Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Primi tractatus
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0111
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maiori in qua proportione maius medium excedit
<
lb
/>
minꝰ: tūc cõtinuo vniformiter et eque velociter oīno
<
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ille potentie mouētur. </
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>
<
s
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N1AC12
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xml:space
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preserve
">Uolo dicere / ſi ſint duo me
<
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/>
dia ſe habentia in proportione dupla, per que ex-
<
lb
/>
tenditur cõſimilis latitudo reſiſtentie vniformiter
<
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/>
difformis terminata ad non gradum: et moueatur
<
lb
/>
vna potentia in minori medio incipiendo a nõ gra
<
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/>
du medii, et a nõ gradu potentie, continuo creſcen-
<
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/>
do vniformiter: et in medio maiori moueatur vna
<
lb
/>
alia potentia incipiēdo ſimiliter creſcere a nõ gra
<
lb
/>
du potentie, et a non gradu reſiſtentie: quia inter
<
lb
/>
illa media eſt proportio dupla creſcat cõtinuo po-
<
lb
/>
tentia que mouetur in medio minori in duplo velo-
<
lb
/>
cius altera que mouetur in medio maiori: tunc di-
<
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co ille potentie mouentur equaliter. </
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<
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xml:space
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<
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correlariū vniuerſaliter. </
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<
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xml:space
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">Et ſuppono / in quacū
<
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proportione ſe habent talia media per que extendi
<
lb
/>
tur latitudo eadem vel cõſimilis reſiſtentie vnifor-
<
lb
/>
miter difformis terminate ad nõ gradū: in ea pro-
<
lb
/>
portione ſe habēt puncta equi diſtantia a nõ gradu
<
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in illis mediis. </
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<
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xml:space
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">Quod ptꝫ facile ex diffinitione qua
<
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litatis vniformiter difformis quarto tractatu. </
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<
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xml:space
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<
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ſuppoſito probatur correlarium. </
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<
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N1AC49
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xml:space
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preserve
">Et ſint duo me-
<
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dia ſe habentia in f. proportione et moueatur a. po
<
lb
/>
tentia in maiori continuo vniformiter: et b. in mino
<
lb
/>
ri: et creſcat b. cõtinuo in f. proportione velocius a.
<
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</
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<
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xml:space
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">Quo poſito ſic argumentor / potentia b. que moue-
<
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tur in medio minori nõ mouetur velocius a. nec tar
<
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dius: igitur cõtinuo equaliter. </
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<
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xml:space
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<
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et probatur maior: quia ſi b. mouetur velocius quã
<
lb
/>
a. / ſequitur / b. eſt in puncto magis diſtante a non
<
lb
/>
gradu ſui medii ꝙ̄ a. / igitur mouetur a. minori pro-
<
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portione ꝙ̄ a. / et per conſequēs tardius. </
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<
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xml:id
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N1AC65
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xml:space
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">Patet hec
<
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conſequentia / quia ſi eſſent in punctis equidiſtanti
<
lb
/>
bus mouerentur ab eadem proportione: quoniam
<
lb
/>
tunc f. proportio eſſet inter illa puncta / vt patet ex
<
lb
/>
ſuppoſitione: et inter potentias etiam eſſet f. pro-
<
lb
/>
portio: ergo ſequitur / ille potentie haberent e-
<
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quales proportiones ad ſuas reſiſtentias. </
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>
<
s
xml:id
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N1AC74
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xml:space
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preserve
">Patet
<
lb
/>
conſequentia / quia ſi inter b. et a. eſt f. proportio: et
<
lb
/>
inter reſiſtentiam ipſius b. et reſiſtentiam ipſius a.
<
lb
/>
eſt f. proportio: igitur qualis eſt proportio ipſiꝰ b.
