Alvarus, Thomas
,
Liber de triplici motu
,
1509
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De motu penes cauſã ī medio vniformiṫ difformi īuariato.
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patet ex ſecundo correlario ſuppoſitionis: igitur
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a. potentia continuo in equalibus partibus tēpo-
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ris equalem latitudinem reſiſtentie deperdit: et per
<
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conſequens reſiſtentia ipſius a. potentie continuo
<
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vniformiter decreſcit ſiue diminuitur / qḋ fuit pro-
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bandum. </
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<
s
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xml:space
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<
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xml:id
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xml:space
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">Prima
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cõcluſio
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calcula.</
note
>
<
p
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<
s
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xml:space
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">Secunda concluſio. </
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>
<
s
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N19855
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xml:space
="
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">Oīs potentia a
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non gradu potentie creſcens continuo vniformiter
<
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/>
tranſeundo medium vniformiter difforme īuaria-
<
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/>
tum ad non gradū terminatum, incipiendo ab ex-
<
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/>
tremo remiſſiori: continuo vniformiter mouetur.
<
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/>
</
s
>
<
s
xml:id
="
N19861
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xml:space
="
preserve
">Probatur / ſit c. medium vniformiter difforme ad
<
lb
/>
non gradum terminatum vt in caſu concluſionis:
<
lb
/>
ſit a. potentia que a nõ gradu potentie continuo
<
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/>
vniformiter creſcens c. medium in d. tempore ade-
<
lb
/>
quate pertranſit, ab extremo remiſſiori incipiēdo
<
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/>
moueatur continuo ſecundum proportionem po
<
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/>
tentie ad reſiſtentiam ſibi īmediatam ceteris dedu
<
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/>
ctis: ſit etiam b. potentia que in eodem d. tēpore
<
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/>
adequate continuo vniformiter mouendo per ſui
<
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/>
variationem pertranſeat idem c. medium ab extre
<
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/>
mo remiſſiori incipiendo: et manifeſtum eſt ex con-
<
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/>
cluſione precedenti b. potentiam a non gradu po-
<
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/>
tentie continuo vniformiter intendere potentiã ſuã
<
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/>
</
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>
<
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xml:space
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preserve
">Dico igitur tunc / a. potentia continuo vniformi-
<
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/>
ter mouetur c. medium tranſeundo. </
s
>
<
s
xml:id
="
N19882
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xml:space
="
preserve
">Quod ſic oſten
<
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/>
ditur / quia a. et b. continuo eque velociter mouētur
<
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/>
oīno: et b. cõtinuo vniformiter mouetur tranſeundo
<
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/>
c. mediū / quod etiam pertranſit a. / vt patet ex hypo-
<
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/>
theſi: igitur a. potentia continuo vniformiter mo-
<
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/>
uetur c. medium tranſeundo / quod fuit probandum
<
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/>
</
s
>
<
s
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N19890
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xml:space
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">Cõſequentia ptꝫ cum minore: et arguitur maior / q2
<
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/>
a. et b. potentie cõtinuo ſunt in eodem puncto c. me
<
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/>
dii: igitur cõtinuo eque velociter mouētur omnino
<
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/>
</
s
>
<
s
xml:id
="
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xml:space
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preserve
">Cõſequentia ptꝫ: et probatur antecedens / quia ſi nõ
<
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/>
detur inſtans in quo a. ſit in pūcto citeriori, aut vl-
<
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/>
teriori: et ſit e. / et arguitur ſic / in e. inſtanti d. tēporis
<
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/>
a. eſt in puncto citeriori vel vlteriori ipſius c. medii
<
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/>
quam b. et a. et b. cõtinuo ſunt equalis potentie: igit̄̄
<
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/>
nõ eque cito pertranſibūt c. medium / quod eſt cõtra
<
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/>
hypotheſim. </
s
>
<
s
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xml:space
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">Patet cõſequentia / q2 ſi a. eſt in pūcto
<
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/>
vlteriori: et cõtinuo eſt equalis b. / ſequitur / citius
<
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/>
deueniet ad terminum c. medii quam b. et ſi in cite-
<
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/>
riori et cõtinuo eſt equalis ipſi b. / ſequitur / tardiꝰ
<
lb
/>
deueniet ad terminū c. medii. </
s
>
<
s
xml:id
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N198B2
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xml:space
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preserve
">Alias eadem potētia
<
lb
/>
vel equalis eque cito abſolueret totam reſiſtētiam
<
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/>
et partem eius adequate / quod eſt impoſſibile dedu
<
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/>
ctis litigioſis captiūculis. </
s
>
<
s
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xml:space
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preserve
">Sed tã probo illas po-
<
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tentias continuo eſſe equales / q2 detur oppoſitum
<
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/>
videlicet / aliquãdo altera illarum ſit altera ma-
<
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/>
ior: et ſequitur cum cõtinuo vniformiter creſcant in
<
lb
/>
eodem tempore a nõ gradu potētie / ipſa cõtinuo
<
lb
/>
erit maior: et per cõſequēs citius abſoluet c. mediū
<
lb
/>
quam altera / quod eſt contra hypotheſim. </
s
>
<
s
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xml:space
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preserve
">Patet
<
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cõſequentia / quia potentia continuo maior maius
<
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/>
ſpacium pertranſit in eodem tēpore quam poten-
<
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/>
tia in eodē tēpore continuo minor ea.
