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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IO. BAPT. BENED.
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398
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xlink:href
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ipſius
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ad compoſitum quintupli ipſius
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cum decuplo ipſius
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cum decuplo
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ipſius
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cum quintuplo ipſius
<
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eadem ſit quæ ipſius
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>.g.h.</
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ad
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>.a.d.</
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& vult proba-
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re
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eſſe duas quintas ipſius
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.</
s
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</
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<
p
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<
s
xml:id
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xml:space
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<
var
>.a.c.</
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ad
<
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>.c.d.</
var
>
& ipſius
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>.c.d.</
var
>
ad
<
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>.d.e.</
var
>
eſſe vt ipſius
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<
var
>a.b.</
var
>
a
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unsure
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d.b.c. & cętera, verum dicit ex .19. quinti Eucli. eo quod cum ex hypotheſi ſit
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ipſius,
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>a.b.</
var
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totalis ad
<
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>.c.b.</
var
>
totalom vt ipſius
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>.c.b.</
var
>
partialis (ſumptæ vt pars abſciſa ab
<
var
>.a.
<
lb
/>
b.</
var
>
pro nunc) ad
<
var
>.d.b.</
var
>
partialem (abſciſam ab
<
var
>.c.b.</
var
>
) erit ex .19. dicta ipſius
<
var
>.a.c.</
var
>
(reſidui
<
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/>
ex
<
var
>.a.b.</
var
>
) ad
<
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>.c.d.</
var
>
(reſiduum ex
<
var
>.c.b.</
var
>
) vt ipſius
<
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>.a.b.</
var
>
ad
<
var
>.c.b.</
var
>
& ita probabitur de pro-
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portione ipſiuas
<
var
>.c.d.</
var
>
ad
<
var
>.d.e.</
var
>
eadem ratione.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4582
"
xml:space
="
preserve
">Cum verò ex .18. quinti ſit ipſius
<
var
>.a.b.</
var
>
cum
<
var
>.c.b.</
var
>
ad
<
var
>.c.b.</
var
>
vt ipſius
<
var
>.a.d.</
var
>
ad
<
var
>.d.e.</
var
>
ergo ex
<
lb
/>
22. eiuſdem, ita erit ipſius
<
var
>.a.b.</
var
>
cum
<
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>.c.b.</
var
>
ad
<
var
>.d.b.</
var
>
vt
<
var
>.a.d.</
var
>
ad
<
var
>.d.e.</
var
>
& exijſdem rationibus
<
lb
/>
eadem proportio erit ipſius
<
var
>.c.b.</
var
>
cum
<
var
>.d.b.</
var
>
ad
<
var
>.b.e.</
var
>
vt
<
var
>.a.d.</
var
>
ad
<
var
>.d.e.</
var
>
quod inquit Archi.
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</
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>
<
s
xml:id
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xml:space
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">Verum etiam erit (ex .13. quinti) cum dicit eandem proportionem eſſe ipſius
<
var
>.a.d.</
var
>
<
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/>
ad
<
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>.d.e.</
var
>
quę dupli primi antecedentis cum ſimplo ſecundi antecedentis ad duplum
<
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/>
primi conſequentis cum ſimplo ſecundi conſequentis, hoc eſt dupli ipſius
<
var
>.a.b.c.</
var
>
<
reg
norm
="
cum
"
type
="
context
">cũ</
reg
>
<
lb
/>
ſimplo
<
var
>.c.b.d.</
var
>
ad duplum ipſius
<
var
>.d.b.</
var
>
cum ſimplo
<
var
>.e.b.</
var
>
hoc eft dupli
<
var
>.a.b.</
var
>
cum triplo ip-
<
lb
/>
ſius
<
var
>.b.c.</
var
>
cum ſimplo
<
var
>.d.b.</
var
>
ad duplum ipſius
<
var
>.d.b.</
var
>
