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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<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 445
>
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<
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390
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IO. BAPT. BENED.
"
n
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402
"
file
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0402
"
xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0402
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<
s
xml:id
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xml:space
="
preserve
">Vbiautem ſcriptum eſt
<
lb
/>
<
q
open
="
„
"
close
="
">ad vtrunque ſimul
<
var
>.b.d</
var
>
:
<
var
>d.a.</
var
>
cum dupla
<
var
>.b.c.</
var
>
</
q
>
<
lb
/>
dicendum eſt ita,
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lb
/>
ad vtranque ſimul
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var
>.b.d.b.a.</
var
>
cum dupla
<
var
>.b.c</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4627
"
xml:space
="
preserve
">Inquit deinde Archi. quod ſicut ſe haber
<
var
>.e.a.</
var
>
ad
<
var
>.d.a.</
var
>
ita ſe habebit duplum
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var
>.M.N.</
var
>
<
lb
/>
ad duplum
<
var
>.N</
var
>
. </
s
>
<
s
xml:id
="
echoid-s4628
"
xml:space
="
preserve
">Quod quidem verum eſt ex .13. quinti, huiuſmodi verò antecedons
<
lb
/>
& conſequens, Archi. manifeſtat ex ſuis partibus, ſumendo duplum
<
var
>.e.b.</
var
>
cum duplo
<
lb
/>
<
var
>b.d.</
var
>
pro duplo
<
var
>.M.</
var
>
& duplum
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var
>.b.d.</
var
>
cum duplo
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var
>.a.b.</
var
>
cum quadruplo
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var
>.b.c.</
var
>
pro duplo
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var
>.N.</
var
>
<
lb
/>
quę ſimul iuncta æquantur duplo
<
var
>.e.b.</
var
>
cum duplo
<
var
>.a.b.</
var
>
cum quadruplo
<
var
>.b.d.</
var
>
cum qua-
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lb
/>
druplo
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var
>.b.c.</
var
>
ex quo æquabuntur
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var
>.A.</
var
>
vocentur igitur hæc omnia
<
var
>.A.</
var
>
potius quàm du-
<
lb
/>
plum ipſius
<
var
>.M.N</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4629
"
xml:space
="
preserve
">Verum etiam ſcribit, vbi dicit, quod proportio
<
var
>.e.a.</
var
>
ad tres quintas ipſius
<
var
>.a.d.</
var
>
erit
<
lb
/>
vt
<
var
>.A.</
var
>
ad tres quintas dupli
<
var
>.N.</
var
>
ex .22. quinti. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Sed cum ex ſuppoſito ita ſe habeat
<
var
>.f.
<
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/>
g.</
var
>
ad tres quintas ipſius
<
var
>.a.d.</
var
>
quemadmodum
<
var
>.b.e.</
var
>
ad
<
var
>.e.a.</
var
>
erit ex .16. quinti verum
<
reg
norm
="
quod
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type
="
simple
">ꝙ</
reg
>
<
lb
/>
dicit Archimed. </
s
>
<
s
xml:id
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"
xml:space
="
preserve
">hoc eſt, ita ſe habere
<
var
>.b.e.</
var
>
ad
<
var
>.f.g.</
var
>
vt
<
var
>.e.a.</
var
>
ad tres quintas ipſius
<
var
>.a.d</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4632
"
xml:space
="
preserve
">Et per .11. eiuſdem verum etiam erit quod ſicut ſe habet
<
var
>.e.b.</
var
>
ad
<
var
>.f.g.</
var
>
ita ſe habe-
<
lb
/>
bit
<
var
>.A.</
var
>
ad tres quintas dupli
<
var
>.N.</
var
>
quod quidem duplum
<
var
>.N.</
var
>
ſignificetur per
<
var
>.Q</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Sed ſuperius iam demonſtratum fuit (vbi
<
var
>.X.</
var
>
) quod
<
var
>.o.b.</
var
>
ad
<
var
>.b.e.</
var
>
ita ſe habebat vt
<
lb
/>
<
var
>H.A.</
var
>
ad
<
var
>.A.</
var
>
&
<
reg
norm
="
nunc
"
type
="
context
">nũc</
reg
>
demum probatum fuit ita eſſe
<
var
>.A.</
var
>
ad tres quintas ipſius
<
var
>.Q.</
var
>
vt
<
var
>.e.b.</
var
>
<
lb
/>
ad
<
var
>.f.g</
var
>
. </
s
>
<
s
xml:id
="
echoid-s4634
"
xml:space
="
preserve
">Quare ex .22. quinti ita erit
<
var
>.H.A.</
var
>
ad tres quintas ipſius
<
var
>.Q.</
var
>
vt
<
var
>.o.b.</
var
>
ad
<
var
>.f.g.</
var
>
vt
<
lb
/>
<
note
xlink:label
="
note-0402-01
"
xlink:href
="
note-0402-01a
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position
="
left
"
xml:space
="
preserve
">Y</
note
>
idem inquit.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Sed
<
var
>.H.A.</
var
>
ad
<
var
>.Q.</
var
>
(vt ex ſuis partibus videre eſt) ita ſe habet vt tres ad duo ex .13.
<
lb
/>
quinti, vt inquit Archimedes.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4636
"
xml:space
="
preserve
">Ipſe etiam dicit proportionem
<
var
>.H.A.</
var
>
ad tres quintas ipſius
<
var
>.Q.</
var
>
eſſe vt quinque
<
lb
/>
ad duo. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Pro cuius rei euidentia imaginemur tam
<
var
>.H.A.</
var
>
quam
<
var
>.Q.</
var
>
diuiſa per
<
reg
norm
="
quinque
"
type
="
simple
">quinq;</
reg
>
<
lb
/>
partes æquales, vnde ex .16. quinti habebimus quamlibet quintam
<
reg
norm
="
partem
"
type
="
context
">partẽ</
reg
>
ipſius
<
var
>.Q.</
var
>
<
lb
/>
<
reg
norm
="
æqualem
"
type
="
context
">æqualẽ</
reg
>
eſſe duabus tertijs vniuſcuiuſque quintæ partis
<
var
>.H.A.</
var
>
vnde tres quintæ ipſius
<
lb
/>
Q. erunt, ex communi conceptu, ſex tertiæ vnius quintæ ipſius
<
var
>.H.A.</
var
>
hoc eſt duæ
<
lb
/>
quintæ. ipſius
<
var
>.H.A</
var
>
. </
s
>
<
s
xml:id
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echoid-s4638
"
xml:space
="
preserve
">Quare
<
var
>.o.b.</
var
>
ita ſe habebit ad
<
var
>.f.g.</
var
>
vt quinque ad duo ex commu
<
lb
/>
ni
<
reg
norm
="
conceptu
"
type
="
context
">cõceptu</
reg
>
, cum
<
var
>.o.b.</
var
>
ad
<
var
>.f.g.</
var
>
probatum fuerit ſe habere vt
<
var
>.H.A.</
var
>
ad tres quintas ipſius
<
lb
/>
Q. (vbi
<
var
>.Y.</
var
>
) ſed iam probatum fuit (vbi. ω) quod
<
var
>.o.a.</
var
>
ad
<
var
>.h.g.</
var
>
erat etiam vt
<
lb
/>
quinque ad duo, hoc eſt quod
<
var
>.f.h.</
var
>
erit duæ quintę ipſius
<
var
>.a.b</
var
>
. </
s
>
<
s
xml:id
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"
xml:space
="
preserve
">Quod eſt propoſitum.</
s
>
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