Benedetti, Giovanni Battista de
,
Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]
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176
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IO. BAPT. BENED.
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n
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188
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file
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0188
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0188
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ſed proportio
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ad
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maior eſſet ea, quæ eſt
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ad
<
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ex. octaua lib. quinti, vn-
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de ex .12. eiuſdem lib. maior eſſet
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ad
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quàm.o.f. ad
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ex .33. igitur eiuſdem,
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maior erit proportio
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ad
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quàm.p.f. ad
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>.q.i</
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. </
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<
s
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xml:space
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">Sic quoque ſe habebunt ad inui
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cem velocitates, quod eſt propoſitum. </
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<
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xml:space
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ad
<
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>.q.n.</
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>
maior ſit,
<
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quàm.p.f. ad
<
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>.q.i.</
var
>
permurando igitur maior erit proportio
<
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>.p.o.</
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>
ad
<
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>.p.f.</
var
>
quam
<
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>.q.n.</
var
>
ad
<
var
>.
<
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q.i.</
var
>
aut euerſim maior erit proportio
<
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>.q.i.</
var
>
ad
<
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>.q.n.</
var
>
quàm.p.f. ad
<
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>.p.o.</
var
>
vnde ſi proportio
<
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<
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>p.f.</
var
>
ad
<
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eſſet ac ea, quæ eſt
<
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>.o.g.</
var
>
ad
<
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>.f.g.</
var
>
non eſſet
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>.q.i.</
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>
ad
<
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>.q.n.</
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ut eſt
<
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>.o.g.</
var
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ad
<
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>.f.g.</
var
>
aut
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vt
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ad
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>.i.k.</
var
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quodidem
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eſt, de quibus quidem re-
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xlink:label
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fig-0188-01
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xlink:href
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number
="
254
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file
="
0188-01
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0188-01
"/>
</
figure
>
bus, exemplis propoſitis
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quinto capite
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feci.</
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<
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xml:space
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">Velocitatibus autem ſe-
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quentibus pondera, ſequi
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tur proportionem veloci-
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citatum duorum corporum hetereogeneorum eandem non eſſe per diuerſa media,
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contra id, quod ſequeretur ſi Ariſtotelis opinionem .8. cap. lib. 4. phyſicorum re-
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ciperemus.</
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>
</
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<
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<
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style
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xml:space
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">Longe aliter ueritatem ſe habere quam Aristoteles
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doceat in fine libri ſeptimi phyſicorum.</
head
>
<
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xml:space
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">CAP. XIII.</
head
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<
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xml:space
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">NOn tam facile eſt aſſignare proportionem velocitatum duorum corporum na
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turalium, quam Ariſtoteles vltimo cap. lib. 7. phyſicorum putauit.</
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>
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<
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xml:space
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">Quamobrem ſint duo corpora
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var
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et
<
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>.D.</
var
>
materia
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norm
="
magnitudineque
"
type
="
simple
">magnitudineq́;</
reg
>
diuerſa, pondere
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/>
tamen, & figura ſimilia, & proportio reſiſtentiarum, quas recipiunt à medio
<
reg
norm
="
dum
"
type
="
context
">dũ</
reg
>
mo-
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uentur, ſit. ut
<
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>.o.i.</
var
>
ad
<
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>.a.e.</
var
>
denotentur deinde velocitates totales abſque vlla reſiſten-
<
lb
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tia ab
<
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>.a.u.</
var
>
et
<
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>.o.c.</
var
>
quæ æquales erunt ad inuicem per communem ſcientiam ex ſup-
<
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poſito, ſint alia deinde duo corpora
<