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xml:space
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">Contra
<
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calcula-
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torē.</
note
>
</
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<
s
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xml:space
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">¶ Et ſic patet
<
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concluſio / que eſt prima calculatoris in ſecūdo eius
<
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/>
capite de medio non reſiſtente quam aliter nititur
<
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/>
demonſtrare: ſed ſaluo meliori iudicio demonſtra
<
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/>
tio eſt inefficax. </
s
>
<
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xml:space
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preserve
">Innititur em̄ huic cõſequentie per
<
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/>
nullū tēpus terminatū ad principiū a. intendit mo
<
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/>
tum ſuū nec remittit: ergo a. nun̄ intendit motum
<
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/>
ſuū aut remittit. </
s
>
<
s
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="
N198EC
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xml:space
="
preserve
">Modo illa cõſequētia nõ eſt bona
<
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</
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>
<
s
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xml:space
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">Stat em̄ / a. potentia per nullū tēpus terminatuꝫ
<
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/>
ad inſtans initiatiuū intendat aut remittat motuꝫ
<
lb
/>
ſuū: et tamen per aliquod tēpus nõ terminatum ad
<
lb
/>
principium tēporis intēdat aut remittat motū ſuū
<
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chead
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De motu penes cauſã ī medio vniformiṫ difformi īuariato.
"/>
</
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<
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xml:space
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">Diuiſa em̄ hora per partes proportionales mino
<
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/>
ribus verſus inſtans initiatiuū motus terminatis
<
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/>
a. potentia in qualibet impari intendente motum:
<
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/>
et in qualibet pari remittente: tunc per nullū tēpus
<
lb
/>
terminatum ad principium intendit motum ſuum:
<
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/>
nec per aliquod tale remittit: et tamen intendit mo
<
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/>
tuꝫ ſuū: et remittit per aliquod tēpus nõ terminatū
<
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/>
ad principium temporis. </
s
>
<
s
xml:id
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xml:space
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preserve
">Et hoc forte nare ſagaci
<
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/>
ol faciens calculator adiecit ſecundam probationē
<
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/>
aſſumens / a. potentia per nullum tempus inten-
<
lb
/>
dit motum ſuū nec remittit: ita arguens: quia ſi ſic
<
lb
/>
ſit illud inſtans c. in quo incipit iutendere motum
<
lb
/>
ſuū aut remittere: et ſit f. proportio ex qua cõtinuo
<
lb
/>
vniformiter mouebitur ante c. / et ſequitur / conti-
<
lb
/>
nuo ante in f. proportione tardius creſcit reſiſtētia
<
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/>
̄ eius potentia .etc̈. </
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>
<
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xml:space
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">In qua probatione calculator
<
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duo aſſumit dubia et probãda que aduerſarius de
<
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/>
monſtrationem vndiqua certam et inuiolabilem
<
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/>
efflagitans negaret. </
s
>
<
s
xml:id
="
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xml:space
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preserve
">Aſſumit em̄ primo pro certo et
<
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manifeſto / aliquod eſt inſtans intrinſecum tēpo-
<
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/>
ris in quo primo incipit intendere motum ſuū aut
<
lb
/>
in quo primo incipit remittere motum ſuum ita
<
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/>
nun̄ antea remittit nec intendit motum ſuum. </
s
>
<
s
xml:id
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xml:space
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preserve
">Ad
<
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/>
amuſſim vero omnia dubitabilia ſibi demonſtrari
<
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/>
expetens diceret nullum tale eſſe inſtans: ſicut con-
<
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/>
tingeret cum in qualibet parte pari intenderet in
<
lb
/>
qualibet vero impari remitteret / vt dictum eſt. </
s
>
<
s
xml:id
="
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xml:space
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preserve
">Se-
<
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/>
cundo aſſumit / ante illud c. inſtans intrinſecū a.
