Alvarus, Thomas
,
Liber de triplici motu
,
1509
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De motu penes cauſã in medio vniformiṫ difformi īuariato.
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pars correlarii patet ex prima parte eiuſdem, et ex
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prima concluſione huius. </
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<
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xml:space
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</
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<
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xml:space
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">¶ Innumera poteris ſtudio ſe lector proprio labo-
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re his ſimilia inferre correlaria.</
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<
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xml:id
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xml:space
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cõcluſio
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calcula.</
note
>
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<
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xml:space
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<
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xml:space
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">Duabus potentiis
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aliquod medium vniformiter difforme ad nõ gra-
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dum terminatum tranſeundo vniformiter cõtinuo
<
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mouentibus, vna altera velocius continuo creſcē
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te in ea proportione que proportionem a qua mo-
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uetur altera per proportionem duplam excedit: po
<
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tentia que velocius continuo creſcit velocius conti-
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nuo mouetur in proportione dupla ipſa potentia
<
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minore. </
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>
<
s
xml:id
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xml:space
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preserve
">Probatur / ſit a. potentia que c. mediū .etc̈.
<
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/>
tranſeundo continuo mouetur ab f. proportione ꝑ
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/>
ſui a non gradu potentie continuū et vniforme cre-
<
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/>
mentum: ſit h. proportio que f. proportionem ex-
<
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/>
cedat per proportionem duplam, et ſit b. potentia
<
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/>
que idem c. medium tranſeundo a nõ gradu poten-
<
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/>
tie cõtinuo in h. proportione velocius creſcat quaꝫ
<
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/>
a. potentia: tunc dico / b. potentia continuo in du
<
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/>
plo velocius mouetur a. potētia minore. </
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>
<
s
xml:id
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xml:space
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">Quod ſic
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probatur / quia b. mouetur velocius a. / vt conſtat, et
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non mouetur velocius in maiori proportione quã
<
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/>
dupla, nec in minori: igitur b. mouetur adequate ī
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duplo velocius: quod fuit probandū. </
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>
<
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xml:space
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tia ptꝫ cum maiore, et prima pars minoris proba-
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tur / quia ſi b. mouetur in maiori proportiõe quam
<
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dupla velocius ipſa potentia a. / ſequitur / reſiſten
<
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/>
tie ipſius b. ad reſiſtentiã ipſius a. eſt maior quam
<
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dupla et proportio ipſius b. ad reſiſtentiam ipſius
<
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/>
a. componitur adequate ex duplici f. et proportiõe
<
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/>
dupla: igitur demendo a proportione ipſius b. ad
<
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/>
reſiſtentiam ipſius a. proportionem que eſt reſiſten
<
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tie ipſius b. ad reſiſtentiam ipſius a. non manet du
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/>
plex f. ſed minus. </
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<
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">Patet cõſequētia / quia per te pro
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portio reſiſtentie ipſius b. ad reſiſtentiã ipſius a. eſt
<
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maior quam ſit proportio dupla: et vltra demendo
<
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/>
a proportione ipſius b. ad reſiſtentiã ipſius a. pro-
<
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portionē que eſt reſiſtentie ipſius b. ad reſiſtentiaꝫ
<
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/>
ipſius a. nõ manet duplex f. ſed minus, et demendo
<
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a proportione ipſius b. ad reſiſtentiã ipſius a. pro-
<
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portionem que eſt reſiſtentie ipſius b. ad reſiſtentiã
<
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/>
ipſius a. non manet niſi proportio que eſt ipſius b.
<
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/>
ad reſiſtentiam eiuſdem b. / igitur proportio que eſt
<
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/>
ipſius b. ad reſiſtentiam eiuſdem b. nõ eſt duplex f.
<
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/>
ſed minus, et ab illa proportione continuo b. poten
<
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tia mouetur: igitur continuo b. mouetur a propor-
<
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tione que nõ eſt duplex f. ſed minus: et a. potentia cõ
<
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/>
tinuo mouetur ab f. proportione: igitur b. potētia
<
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/>
mouetur velocius a. in minori proportione quam
<
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/>
dupla: et per conſequens nõ in maiori proportione
<
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quam dupla: quod fuit probandū. </
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<
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xml:space
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tio ipſius b. ad reſiſtentiam ipſius a. componitur
<
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adequate ex duplici f. et proportione dupla: patet /
<
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/>
quia proportio ipſius b. ad reſiſtentiam ipſius a.
<
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cõponitur adequate ex proportione h. que eſt ipſiꝰ
<
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/>
b. ad ipſum a. et ex proportiõe f. que eſt ipſius a. ad
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reſiſtentiam ipſius a. / vt conſtat. </
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<
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xml:space
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">et proportio h. eſt
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vnū f. et proportio dupla adequate / vt ptꝫ: q2 h. exce
<
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dit f. per duplam proportionem adequate ex hypo
<
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/>
theſi: igitur proportio ipſius b. ad reſiſtentiam ip-
<
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/>
ſius a. cõponitur adequate ex duplici f. et ex propor
<
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tione dupla / quod fuit probandum. </
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>
<
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xml:space
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">Et ſic patet pri
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ma pars minoris. </
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<
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xml:space
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">Iam probatur ſecunda pars mi
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noris videlicet / b. nõ mouetur velocius a. in mino
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ri proportione quam dupla: quia ſi b. mouetur ve-
<
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locius a. in minori proportione quam dupla: ſequi
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tur / continuo reſiſtentie ipſius b. ad reſiſtentiam
<
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ipſius a. eſt minor preportio ꝙ̄ dupla proportio, et
<
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De motu penes cauſã in medio vniformiṫ difformi īuariato.