<
lb
/>
ad a. talis eſt reſiſtentie ipſius b. ad reſiſtentiam
<
lb
/>
ipſius a. et ſi talis eſt proportio ipſius b. ad a. qua-
<
lb
/>
lis eſt reſiſtentie ipſius b. ad reſiſtentiam ipſius a. /
<
lb
/>
ſequitur permutatim ex ſecunda concluſione tertii
<
lb
/>
capitis ſecunde partis / talis eſt proportio ipſius
<
lb
/>
b. ad reſiſtentiam ipſius b. qualis eſt ipſiꝰ a. ad re-
<
lb
/>
ſiſtentiam ipſius a. / et ſic ptꝫ conſequentia. </
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<
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<
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ex ↄ̨ſequēti ille potentie a. et b. / tunc haberent equa-
<
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/>
les proportiones ad ſuas reſiſtentias: ergo modo
<
lb
/>
proportio ipſius b. ad ſuam reſiſtentiam eſt minor
<
lb
/>
quam proportio ipſius a. ad ſuam reſiſtentiam: et
<
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/>
per conſequens mouetur tardius. </
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<
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<
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tia / quia b. eſt in maiori reſiſtentia quam tunc eſſet.
<
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</
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<
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xml:space
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">Et per hoc ptꝫ minor / quia ſi b. mouetur tardiꝰ quã
<
lb
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a. / ſequitur / eſt in minori reſiſtentia quam eſſet ſi
<
lb
/>
moueretur equaliter ſicut a. ſed ſi moueret̄̄ equali-
<
lb
/>
ter ſicut a. moueretur ab eadem proportione: et mo
<
lb
/>
do mouetur in minori reſiſtentia quam tunc: ergo
<
lb
/>
a. maiori proportione/ et per conſequens velocius et
<
lb
/>
nõ tardius / quod eſt oppoſitum conceſſi. </
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>
<
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xml:space
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">Et ſic patꝫ
<
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antecedens et per conſequens totum correlarium.
<
lb
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<
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xml:space
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">3. correĺ.</
note
>
</
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<
s
xml:id
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xml:space
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">¶ Sequitur tertio / ſi ſint duo media ineq̈lia qua
<
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/>
lificata eadem vel conſimili reſiſtentia vniformiter
<
lb
/>
difformi terminata ad nõ gradum: et incipiant due
<
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/>
potentie non variate in eodem inſtanti moueri per
<
lb
/>
illa media: et talis ſit proportio potentie mouentis
<
lb
/>
in medio minori ad reliquam potentiaꝫ qualis eſt
<
cb
chead
="
Capitulū duodecimū.
"/>
proportio medii maioris ad medium minus: tunc
<
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tales potētie cõtinuo eque velociter mouētur. </
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<
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xml:space
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">Pro
<
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batur: et ſint duo media īter que eſt ꝓportio f. et ſint
<
lb
/>
due potentie a. et b. et b. ad a. ſit f. proportio: et in-
<
lb
/>
cipiat b. moueri in minori medio ad non gradu et
<
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/>
a. in maiori. </
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<
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">Quo poſito arguo ſic / a. et b. continuo
<
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ſunt in punctis equidiſtantibus a nõ gradu ſui me-
<
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dii: ergo continuo eque velociter mouentur. </
s
>
<
s
xml:id
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N1ACDD
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xml:space
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">Patet
<
lb
/>
conſequentia / quia pūcta equaliter diſtantia ſe ha
<
lb
/>
bent in f. proportione: vt patet ex ſuppoſitione ſu-
<
lb
/>
perioris correlarii: ergo ſequitur / ſi potētie ſunt
<
lb
/>
in punctis eque diſtantibus ipſe mouentur ab e-
<
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quali proportione. </
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>
<
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xml:id
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N1ACEA
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xml:space
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">Patet conſequentia vt in ſupe
<
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riori correlario. </
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>
<
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xml:id
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N1ACEF
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xml:space
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preserve
">Et ex conſequenti ſequitur: ſi b.
<
lb
/>
eſt in puncto magis propinquo non gradui ꝙ̄ a.
