte
ret motū ſuū: et ſic de primo ad vltimū ptꝫ illa ↄ̨ña
ꝓbanda. Cõſequētia ptꝫ videlicet / ſi ſolū finite ve
lociter accreſceret ſibi potētia: reſiſtētia in īfinitū
velociter ei accreſceret ſequeret̄̄ / in īfinitū velociꝰ
ꝓportionabiliter accreſceret ei reſiſtentia quã po-
tentia: qm̄ ſi cõtinuo eque velociter accreſceret ſibi
reſiſtētia ſicut potētia: velocius ꝓportiõabiliter ac
creſceret quã potētia / vt ptꝫ ex octaua ſuppõe q̈rta
capitꝪ ſcḋe partꝪ: hoc addito / ↄ̨tinuo potētia ma
net maior: ſꝫ modo ī īfinitū velociꝰ accreſcit ſibi re
ſiſtētia quã potētia: g̊ in īfinitū velociꝰ ꝓportiõabi
liṫ accreſcit ſibi reſtētia quã potētia / qḋ fuit ꝓbãdū
Reſpõdeo negãdo ſeq̄lã: ad ꝓbatio-
nē nego ↄ̨ñam / q̄ nulliꝰ eſt apparētie. Stat em̄ / ali
quid in īfinitū velociṫ intēdi in hora: et tñ ſolū finite
intēdi: vt ſatis cõſtat ſi diuiſa hora ꝑ partes ꝓpor
tiõales ꝓportiõe q̈drupla: in ṗma illaꝝ acq̇rit̄̄ ali-
cui corpori vnꝰ gradꝰ calditatis, et in ſcḋa dimidiꝰ
et ī ṫcia, vna q̈rta, et ſic ↄ̨ñter: ꝑ partes ꝓportioãles
ꝓportione dupla: tunc manifeſtuꝫ eſt / tota illa ca
liditas erit duorum graduum in fine adequate / vt
patet ex ſecundo correlario tertie concluſionis quī-
ti capitis prime partis: Ibi enim acquiritur illa q̈-
litas per partes ꝓportionales ꝓportione dupla:
igitur reſiduuꝫ a prima eſt equale prime: et prima
erit vnus gradus: ergo totum eſt duorum graduuꝫ
adequate / vt patet ex ſucūdo correlario preallega-
to: et tamen in infinitum velociter acquiritur illa ca
liditas: quoniam qualitas illa acquiritur in ſecun
da parte ꝓportionali in duplo velocius quã in pri
ma et in tertia in duplo velocius quam in ſecunda. /
nē nego ↄ̨ñam / q̄ nulliꝰ eſt apparētie. Stat em̄ / ali
quid in īfinitū velociṫ intēdi in hora: et tñ ſolū finite
intēdi: vt ſatis cõſtat ſi diuiſa hora ꝑ partes ꝓpor
tiõales ꝓportiõe q̈drupla: in ṗma illaꝝ acq̇rit̄̄ ali-
cui corpori vnꝰ gradꝰ calditatis, et in ſcḋa dimidiꝰ
et ī ṫcia, vna q̈rta, et ſic ↄ̨ñter: ꝑ partes ꝓportioãles
ꝓportione dupla: tunc manifeſtuꝫ eſt / tota illa ca
liditas erit duorum graduum in fine adequate / vt
patet ex ſecundo correlario tertie concluſionis quī-
ti capitis prime partis: Ibi enim acquiritur illa q̈-
litas per partes ꝓportionales ꝓportione dupla:
igitur reſiduuꝫ a prima eſt equale prime: et prima
erit vnus gradus: ergo totum eſt duorum graduuꝫ
adequate / vt patet ex ſucūdo correlario preallega-
to: et tamen in infinitum velociter acquiritur illa ca
liditas: quoniam qualitas illa acquiritur in ſecun
da parte ꝓportionali in duplo velocius quã in pri
ma et in tertia in duplo velocius quam in ſecunda. /