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>.V.</
var
>
et
<
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>.M.</
var
>
eodem modo ſe habentia ut prima
<
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>.B.</
var
>
<
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/>
et
<
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>.D.</
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>
in eodem medio, ſed ex diuerſa materia ab ea, quæ eſt illorum duorum corpo
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rum, magnitudine tamen & figura ijſdem ſimilia: </
s
>
<
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xml:space
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">ſignificentur quoque eo-
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rundem reſiſtentiæ per
<
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var
>
et
<
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>.n.r.</
var
>
& eorundem velocitates à nulla ex reſiſtentijs di-
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minutæ, per
<
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>.n.x.</
var
>
et
<
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>.t.g.</
var
>
vnde
<
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>.n.r.</
var
>
æqualis erit
<
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>.a.e.</
var
>
et
<
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>.t.s.</
var
>
ipſi
<
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>.o.i.</
var
>
et
<
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>.n.x.</
var
>
ipſi
<
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>.t.g</
var
>
:
<
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>n.x.</
var
>
ta-
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men et
<
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>.t.g.</
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>
non erunt ęqualia
<
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>.a.u.</
var
>
et
<
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>.o.c</
var
>
. </
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>
<
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xml:space
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">Sed exempli gratia, ponamus ea eſſe mi-
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nora. </
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<
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xml:space
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">Supponamus nunc
<
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>.e.u.</
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>
velocitatem eſſe quæ remanet ipſi
<
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>.B.</
var
>
cum applicata
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erit reſiſtentia
<
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>.a.e.</
var
>
dicto corpori
<
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>.B.</
var
>
quæ diminutam facit totam
<
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>.a.u.</
var
>
per
<
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>.a.e.</
var
>
<
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norm
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ſitque
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type
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">ſitq́;</
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<
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>.i.c.</
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<
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ea, quę remanet ipſi
<
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>.o.c.</
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>
corporis
<
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>.D.</
var
>
et
<
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>.r.x.</
var
>
ea, quæ remanet
<
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>.n.x.</
var
>
corporis
<
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>.V.</
var
>
et
<
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>.s.g.</
var
>
<
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/>
ea, quæ eſt ex
<
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>.t.g.</
var
>
corporis
<
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>.M</
var
>
. </
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>
<
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xml:id
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xml:space
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">Vnde communi omnium
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type
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aſſequemur
<
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>
ma
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iorem futuram
<
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>.r.x.</
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>
et
<
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>.i.c.</
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ipſa
<
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>.s.g</
var
>
. </
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>
<
s
xml:id
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xml:space
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preserve
">Scindatur deinde
<
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>.a.m.</
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ad ęqualitatem
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var
>
et
<
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>.o.z.</
var
>
<
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ipſius
<
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>.t.g.</
var
>
vnde
<
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>.a.m.</
var
>
ad
<
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>.o.z.</
var
>
et
<
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>.m.u.</
var
>
ad
<
var
>.z.c.</
var
>
æquales habebimus, ut quoque
<
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>.e.m.</
var
>
ad
<
var
>.r.
<
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x.</
var
>
et
<
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>.i.z.</
var
>
ad
<
var
>.s.g.</
var
>
quamobrem
<
var
>.e.m.</
var
>
maior erit ipſa
<
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>.z.i.</
var
>
maior igitur erit proportio
<
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>.z.c.</
var
>
<
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/>
ad
<
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>.z.i.</
var
>
quàm.m.u. ad
<
var
>.m.e.</
var
>
(quia
<
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>.z.c.</
var
>
ad
<
var
>.z.i.</
var
>
ita ſe habet vt
<
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>.m.u.</
var
>
ad
<
var
>.i.z.</
var
>
ex .7. lib. quin-
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ti, ſed
<
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>.m.u.</
var
>
ad
<
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>.i.z.</
var
>
maior eſt quam ad
<
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>.m.e.</
var
>
ex .8. dicti lib. vnde ex .12. eiuſdem
<
var
>.z.c.</
var
>
ad
<
lb
/>
ad
<
var
>.z.i.</
var
>
maior erit, quàm.m.u. ad
<
var
>.m.e</
var
>
. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Ergo ex .28. maior proportio erit
<
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>.c.i.</
var
>
ad
<
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>.z.i.</
var
>
</
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