<
lb
/>
iã mouetur a. maiori ꝓportione ꝙ̄ a. q2 eſt in remiſ
<
lb
/>
ſiori puncto quã eſſet ſi eſſet in puncto equidiſtanti
<
lb
/>
ſicut a. / et per cõſequens moueretur velocius ꝙ̄ a. </
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>
<
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xml:id
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N1ACFA
"
xml:space
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preserve
">Et
<
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/>
ſi eſſet in puncto magis diſtanti a nõ gradu ꝙ̄ a. / iã
<
lb
/>
ſequitur / tunc moueretur cū reſiſtentia intenſiori
<
lb
/>
quã ſi eſſet in puncto equidiſtãti ſicut pūctus in quo
<
lb
/>
eſt a. / et per ↄ̨ſequēs moueret̄̄ tardiꝰ quã a. et ſic nõ ve
<
lb
/>
lociꝰ. </
s
>
<
s
xml:id
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N1AD07
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xml:space
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preserve
">Patet cõſequētia / q2 ſi eſſet in puncto equidi-
<
lb
/>
ſtanti ſicut a. moueretur ab equali ꝓportione: ergo
<
lb
/>
quãdo eſt in intēſiori mouetur a minori. </
s
>
<
s
xml:id
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N1AD0E
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xml:space
="
preserve
">Et ſic patꝫ
<
lb
/>
veritas correlarii / qm̄ ad b. moueri velociꝰ a. / ſequit̄̄
<
lb
/>
ipſum moueri tardius: et ad b. moueri tardius, ſe-
<
lb
/>
quitur ipſum moueri velocius. </
s
>
<
s
xml:id
="
N1AD17
"
xml:space
="
preserve
">Opus eſt dicere igi
<
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/>
tur / continuo mouetur equaliter cum ipſo a.</
s
>
</
p
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<
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right
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xml:id
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xml:space
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">4. correĺ.</
note
>
<
p
xml:id
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N1AD36
">
<
s
xml:id
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N1AD37
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xml:space
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preserve
">¶ Sequitur quarto: dabile eſt medium vniformi
<
lb
/>
ter difforme in reſiſtentia ad nõ gradum termina-
<
lb
/>
tum: quod potentia a non gradu potentie creſcens
<
lb
/>
vniformiter continuo, nõ valet vniformiter conti-
<
lb
/>
nuo mouendo ſuo motu abſoluere ab extremo re-
<
lb
/>
miſſiori inchoando. </
s
>
<
s
xml:id
="
N1AD44
"
xml:space
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preserve
">Probatur / et capio vnū mediū
<
lb
/>
difforme in quantitate vniformiter difforme in re-
<
lb
/>
ſiſtentia terminata ad non gradū: cuius medii pri-
<
lb
/>
ma medietas puta remiſſior ſit longior quam ſecū
<
lb
/>
da in ſexquialtero / vt patet in figura.</
s
>
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number
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8
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<
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file
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0111-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0111-01
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<
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xml:id
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xml:space
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preserve
">Et incipiat b. potentia ab extremo remiſſiori talis
<
lb
/>
medii moueri creſcendo a nõ gradu potentie conti-
<
lb
/>
nuo vniformiter inchoando ab extremo remiſſiori
<
lb
/>
vt ſepius poſitū eſt: et moueatur quo ad vſ ad ex-
<
lb
/>
tremū intenſius deueniat per lineã rectam: tunc di
<
lb
/>
co / ipſa potentia b. nõ cõtinuo vniformiter moue
<
lb
/>
tur illud medium tranſeundo. </
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>
<
s
xml:id
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N1AD63
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xml:space
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preserve
">Quod ſic probatur /
<
lb
/>
q2 ſi b. potentia cõtinuo vniformiter moueretur pu
<
lb
/>
ta a. proportione f. exempli gratia in ſexquialtero
<
lb
/>
minori tēpore totam ſecundã medietatē magis re-
<
lb
/>
ſiſtentē abſolueret quaꝫ primã quia ipſa eſt in ſex-
<
lb
/>
quialtero breuior ex hypotheſi: et ex cõſequenti ſe-
<
lb
/>
quitur / b. potentia tranſeundo ſecundã medieta-
<
lb
/>
tem in ſexquialtero minorē potētiam acquirit quã
<
lb
/>
tranſeundo primam medietatem: cum vniformiter
<
lb
/>
continuo intendatur: et tranſeundo eandē ſecundã
<
lb
/>
medietatē ſue reſiſtentie, tantam latitudinē acqui-
<
lb
/>
rit adequate ſicut tranſeūdo primã q2 reſiduã me-
<
lb
/>
dietatē latitudinis: igitur tranſeundo ſecundã me-
<
lb
/>
dietatem inter acquiſitū potentie et acquiſitū reſi-
<
lb
/>
ſtentie nõ eſt tanta proportio ſicut tranſeundo pri-
<
lb
/>
mam: et tranſeundo primam eſt proportio f. / vt pa-
<
lb
/>
tet / quia continuo ab f. proportiõe mouetur per te: </
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