Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Primi tractatus
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formiter continuo et eque velociter omnino cum ea
<
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moueretur. </
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>
<
s
xml:id
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N19F92
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xml:space
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preserve
">Probatur et ſit a. poña / que vniformi-
<
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ter cõtinuo mouetur etc. per ſui a non gradu poten
<
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tie vniforme et continuum crementum. </
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>
<
s
xml:id
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N19F99
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xml:space
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">ſit b. poña
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minor a. vtcū volueris (non eſt cura) omnino eo-
<
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dem mõ creſcens cum a. / tunc dico / b. poña omni-
<
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no eodem mõ creſcens cum a. ad aliquem punctum
<
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/>
c. medii poſſe incipere moueri verſus puncta inten
<
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ſiora vniformiter continuo et eque velociter cum ea
<
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/>
mouendo. </
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>
<
s
xml:id
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N19FA8
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xml:space
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preserve
">Quod ſic ꝓbatur / quia cum a. poña c. me
<
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dium tranſeundo a non gradu potentie vniformi-
<
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ter continuo creſcat: manifeſtum eſt / a. poña ãtea
<
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/>
̄ ad punctum in quomodo eſt deuenerit fuit ad ali
<
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/>
quod punctum tante potentie adequate quante mõ
<
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/>
eſt ipſa b. poña minor. </
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>
<
s
xml:id
="
N19FB5
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xml:space
="
preserve
">ponãtur / igitur a. et b. ſimul
<
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/>
ad illud punctuꝫ ad quod a. erat tãte poñe adequa
<
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/>
te quante mõ eſt ipſa b. poña minor et in eodem in-
<
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ſtanti incipiant moueri verſus extremum intenſius
<
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ipſius c. medii </
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>
<
s
xml:id
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N19FC0
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xml:space
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preserve
">Quo poſito manifeſtum eſt / b. po-
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tentia vniformiter continuo et eque velociter moue
<
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/>
tur cum a. cum continuo a. et b. per eandem reſiſten-
<
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tiam mouentes ſint equales / igitur b. poña omnino
<
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/>
eodem modo creſcens cum a. ad aliquem punctum
<
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/>
c. medii poteſt incipere moueri verſus puncta inten
<
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/>
ſiora vniformiter continuo et eque velociter ſicut a.
<
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/>
mouendo / quod fuit probandum. </
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>
<
s
xml:id
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xml:space
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">Patet igitur cor
<
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relarium.</
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</
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<
head
xml:id
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N19FDB
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xml:space
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">Capitulum vndecimum / in quo pulchre
<
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/>
admodum comparantur motus diuerſa-
<
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rum potentiarum in eodem medio vnifor
<
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/>
miter difformi inuariato mouentium per
<
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/>
earum potentiarum vniforme crementum</
head
>
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<
s
xml:id
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N19FE7
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xml:space
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preserve
">TRadita (vt potuimus) noti-
<
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cia velocitatis et tarditatꝪ motus penes
<
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/>
cauſam potentie per ſui crementū in me
<
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/>
dio vniformiter difformi inuariato mouentis: con
<
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/>
ſequens eſt / vt comparando motus diuerſarum po
<
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/>
tentiarum in medio vniformiter difformi inuaria-
<
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/>
to mouentium per earuꝫ poñarum vniforme cremē
<
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/>
tum concluſiones inducamus. </
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>
<
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xml:space
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">Pro quo ſit iſta ſup
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poſitio.</
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</
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<
s
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xml:space
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">Quelibet potentia medium vniformi
<
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ter difforme inuariatum ad non gradum termina-
<
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tum ſuo continuo motu abſoluens ab extremo re-
<
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/>
miſſiori inchoando: in ea ꝓportione cum maiori re
<
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/>
ſiſtentia mouetur continuo in qua plus a remiſſio-
<
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/>
ri termino eiuſdem medii ipſa potentia diſtat.</
s
>
</
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>
<
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<
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xml:id
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">Probatur hec ſuppoſitio. </
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>
<
s
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xml:space
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">quia in reſiſtentia vni-
<
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formiter difformi omnis reſiſtentia in ea ꝓportiõe
<
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/>
eſt maior adequate in qua plus diſtat ab extremo ī
<
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/>
quo eſt non gradus / vt patet ex diffinitione qualita
<
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/>
tis vniformiter difformis quarto tractatu: igitur
<
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/>
omnis poña medium vniformiter difforme ad non
<
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/>
gradum terminatum ſuo motu abſoluens ab extre
<
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/>
mo remiſſiori inchoando: in ea ꝓportione ma
<
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/>
iori reſiſtentia mouetur continuo in qua ſua reſiſtē
<
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/>
tia plus diſtat ab extremo remiſſiori eiuſdeꝫ medii /
<
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/>
et per conſequens in ea ꝓportione cum maiori reſi-
<
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/>
ſtētia mouetur in qua ipſamet poña plus diſtat ab
<
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/>
eodem extremo remiſſiori eiuſdem medii: quod fuit
<
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probandum. </
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<
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">Patet conſequentia / quia tantum di
<
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/>
ſtat potētia in tali medio vniformiter difformi ab
<
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/>
extremo remiſſiori eiuſdem medii adequate quãtuꝫ
<
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/>
reſiſtētia eiuſdem medii ad quam eſt extremitas ta
<
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/>
lis potentie. </
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>
<
s
xml:id
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xml:space
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preserve
">Et ſic patet ſuppoſitio.
