Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Secundi tractatus
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quate tantam latitudinem ſicut a. ita in fine a. et
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b. maneant equales. </
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<
s
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xml:space
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">Quo poſito ſic argumentor / ve
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locitas ipſius motus a. correſpõdet gradui medio
<
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inter extremum ipſorum a. et b. in principio et ertre
<
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mum eorundem in fine (dico eorundem / quia illi mo
<
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tus tam in principio ꝙ̄ in fine ſunt equales / vt po
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nit caſus) </
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>
<
s
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N1EE8C
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xml:space
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">Sed b. motus in quolibet inſtanti intrin
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ſeco illius temporis erit remiſſior ipſo a. motu: igi
<
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tur b. motus remiſſiori gradui correſpondet quam
<
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a. motus et a. motus correſpondet gradui medio in
<
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/>
ter extrema ipſius b. / igitur b. motus correſpondet
<
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/>
gradui remiſſiori quam ſit gradus medius inter ex
<
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trema eiuſdem b. motus. </
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>
<
s
xml:id
="
N1EE9B
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xml:space
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">Conſequentia patet /
<
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quia extrema b. motus et a. motus ſunt equalia. </
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>
<
s
xml:id
="
N1EEA0
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xml:space
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">Et
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maior patet ex prima ꝓpoſitione: et minor proba-
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tur ſic: quia ſi non detur oppoſitum illius minoris
<
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/>
videlicet / non in quolibet inſtanti etc. ſed in aliquo
<
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/>
equalis vel intenſior: et et ſit illud c. terminans vnaꝫ
<
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/>
ſextã gr̄a argumēti / et arguo ſic / ī illo īſtãti c. ꝑ te mo
<
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/>
tus a. et motus b. ſunt equales: et in principio erant
<
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/>
equales et equalem latitudinem debent deperdere:
<
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/>
ergo equalem latitudinem deperdiderunt: et eq̈les
<
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/>
reſtant ab eis deperdende, et a. in qualibet ſexta ſe
<
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/>
quente c. tantã deperdet ſicut in precedēte quia vni
<
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/>
formiter deperdet et b. in qualibet ſequēte ſexta mi
<
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/>
nus deperdet quã in precedente quia continuo tar-
<
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/>
dius et tardius deperdit / vt dicit caſus: et in precedē
<
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/>
te deperdet tantum ſicut a: igitur in qualibet ſexta
<
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/>
ſequente c. inſtans b. minus deperdet quã a. ei ante
<
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/>
c. inſtans equalem latitudinem deperdit: ergo in to
<
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/>
to tempore illius hore b. minorem latitudinem de-
<
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/>
perdit quã a. / quod eſt contra caſum. </
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>
<
s
xml:id
="
N1EEC7
"
xml:space
="
preserve
">Et eodem mo-
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do probabitur iuuamine tamen loci a maiore b.
<
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motus in inſtanti non eſt intenſior a c. motu. </
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>
<
s
xml:id
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xml:space
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">Et
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ſic patet minor: et per conſequens tota propoſitio.
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<
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position
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xlink:href
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note-0153-01a
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xlink:label
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note-0153-01
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xml:id
="
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xml:space
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">53. cal. ī c.
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de mo. lo</
note
>
</
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>
<
s
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="
N1EEDA
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xml:space
="
preserve
">Et hec eſt quiuq̈geſima tertia ↄ̨cluſio calculatoris
<
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/>
in dicto capitulo de motu locali.
