Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Primi tractatus
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0097
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97
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remiſſioris medietatis vt cõſtat: igitur per equaleꝫ
<
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/>
latitudinem diſtat ab vtra: et per conſequens per
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quantum excedit extremū remiſſius medietatis re
<
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/>
miſſioris cuius eſt extremuꝫ intenſiua, per tantum
<
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exceditur ab extremo intenſiori intenſioris medie-
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tatis cuiꝰ medietatis eſt extremū remiſſius. </
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<
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N196AD
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xml:space
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hec cõſequentia ex vltima ſuppoſitione ſecūdi capi
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tis ſecūde partis. </
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<
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xml:space
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">Itē captis tribus tertiis per tan
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tum extremū intenſius remiſſioris tertie excedit ex
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/>
tremū remiſſius eiuſdē tertie, per quantuꝫ extremū
<
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/>
intenſius tertie īmediate ſequētis excedit extremū
<
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/>
remiſſius eiuſdem tertie: et per quantum extremum
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intenſius vltime tertie excedit extremum remiſſius
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eiuſdem. </
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N196C3
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xml:space
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">Quod probatur ſic / quia extremū intenſiꝰ
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/>
tertie remiſſioris eſt gradus medius inter extremū
<
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/>
intenſius tertie īmediate ſequentis et extremum re-
<
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/>
miſſius remiſſioris tertie: igitur equali latitudine
<
lb
/>
diſtat ab extremo intenſiori tertie īmediate ſequē-
<
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/>
tis et ab extremo remiſſiori tertie remiſſioris: et per
<
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/>
cõſequens ille gradus medius per equalem latitu-
<
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/>
dinem excedit extremū remiſſius tertie remiſſioris
<
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/>
cuiꝰ eſt extremū intenſius ſicut exceditur ab extre-
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/>
mo intenſiori tertie īmediate ſequentis cuiꝰ eſt ex-
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tremū remiſſius. </
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<
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xml:space
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intenſius ſecunde tertie per equalem latitudinem
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/>
excedit extremū remiſſius eiuſdem tertie: ſicut extre
<
lb
/>
mū intenſius vltime tertie īmediate ſequentis exce
<
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/>
dit ſuū extremum remiſſius. </
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>
<
s
xml:id
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N196E5
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xml:space
="
preserve
">Et ſic habebis / per
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equalem latitudinem cuiuſlibet illarum tertiarum
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/>
extremum intenſius excedit extremum remiſſius
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eiuſdem. </
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<
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xml:space
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ſiue tribus, ſiue quattuor que nõ ſunt pars aut par
<
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/>
tes aliquote: cuiuſlibet illarū extremū intēſius per
<
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/>
equalem latitudinē excedit ſuū extremū remiſſius.
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/>
</
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<
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xml:id
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N196F8
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xml:space
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preserve
">Quod ſic probatur / q2 captis duabus illarū īme-
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diatis extremū intēſius remiſſioris partis eſt gra-
<
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/>
dus medius inter extremū intenſius intēſioris par
<
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/>
tis et extremū remiſſius remiſſioris illarum: igitur
<
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/>
per equalem latitudinem diſtat ab extremo inten-
<
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/>
ſiori intēſioris partis et ab extremo remiſſiori par
<
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/>
tis remiſſioris: et per conſequēs ille gradus mediꝰ
<
lb
/>
per equalem latitudinē excedit extremū remiſſius
<
lb
/>
remiſſioris partis illarum cuiꝰ eſt extremū intenſi
<
lb
/>
us: et exceditur ab extremo intenſiori partis inten-
<
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/>
ſioris cuiꝰ eſt extremū remiſſius. </
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>
<
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xml:space
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">Et iſto modo pro-
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babis ſignatis tribus / per equalē latitudinē ex-
<
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/>
tremū intenſius tertie excedit ſuū extremū remiſſiꝰ
<
lb
/>
et extremū intenſius ſecunde excedit ſuū extremum
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/>
remiſſius. </
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>
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xml:space
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">Et ſic habebis / cuiuſlibet illarū trium
<
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partiū extremū intenſius per equalem latitudineꝫ
<
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/>
excedit extremū remiſſius. </
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>
<
s
xml:id
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N19721
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xml:space
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preserve
">Et ſic in omnibus aliis
<
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partibus equalibꝰ operaberis. </
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>
<
s
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N19726
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xml:space
="
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">Patet igitur ſup-
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poſitio.