"/>
vltra reſiſtentie ipſius b. ad reſiſtentiam ipſius a. cõ
<
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/>
tinuo eſt minor proportio ꝙ̄ dupla: et proportio ip
<
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ſius b. ad reſiſtentiam ipſius a. cõponitur adequa-
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te ex duplici f. et ex proportione dupla / vt ſupra ar-
<
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gutum eſt: igitur demendo a proportione ipſius b.
<
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/>
ad reſiſtentiam ipſius a. proportionem que eſt reſi
<
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ſtentie ipſius b. ad reſiſtentiam ipſius a. manet ma
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gis quam duplex f. </
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>
<
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">Patet cõſequentia / quia per te
<
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proportio que eſt reſiſtentie ipſius b. ad reſiſtentiã
<
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ipſius a. eſt minor proportio quam dupla: et vltra
<
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demendo a proportione ipſius b. ad reſiſtentiã ip-
<
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ſius a. proportionem que eſt reſiſtentie ipſius b. ad
<
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reſiſtentiam ipſius a. manet magis quam duplex f.
<
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et demendo a proportione ipſius b. ad reſiſtentiam
<
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ipſius a. proportionem que eſt reſiſtentie ipſius b.
<
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ad reſiſtentiam ipſius a. manet proportio ipſius b.
<
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ad reſiſtentiam eiuſdem b. / igitur proportio b. ad re
<
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ſiſtentiam eiuſdem b. eſt maior quam duplex f. et ab
<
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illa proportione b. potentia continuo mouetur: igi
<
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tur b. continuo mouetur a maiori proportione quã
<
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dupla ad f. et a. potentia cõtinuo mouetur ab f. pro
<
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portione: igitur b. continuo mouetur velocius a. in
<
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maiori proportione quam dupla: et per conſequēs
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non mouetur velocius in minori proportione quaꝫ
<
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dupla / quod fuit probanduꝫ. </
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<
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xml:space
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">Et ſic patet concluſio /
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que eſt octaua concluſio calculatoris in ſecundo ca
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pite de medio non reſiſtente.
<
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xlink:href
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xml:space
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</
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<
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xml:space
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">¶ Ex quo ſequitur pri-
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mo / ſi in caſu cõcluſionis a. potentia cõtinuo mo-
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ueatur a proportione ſexquialtera: et b. potētia ma
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ior creſcat in triplo velocius continuo ipſa a. potē-
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tia minore: ipſa potentia b. mouetur cõtinuo in du-
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plo velocius a. potētia minore. </
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<
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pla excedit ſexquialteram per duplam / vt patet ex
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quarta concluſione quarti capitis ſecunde partis /
<
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igitur ex hac concluſione ſequitur / ſi a. potentia
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minor moueatur a proportione ſexquialtera, et b.
<
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potentia maior creſcat in triplo velocius b. potē
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tia maior mouetur cõtinuo in duplo velocius a. po
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tentia minore / quod fuit probandum.
<
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xlink:href
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xml:id
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xml:space
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</
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<
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xml:space
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">¶ Sequitur
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ſecundo / ſi a. potentia minor moueatur a. propor
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tione dupla, et b. potentia maior creſcat in quadru
<
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plo velocius continuo: ipſa potentia b. mouetur cõ
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tinuo in duplo velocius a. potentia minore. </
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<
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quia quadrupla excedit duplam per duplam / vt ptꝫ
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ex quarta concluſione preallegata igitur
<
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xlink:href
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xml:id
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xml:space
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">3. correĺ.</
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<
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xml:space
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">¶ Sequit̄̄
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tertio / ſi a. potētia minor moueatur a proportiõe
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quadrupla et b. potentia maior creſcat in octuplo
<
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velocius: tunc b. potentia maior mouetur continuo
<
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in duplo velocius. </
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<
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">Patet / quia octupla quadruplã
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per duplam excedit / vt patet ex quarta concluſione
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preallegata.
<
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xlink:href
="
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note-0108-04
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xml:id
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xml:space
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">4. correĺ.</
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</
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<
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xml:space
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">¶ Sequitur quarto / ſi a. potentia
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minor moueatur cõtinuo a proportione ſexquiter-
<
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tia et b. potentia maior continuo creſcat in propor
<
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tione dupla ſuprabipartiēte tertias velociꝰ b. potē
<
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tia maior mouetur cõtinuo in duplo velocius. </
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<
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xml:id
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">Ptꝫ /
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quia dupla ſuprabipartiens tertias ſexquitertiaꝫ
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per duplam excedit / vt patet ex quarta concluſione
<
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preallegata. </
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>
<
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xml:id
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xml:space
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">Et iſto modo infinita talia correlaria
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poteris inferre,</
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<
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bus predictarum concluſionum pre-
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cedentium capitum obiiciens.</
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>
<
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<
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xml:id
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xml:space
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">HIs concluſionibus velocitatē
<
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motus in medio vniformiter difformi in-
<
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uariato declarantibus (vt potuimus) ali-
<
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/>
qua ex parte expeditis: nunc opere precium eſt lima
<
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diſputationis ea que dicta ſunt polire at limare.</
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>
</
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>
<
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<
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xml:id
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xml:space
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">Et ideo ſecūde concluſioni decimi ca- </
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</
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