<
note
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left
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xlink:href
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note-0153-02
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xml:id
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xml:space
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">correlar.</
note
>
</
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>
<
s
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xml:space
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">¶ Ex hac pro-
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poſitione ſequitur / ſi mobile a. moueatur vnifor-
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miter difformiter ab octauo vſ ad quartum per-
<
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/>
dendo latitudinem motus vt 4. vniformiter conti-
<
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/>
nuo ī hora et mobile b. moueatur in eadem hora ab
<
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/>
octauo vſ ad quartum perdendo etiam latitudi-
<
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/>
nem vt .4. continuo tardius et tardius: tunc ſi a. per
<
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/>
tranſeat .6. pedalia b. pertranſibit minus. </
s
>
<
s
xml:id
="
N1EEF5
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xml:space
="
preserve
">Proba
<
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tur / quia ſi a. tranſit .6. pedalia illa .6. pedalia. </
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>
<
s
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xml:space
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">ſunt
<
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ſpacium natum tranſiri a gradu medio ipſius mo
<
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tus a. vniformiter difformis, et motus b. correſpon
<
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/>
det remiſſiori gradui gradu medio: igitur mobile
<
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/>
b. minus pertranſit quam ſex pedalia. </
s
>
<
s
xml:id
="
N1EF05
"
xml:space
="
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">Minor pa-
<
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tet ex precedenti propoſitione.</
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>
</
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>
<
p
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<
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xml:space
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">Sexta ꝓpoſitio </
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>
<
s
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xml:space
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">Omnis latitudo mo
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tus conſimiliter omnino perdita et acq̇ſita vni gra
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dui omnino correſpondet. </
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>
<
s
xml:id
="
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xml:space
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">Uolo dicere / ſi ſit ali-
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quis motus qui gratia exempli incipiat a non gra
<
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/>
du et intendatur vſ ad octauum in hora adequate
<
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/>
vniformiter: et alter motus vel idem remittatur in
<
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/>
hora vniformiter ſicut intendebatur ab octauo vſ
<
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ad non gradum: tales motus eidem gradui correſ
<
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pondet: et ſic exemplificatu in aliis. </
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>
<
s
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">Probatio hu-
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ius concluſionis facilis eſt quoniam tanta oīno eſt
<
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latitudo motus in via intenſionis quanta in via re
<
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miſſionis quoniam omnino eodem modo intendi-
<
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tur ſicut remittitur. </
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>
<
s
xml:id
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xml:space
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">igitur eidem gradui correſpon
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det. </
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>
<
s
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xml:space
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">Et ſic patet iſta propoſitio / que etiam ſuperius
<
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probata eſt in tractatu de motu penes cauſam.
<
note
position
="
left
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xlink:href
="
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note-0153-03
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xml:id
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xml:space
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">.56. cal. ī
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c. ḋ mo. l.</
note
>
</
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<
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xml:space
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">Et
<
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hec eſt quinquageſima ſexta concluſio calculatoris
<
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in capitulo preallegato de motu locali. </
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>
<
s
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xml:space
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">In quo lo-
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co idem calculator facit paruam obiectionem con-
<
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chead
="
Capitulum tertium
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tra hanc concluſionem </
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>
<
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">Uide eum ibi.</
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>
</
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<
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<
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xml:space
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">Notanduꝫ eſt quarto / vt ſuperius ta-
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ctum eſt velocitates motuum dupliciter inueſtigari
<
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poſſe videlicet ex cõmenſuratione ſpaciorum ꝑtran
<
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ſitorum: et hoc ab effectu: et a poſteriori quod in p̄-
<
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ſenti tractatu inquirimus. </
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>
<
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xml:space
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">Alio vero modo ex cõ-
<
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menſuratione et proportionalitate proportionum
<
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a quibus proueniunt velocitates ille: </
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<
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xml:space
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">Et cuꝫ aliqua
<
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ars ab huius ſcientie primoribus tradita ſit ad in
<
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/>
ueſtigandas proportiões a quibus velocitates mo
<
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tuum proueniunt. </
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>
<
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xml:id
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xml:space
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">Ideo non abs re aliquas propo
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ſitiones huic famulantes inueſtigationi pñti operi
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inſerendas cenſui.</
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>
</
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<
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xml:space
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">ↄ̨cluſiõſe
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horen.