<
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xml:id
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xml:space
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">1. correĺ.</
note
>
</
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<
s
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xml:space
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preserve
">¶ Ex quo ſequitur / oīs potentia latitudi
<
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/>
nem vniformiter difformē īuariatam pertranſiēs:
<
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/>
equales partes tranſeundo incipiēdo ab extremo
<
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/>
remiſſiori equalem latitudinē reſiſtentie adequate
<
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acquirit. </
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<
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xml:space
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">Probatur / q2 talis potentia tranſeundo
<
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/>
aliquam partē adequate, acquirendo reſiſtentiam
<
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/>
illã reſiſtentiã adequate acquirit per quã extremū
<
lb
/>
intenſius illius partis excedit extremum remiſſius
<
lb
/>
eiuſdem partis / vt ſatis conſtat: et cuiuſlibet partis
<
lb
/>
equalis (ex precedenti ſuppoſitione) extremū inten
<
lb
/>
ſius per equalem latitudinem excedit extremum re
<
lb
/>
miſſius: igitur talis potentia latitudinem reſiſten
<
lb
/>
tie vniformiter difformem inuariatam pertranſi-
<
lb
/>
ens: equalem latitudinem reſiſtentie adequate ac-
<
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/>
quirit. </
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<
s
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xml:space
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">Et ſic ptꝫ correlarium.
<
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note-0097-02
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xml:id
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xml:space
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preserve
">2. correĺ.</
note
>
</
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<
s
xml:id
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N1975A
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xml:space
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">¶ Sequitur ſecundo /
<
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omnis potentia latitudinem reſiſteutie vniformi
<
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/>
ter difformē īuariatã pertranſiens incipiendo ab
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chead
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Capitulū decimū.
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extremo intēſiori, equales partes tranſeūdo, equa
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lem latitudinē reſiſtentie adequate deperdit. </
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<
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">Ptꝫ /
<
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quia incipiēdo ab extremo remiſſiori, equales par
<
lb
/>
tes tranſeundo equalem latitudinē reſiſtentie ade-
<
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/>
quate acquirit / vt ptꝫ ex precedenti correlario: igit̄̄
<
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/>
incipiendo ab extremo intenſiori, equales partes
<
lb
/>
tranſeundo equalem latitudinē reſiſteutie adequa
<
lb
/>
te deperdit: quia in eiſdem partibus eandem lati-
<
lb
/>
tudinem reſiſtentie adequate deperdit quaꝫ antea
<
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/>
in eiſdem acquirebat. </
s
>
<
s
xml:id
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N19779
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xml:space
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preserve
">Et ſic patet correlarium.</
s
>
</
p
>
<
p
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<
s
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xml:space
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preserve
">Hoc iacto fundamento ſit prima con-
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cluſio. </
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>
<
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N19792
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xml:space
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preserve
">Omnis potentia mouens continuo vnifor-
<
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miter mediū vniformiter difforme īuariatum tran
<
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/>
ſeundo incipiendo ab extremo remiſſiori: continuo
<
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/>
vniformiter intendit potentiam ſuam, ceteris iuua
<
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/>
mentis ac impedimētis deductis. </
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>
<
s
xml:id
="
N1979D
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xml:space
="
preserve
">Probatur: ſit c.
