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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151 - 163
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396
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IO, BAPT. BENED.
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408
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0408
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0408
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<
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xml:space
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ſimiliter tres quintæ eſt ipſius
<
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var
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ex .8. prædicta. </
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<
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xml:space
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tres quintæ
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erit ipſius
<
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>
ex .19. quinti.</
s
>
</
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<
p
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<
s
xml:id
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xml:space
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preserve
">Dicamus igitur hoc modo cum
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>
totum ad totum
<
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>.b.r.</
var
>
ita ſe habeat vt abſciſ-
<
lb
/>
ſum
<
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>.b.g.</
var
>
ad abſciſſum
<
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>.q.b.</
var
>
ex .7. et .8. dicti primi libri eiuſdem ideo reſiduum
<
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>.f.g.</
var
>
ex
<
lb
/>
<
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>f.b.</
var
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ad reſiduum
<
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>.r.q.</
var
>
ex
<
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>.r.b.</
var
>
erit vt totum
<
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>.f.b.</
var
>
ad. totum
<
var
>.r.b.</
var
>
ex .19. quinti Eucli.</
s
>
</
p
>
<
p
>
<
s
xml:id
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echoid-s4694
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xml:space
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preserve
">Sed iam ſub. β. probauimus ita ſe habere fruſtum
<
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>.a.d.e.c.</
var
>
ad parabolam
<
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>.d.b.e.</
var
>
vt
<
lb
/>
<
var
>m.t.</
var
>
ad
<
var
>.t.n.</
var
>
ſed vt
<
var
>.m.t.</
var
>
ad
<
var
>.t.n.</
var
>
ita aſſ umpta fuit (vbi
<
var
>.A.</
var
>
).
<
var
>i.r.</
var
>
ad quam ſic ſe haberet
<
var
>.f.
<
lb
/>
h.</
var
>
hoc eſt tres quintæ ipſius
<
var
>.f.g.</
var
>
hoc eſt
<
var
>.q.r</
var
>
. </
s
>
<
s
xml:id
="
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xml:space
="
preserve
">quare ex .11. quinti prop ortio fruſti
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>.a.
<
lb
/>
d.e.c.</
var
>
ad parabolam partialem erit vt
<
var
>.q.r.</
var
>
ad
<
var
>.r.i</
var
>
. </
s
>
<
s
xml:id
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xml:space
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preserve
">Exiſtente igitur
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centro totius pa
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/>
rabolæ et
<
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>.q.</
var
>
centro partialis, ergo
<
var
>.i.</
var
>
centrum erit fruſti propoſiti.</
s
>
</
p
>
<
p
>
<
s
xml:id
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xml:space
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">Sed ſi nullo ſolido intercedente, voluerimus centrum
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>
fruſti
<
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>.a.e.</
var
>
citius inuenire,
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lb
/>
inueniemus primò centrum
<
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>.r.</
var
>
totius figuræ ex .8. ſecundi eiuſdem conſtituendo
<
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>.b.r.</
var
>
<
lb
/>
tres quintas totius axis
<
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>.b.f.</
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>
& centrum
<
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>.q.</
var
>
parabolæ
<
var
>.d.b.e.</
var
>
partialis ſimiliter.</
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>
</
p
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<
p
>
<
s
xml:id
="
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xml:space
="
preserve
">Nunc igitur manifeſtum eſt nobis, eandem proportionem fore ipſius
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>.q.r.</
var
>
<
lb
/>
ad
<
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>.r.i.</
var
>
quæ fruſti
<
var
>.a.e.</
var
>
ad portionem
<
var
>.d.b.e.</
var
>
ex .8. dicta. </
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>
<
s
xml:id
="
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xml:space
="
preserve
">Vnde ex coniuncta pro-
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lb
/>
portionalitate ita ſe habebit
<
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>.q.i.</
var
>
ad
<
var
>.i.r.</
var
>
vt
<
var
>.a.b.c.</
var
>
ad
<
var
>.d.b.e.</
var
>
ſed vt
<
var
>.a.b.c.</
var
>
ad
<
var
>.d.b.e.</
var
>
ita ſe
<
lb
/>
habet
<
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>.m.n.</
var
>
ad
<
var
>.n.t.</
var
>
eo quod vnaquæque harum duarum proportionum ſeſquialtera
<
lb
/>
eſt proportioni
<
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>.f.b.</
var
>
ad
<
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>.b.g.</
var
>
eo. quod
<
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>.f.b.</
var
>
ad
<
var
>.b.g.</
var
>
ita ſe habet. vt
<
var
>.m.n.</
var
>
ad
<
var
>.o.n.</
var
>
</
s
>
<
s
xml:id
="
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xml:space
="
preserve
">quare
<
lb
/>
<
var
>m.n.</
var
>
ad
<
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>.t.n.</
var
>
ita ſe habebit vt
<
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>.g.i.</
var
>
ad
<
var
>.r.i.</
var
>
vnde diſiunctim
<
var
>.m.t.</
var
>
ad
<
var
>.t.n.</
var
>
ita ſe habebit vt
<
lb
/>
<
var
>q.r.</
var
>
ad
<
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>.r.i</
var
>
. </
s
>
<
s
xml:id
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xml:space
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preserve
">Iungatur igitur
<
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>.r.i.</
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>
quæ quidem
<
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>.r.i.</
var
>
ita ſe habeat ad
<
var
>.r.q.</
var
>
vt
<
var
>.t.n.</
var
>
ad
<
var
>.t.m.</
var
>
vt
<
lb
/>
habeatur centrum fruſti.</
s
>
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