<
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xlink:href
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xlink:label
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xml:id
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xml:space
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">correla.</
note
>
</
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<
s
xml:id
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N1A03F
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xml:space
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">¶ Naſcitur hīc
<
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omnem poñam altera continuo velocius medium
<
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vniformiter difforme inuariatum et ad non gradū
<
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/>
terminatum abſoluentē, in ea ꝓportione continuo
<
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="
Capitulum vndecimum
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moueri cum maiori reſiſtentia ꝙ̄ altera: in qua ip̄a
<
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/>
velocius quam altera continuo mouetur. </
s
>
<
s
xml:id
="
N1A04D
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xml:space
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preserve
">Patet
<
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correlarium / quia talis poña continuo in ea ꝓpor-
<
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tione mouetur cum maiori reſiſtentia. </
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>
<
s
xml:id
="
N1A054
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xml:space
="
preserve
">in qua plꝰ di
<
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ſtat ab extremo remiſſiori eiuſdem medii termina-
<
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ti ad non gradum / vt patet ex ſuppoſitione. </
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>
<
s
xml:id
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N1A05B
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xml:space
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preserve
">et talis
<
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poña continuo in ea ꝓportione pluſ̄ altera diſtat
<
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/>
ab extremo remiſſiori eiuſdem medii terminati ad
<
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/>
non gradum in qua velocius mouetur adequate / vt
<
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conſtat. </
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>
<
s
xml:id
="
N1A066
"
xml:space
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">igitur talis poña continuo in ea ꝓportiõe
<
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mouetur cum maiori reſiſtentia in qua ipſa velociꝰ
<
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̄ altera continuo mouetur / quod fuit probandum
<
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/>
</
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>
<
s
xml:id
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N1A06E
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xml:space
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preserve
">Et ſic patet correlarium.</
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>
</
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<
p
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<
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xml:id
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xml:space
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preserve
">Hoc premiſſo ſit prima cõcluſio </
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>
<
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xml:id
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N1A07F
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">Dua
<
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/>
bus potentiis aliquod medium vniformiter diffor
<
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/>
me ad non gradum terminatum tranſeundo vnifor
<
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/>
miter continuo mouentibus per earum a non gra-
<
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/>
du poñe vniforme et continuuꝫ crementum vna al
<
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/>
tera in certa ꝓportione velocius continuo creſcen-
<
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/>
te: poña que velocius continuo creſcit velocius con
<
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/>
tinuo mouetur: in minori tamen ꝓportione velociꝰ
<
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/>
continuo quam ſit ꝓportio in qua continuo velociꝰ
<
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/>
creſcit. </
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>
<
s
xml:id
="
N1A094
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xml:space
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preserve
">Probatur / ſit a. poña que c. medium vnifor
<
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/>
miter difforme terminatum ad nõ gradum tranſe-
<
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/>
undo vniformiter continuo mouetur per ſue poten
<
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/>
tie a non gradu vniforme crementum: et b. poña c.