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trac. pro
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por. c. 4.</
note
>
<
p
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<
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xml:space
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">Prima propoſitio </
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>
<
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xml:id
="
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xml:space
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">Quauis velocita-
<
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te data: et quacun proportione propoſita: cuiuſ-
<
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dam artis ingenio inueſtigari poteſt. </
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>
<
s
xml:id
="
N1EFA6
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xml:space
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">an data ve-
<
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locitas a propoſita proportione: aut a minori aut
<
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maiore proueniat. </
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>
<
s
xml:id
="
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xml:space
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">Exemplum / vt data aliqua velo-
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citate que ſit a. cuius proportionem a qua videlicet
<
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proueniat talis velocitas a. ignoramus: et propoſi
<
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/>
ta quauis proportione videlicet dupla: vel tripla
<
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/>
vel quadrupla inueſtigare et per artem inuenire
<
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/>
videlicet talis velocitas a. proueniat a tali propor
<
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tione dupla propoſita (exempli gratia) an a maio
<
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ri: an a minorl. </
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>
<
s
xml:id
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N1EFBE
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xml:space
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">Ad cuius probationem ſit illa velo
<
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citas a. qua moueatur c. reſiſtentia a b. potētia cu-
<
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ius proportionem ad c. ignoro: et ſit proportio ꝓ-
<
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poſita michi nota dupla exempli gratia: tunc ad ī
<
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/>
ueſtigandum: et inueniendum: an illa velocitas a. ꝓ
<
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/>
ueniat a maiori proportione quã dupla: an a mino
<
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ri: an ab equali: capio vnam aliam potentiam que
<
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/>
ſit d. que ſe habet in proportione dupla ad b. potē
<
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/>
tiam: et moueat vtra illarum potentiarum c. reſi
<
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ſtentiam: et manifeſtum eſt / d. velocius mouet c. re
<
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ſiſtentiam quam b. </
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>
<
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xml:space
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">Tūc his ſic poſitis: arguitur ſic /
<
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vel d. mouet c. reſiſtentiam in duplo velocius quam
<
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/>
b. moueat eãdem reſiſtētiã: vel magis quã in duplo
<
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velocius: vel minus. </
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>
<
s
xml:id
="
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xml:space
="
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">Si in duplo velocius ſequitur /
<
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proportio d. ad c. eſt dupla ad proportionem b.
<
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ad c. </
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>
<
s
xml:id
="
N1EFE5
"
xml:space
="
preserve
">Patet / quia velocitates ſunt duple et talis ꝓ-
<
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portio componitur ex ꝓportione d. ad b. et b. ad c. /
<
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/>
vt patet ex quarto capite ſecunde partis: ergo pro
<
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/>
portio b. ad c. eſt medietas proportionis d. ad c. / er
<
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/>
go reſiduum puta ꝓportio d. ad b. eſt reliqua medi
<
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/>
etas et eſt proportio dupla vt poſitum eū: ergo alia
<
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/>
proportio b. ad c. eſt etiam proportio dupla cum ſit
<
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alia medietas. </
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>
<
s
xml:id
="
N1EFF6
"
xml:space
="
preserve
">Modo omnes medie-
<
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tates ſunt equales. </
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>
<
s
xml:id
="
N1EFFB
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xml:space
="
preserve
">Et ſic inuentum / illa ē veloci-
<
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tas a. prouenit a proportione dupla / quod fuit īue
<
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ſtigandum. </
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>
<
s
xml:id
="
N1F002
"
xml:space
="
preserve
">Si vero d. poña maior moueat c. reſi-
<
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ſtentiam magis quam in duplo velocius quã b. / tūc
<
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/>
ſequitur / ꝓportio d. ad c. eſt maior quã dupla ad
<
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/>
ꝓportionē b. ad c. quia velocitas ꝓueniens a pro-
<
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/>
portione d. ad c. eſt maior ꝙ̄ dupla ad velocitatem
<
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/>
prouenientem a proportione b. ad c. et proportio d.
<
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ad c. componit̄̄ adequate ex ꝓportione d. ad b. et b.
<
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/>
ad c. / ergo proportio b. ad c. eſt minus ꝙ̄ medietas:
<
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/>
quia alias tota proportio non eſſet maior ꝙ̄ dupla
<
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/>
ad illam ſui partem: et totum reſiduum puta ꝓpor-
<
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/>
tio d. ad b. eſt ꝓportio dupla et eſt maius: igitur il-
<
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/>
la proportio b. ad c. eſt minor dupla / quod a princi
<
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/>
pio fuit inueſtigandum. </
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>
<
s
xml:id
="
N1F01D
"
xml:space
="
preserve
">Si autē d. poña maior mo
<
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/>
ueat c. reſiſtentiam minus ꝙ̄ in duplo velocius: tūc
<
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/>
illa proportio d. ad c. eſt minor qnã dupla ad ꝓpor
<
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/>
tionem b. ad c. / patet / quia velocitas eſt minor quam
<
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/>
dupla: et vltra eſt minor quã dupla ad ꝓportioneꝫ
<
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/>
b. ad c. / ergo illa proportio b. ad c. eſt maior quã me
<
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/>
dietas totius ꝓportionis d. ad c. </
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>
<
s
xml:id
="
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xml:space
="
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">Conſequentia pa </
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>
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