<
lb
/>
mediū vniformiter difforme quod inuariatū a. po-
<
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/>
tentia vniformiter continuo mouendo ab f. propor
<
lb
/>
tione pertranſeat ab extremo remiſſiori incipiēdo
<
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/>
moueatur continuo a. potentia ſecundū propor-
<
lb
/>
tionem quam habet ad īmediatem reſiſtentiam, ce
<
lb
/>
teris aliis iuuaminibus et obſtaculis deductis: tūc
<
lb
/>
dico / a. potentia cõtinuo vniformiter intendit po
<
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/>
tentiam ſuam. </
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<
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xml:space
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">Quod ſic oſtenditur / quia a. poten-
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/>
tia continuo ſe habet in f. proportione ad ſuam re-
<
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/>
ſiſtentiam. </
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>
<
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N197B7
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xml:space
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">Nam a. potentia continuo ab f. propor
<
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tione mouetur ex hypotheſi: et ſua reſiſtentia conti-
<
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/>
nuo vniformiter creſcit: igitur a. potentia cõtinuo
<
lb
/>
vniformiter creſcit: et per conſequens a. potentia cõ
<
lb
/>
tinuo vniformiter intendit potentiam ſuam / quod
<
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/>
fuit probandum. </
s
>
<
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N197C4
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xml:space
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preserve
">Patet hec cõſequentia ex proba-
<
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tione prime ſuppoſitionis octaui capitis huiꝰ tra-
<
lb
/>
ctatus / hoc addito / reſiſtentia eſt terminus minor
<
lb
/>
continuo proportionis f. et potentia a. terminꝰ ma-
<
lb
/>
ior. </
s
>
<
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xml:id
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N197CF
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xml:space
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preserve
">Probatur minor / quia a. potentia continuo in
<
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/>
equalibus partibus temporis equales partes illiꝰ
<
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/>
reſiſtentie vniformiter difformis pertranſit conti-
<
lb
/>
nuo acquirendo reſiſtentiam, quia mouetur conti-
<
lb
/>
nuo vniformiter verſus extremū intenſius: et conti-
<
lb
/>
nuo equales partes tranſeundo equalem latitudi-
<
lb
/>
nem reſiſtentie acquirit / vt ptꝫ ex primo correlario
<
lb
/>
ſuppoſitionis: igitur continuo in equalibus parti
<
lb
/>
bus temporis equalem latitudinem reſiſtentie ac-
<
lb
/>
quirit: et per conſequens reſiſtentia ipſius a. poten
<
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/>
tie vniformiter continuo creſcit / quod fuit proban-
<
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/>
dum. </
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<
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xml:space
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">Et ſic patꝫ concluſio.
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note-0097-03
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xml:id
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xml:space
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preserve
">3. correĺ.</
note
>
</
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>
<
s
xml:id
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N197F0
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xml:space
="
preserve
">¶ Ex quo ſequitur / oīs
<
lb
/>
potentia continuo mouens vniformiter, mediū vni
<
lb
/>
formiter difforme inuariatum tranſeundo, incipi-
<
lb
/>
endo ab extremo intenſiori: continuo vniformiter
<
lb
/>
remittit potentiã ſuã: ceteris aliis deductis. </
s
>
<
s
xml:id
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N197FB
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xml:space
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preserve
">Pro-
<
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batur: ſit c. medium vt ſupra quod inuariatū a. po-
<
lb
/>
tentia vniformiter continuo mouendo ab f. propor
<
lb
/>
tione pertranſeat ab extremo intenſiori incipiēdo /
<
lb
/>
tunc dico / a. potentia continuo vniformiter remit
<
lb
/>
tit potentiam ſuam. </
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>
<
s
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N19808
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xml:space
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preserve
">Quod ſic oſtēditur / quia a. po
<
lb
/>
tentia continuo ſe habet in f. proportione ad ſuam
<
lb
/>
reſiſtentiam (cum continuo moueatur ab f. propor-
<
lb
/>
tione ex hypotheſi) et ſua reſiſtentia vniformiter cõ
<
lb
/>
tinuo decreſcit ſiue diminuitur: igitur a. potentia
<
lb
/>
continuo vniformiter remittit potentiam ſuã. </
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xml:space
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">Pa
<
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tet cõſequentia ex probatione prime ſuppoſitionis
<
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/>
octaui capitis preallegati. </
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>
<
s
xml:id
="
N1981C
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xml:space
="
preserve
">Minor probatur / quia
<
lb
/>
a. potentia continuo in equalibus partibus tēpo-
<
lb
/>
ris equales partes illius reſiſtētie vniformiter dif-
<
lb
/>
formis pertranſit continuo deperdendo reſiſten-
<
lb
/>
tiam (cum continuo vniformiter moueatur verſus
<
lb
/>
extremū remiſſius ex hypotheſi) et continuo verſus
<
lb
/>
extremū remiſſius mouēdo, equales partes tran-
<
lb
/>
ſeūdo, equalē latitudinē oīno reſiſtētie deperdit / vt </
s
>
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