<
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/>
potentia mouetur vniformiter / quod eſt probandū
<
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/>
</
s
>
<
s
xml:id
="
N19947
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xml:space
="
preserve
">Et ſic ptꝫ modum illum probandi predictam con-
<
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/>
cluſionem inefficacem eſſe qui et ſi ſcientiam nõ ge-
<
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/>
neret magnam tamen fidem facit.</
s
>
</
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>
<
p
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<
s
xml:id
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xml:space
="
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">Tertia cõcluſio. </
s
>
<
s
xml:id
="
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xml:space
="
preserve
">Si potentia que mo
<
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/>
uetur vniformiter cõtinuo medium vniformiter
<
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/>
difforme īuariatum et ad nõ gradum terminatum
<
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/>
incipiendo ab extremo remiſſiori: et cõtinuo creſcē-
<
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/>
do vniformiter quouſ deueniat ad extremū intē-
<
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/>
ſius: et deīde retrograde moueatur verſus extremū
<
lb
/>
remiſſius cõtinuo vniformiter et eque velociter de-
<
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/>
creſcendo ſicut antea creuit: ipſa continuo vnifor-
<
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/>
miter mouebitur. </
s
>
<
s
xml:id
="
N19973
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xml:space
="
preserve
">Probatur / ſit a. potentia que ab
<
lb
/>
extremo remiſſiori c. medii vniformiter difformis
<
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/>
nõ variati et ad nõ gradum terminati incipiendo,
<
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/>
continuo vniformiter mouetur per continuum ſue
<
lb
/>
potentie vniforme crementum, quo ad vſ ad extre
<
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/>
mū intenſius ipſius c. medii deueniat / ad quod ha-
<
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/>
beat proportionē f. a qua antea continuo moueba
<
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/>
tur: ſit b. potētia ei equalis que (vt oportet) ad idē
<
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/>
extremum intenſius habet f. proportionem. </
s
>
<
s
xml:id
="
N19986
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xml:space
="
preserve
">Uarie-
<
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/>
tur igitur / ipſa b. potentia taliter continuo ab eodē
<
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/>
extremo intenſiori verſus remiſſius, cõtinuo mo
<
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/>
ueatur ab f. proportione: et a. ſimul in eodem inſtãti
<
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/>
incipiat moueri cum b. potentia verſus extremū re
<
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/>
miſſius cõtinuo vniformiter et eque velociter remit-
<
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/>
tendo potentiam ſuam ſicut antea intendebat: ſit
<
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/>
g. tempus in quo a. antea vniformiter potentiã ſuã
<
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/>
intendebat totum c. medium adequate tranſeundo
<
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/>
et h. ſit tempus in quo adequate b. potentia pertrã
<
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/>
ſit c. medium. </
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>
<
s
xml:id
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N1999D
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xml:space
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preserve
">Tunc dico / a. ſic mouendo continuo
<
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vniformiter mouetur. </
s
>
<
s
xml:id
="
N199A2
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xml:space
="
preserve
">Quod ſic oſtēditur / q2 a. et b.
<
lb
/>
continuo eque velociter mouētur: et b continuo vni-
<
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/>
formiter mouet̄̄ ex hypotheſi: ergo a. vniformiṫ mo
<
lb
/>
uetur cõtinuo / qḋ fuit ꝓbandū. </
s
>
<
s
xml:id
="
N199AB
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xml:space
="
preserve
">Conſequentia ptꝫ cū
<
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/>
minore: et arguit̄̄ maior / q2 a. et b. poñe cõtinuo ſunt
<
lb
/>
in eodē pūcto c. medii: igr̄ a. et b. ↄ̨tinuo eque velociṫ
<
lb
/>
mouentur. </
s
>
<
s
xml:id
="
N199B4
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xml:space
="
preserve
">Conſequentia patet: et probatur antece
<
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/>
dens / quia ſi non: detur inſtans in quo a. ſit in pun-
<
lb
/>
cto vlteriori vel citeriori quam b. et ſit illud inſtans
<
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/>
e. / et argr̄ ſic in e. inſtãti a. potētia eſt in puncto vlte- </
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>
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