<
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/>
medium tranſeundo in f. ꝓportiõe velocius creſcat
<
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/>
continuo ꝙ̄ a. poña idem c. medium tranſeundo cõ-
<
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/>
tinuo vniformiter mouendo. </
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>
<
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xml:id
="
N1A0A3
"
xml:space
="
preserve
">tunc dico / b. potētia
<
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/>
mouetur velocius ipſa poña a. in minori tamen ꝓ-
<
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/>
portione velocius quam ſit f. ꝓportio in qua b. po-
<
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/>
tentia velocius continuo creſcit ꝙ̄ poña a. </
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>
<
s
xml:id
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N1A0AC
"
xml:space
="
preserve
">Quod
<
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/>
ſic ꝓbatur / q2 b. poña mouetur velocius continuo ̄
<
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/>
a. / vt conſtat (citius enim vniformiter continuo mo
<
lb
/>
uendo c. medium pertranſit) et b. poña non mouetur
<
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/>
in f. ꝓportione velocius nec in maiori: igitur b. po-
<
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/>
tentia mouetur velocius quam ip̄a poña a. in mino
<
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/>
ri tamen ꝓportione velocius quam ſit f. / quod fuit
<
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ꝓbandum. </
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>
<
s
xml:id
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N1A0BD
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preserve
">Conſequentia patet cum maiore. </
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>
<
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xml:id
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N1A0C0
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xml:space
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preserve
">et ar-
<
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guitur prima pars minoris videlicet / b. poña nõ
<
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/>
mouetur velocius a. poña in f. ꝓportione quia ſi b.
<
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/>
potētia mouetur velocius in f. ꝓportione. </
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>
<
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N1A0C9
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xml:space
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preserve
">ſequitur /
<
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continuo reſiſtentie ipſius b. ad reſiſtentiam ipſi
<
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/>
us a. eſt f. ꝓportio / vt patet ex correlario ſuppoſitio
<
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/>
nis: et ex hypotheſi b. poñe ad a. potentiam eſt f. ꝓ-
<
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/>
portio (cum b. a nõ gradu in f. ꝓportione continuo
<
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/>
velocius creſcat quam a. etiaꝫ a nõ gradu creſcēs) /
<
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/>
igitur qualis eſt ꝓportio ipſius b. potentie ad ipſã
<
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/>
a. poñam talis eſt ꝓportio reſiſtentie ipſius b. ad re
<
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/>
ſiſtentiam ipſius a. quia vtra f. / et per conſequens
<
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/>
permutatim qualis eſt ꝓportio ipſius b. poñe ad re
<
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/>
ſiſtentiam eiuſdem b. potentie talis eſt ꝓportio ip-
<
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ſius a: poñe ad reſiſtentiam eiuſdem a. poñe: et ꝑ cõ-
<
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ſequēs mouentur ab eadem ꝓportione / qḋ eſt fal-
<
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ſum. </
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>
<
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xml:id
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N1A0E6
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xml:space
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preserve
">Et ſic patet / b. nõ mouetur in f. ꝓportione ve
<
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/>
locius ipſa poña a. </
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>
<
s
xml:id
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xml:space
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preserve
">Iam probatur ſecūda pars mi
<
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/>
noris videlicet / b. nõ mouetur in maiori ꝓportio-
<
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/>
ne quam ſit f. velocius a. potentia: quia tunc ſeque
<
lb
/>
retur / continuo tardius moueretur quam a. potē
<
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/>
tia (vt facile deducitur) / quod eſt falſum. </
s
>
<
s
xml:id
="
N1A0F6
"
xml:space
="
preserve
">Et ſic patet
<
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concluſio.
<
note
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xlink:href
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xml:id
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xml:space
="
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">1. correl.</
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>
</
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>
<
s
xml:id
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N1A100
"
xml:space
="
preserve
">¶ Ex quo ſequitur primo / duabus po-
<
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/>
tētiis aliquod medium vniformiter difforme ad nõ
<
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/>
gradum terminatum tranſeundo vniformiter con-
<
lb
/>
tinuo mouentibus per earum a non gradu poten
<
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/>
tie vniforme et continuum crementum. </
s
>
<
s
xml:id
="
N1A10B
"
xml:space
="
preserve
">vna in tri-
<
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/>
plo velociꝰ continuo creſcente ꝙ̄ altera que vnifor-
<
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/>
miter idem medium tranſeundo mouetur a ꝓpor-
<
lb
/>
tione dupla. potentia que in triplo velocius conti-
<
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/>
nuo creſcit mouetur velocius continuo. </
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>
<
s
xml:id
="
N1A116
"
xml:space
="
preserve
">velocius in </
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>
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