cum ſimplo
<
var
>.e.b</
var
>
. </
s
>
<
s
xml:id
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xml:space
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">Nunc duplum
<
var
>.a.b.</
var
>
<
lb
/>
cum triplo
<
var
>.b.c.</
var
>
cum ſimplo
<
var
>.b.d.</
var
>
ſignatum ſit charactere
<
var
>.D.</
var
>
ſuum verò conſequens,
<
lb
/>
hoc eſt duplum
<
var
>.d.b.</
var
>
<
reg
norm
="
cum
"
type
="
context
">cũ</
reg
>
ſimplo
<
var
>.e.b.</
var
>
ſignificetur à charactere
<
var
>.B.</
var
>
hinc proportio ipſius
<
lb
/>
<
note
xlink:label
="
note-0398-01
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xlink:href
="
note-0398-01a
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position
="
left
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xml:space
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preserve
">M</
note
>
<
var
>a.d.</
var
>
ad
<
var
>.d.e.</
var
>
erit vt
<
var
>.D.</
var
>
ad
<
var
>.B</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
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xml:space
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preserve
">Inquit nunc Archimedes, ſi quis ſumeret aliquod maius antecedens æquale ſci-
<
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licet duplo ipſius
<
var
>.a.b.</
var
>
cum quadruplo ipſius
<
var
>.b.e.</
var
>
cum quadruplo ipſius
<
var
>.b.d.</
var
>
cum du-
<
lb
/>
plo ipſius
<
var
>.b.e.</
var
>
<
reg
norm
="
compararetque
"
type
="
simple
">compararetq́;</
reg
>
illud cum
<
reg
norm
="
conſequente
"
type
="
context
">cõſequente</
reg
>
<
var
>.B.</
var
>
clarum eſſet ex .8. quinti quod
<
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tale antecedens maiorem proportionem haberet ad
<
var
>.B.</
var
>
quam ad
<
var
>.D.</
var
>
hoc eſt maiorem
<
lb
/>
quàm ipſius
<
var
>.a.d.</
var
>
ad
<
var
>.d.e.</
var
>
ex .12. quinti.</
s
>
</
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<
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<
s
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xml:space
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">Nunc ſi ſumpta fuerit aliqua linea, puta
<
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var
>
cui
<
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>.a.d.</
var
>
<
reg
norm
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dictam
"
type
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reg
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habeat proportionem
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maiorem, larum erit ex ſecunda parte decimę quinti quod
<
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>.d.o.</
var
>
minor erit ipſa
<
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>.d.e.</
var
>
<
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/>
Corrige igitur impreſſionem Baſileę locando characterem
<
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>.o.</
var
>
inter
<
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>.d.</
var
>
et
<
var
>.e.</
var
>
eo quod
<
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/>
ibi poſitum non fuit.</
s
>
</
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<
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>
<
s
xml:id
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xml:space
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preserve
">Volo nunc quod dictum maius antecedens æquale ſcilicet duplo ipſius
<
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>.a.b.</
var
>
cum
<
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quadruplo ipſius
<
var
>.b.c.</
var
>
cum quadruplo ipſius
<
var
>.b.d.</
var
>
cum duplo ipſius
<
var
>.b.c.</
var
>
ſignificetur à
<
lb
/>
charactere
<
var
>.A</
var
>
. </
s
>
<
s
xml:id
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xml:space
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preserve
">Hinc habebimus proportionem ipſius
<
var
>.a.d.</
var
>
ad
<
var
>.d.o.</
var
>
ut
<
var
>.A.</
var
>
ad
<
var
>.B</
var
>
.</
s
>
</
p
>
<
note
position
="
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"
xml:space
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">β</
note
>
<
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>
<
s
xml:id
="
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xml:space
="
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">Ex .18. quinti poſtea habebimus
<
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>.A.B.</
var
>
ad
<
var
>.B.</
var
>
vt
<
var
>.a.o.</
var
>
ad
<
var
>.d.o.</
var
>
& proportionalitate
<
lb
/>
euerſa in .19. dicti ita erit
<
var
>.A.B.</
var
>
ad
<
var
>.A.</
var
>
vt
<
var
>.a.o.</
var
>
ad
<
var
>.a.d</
var
>
. </
s
>
<
s
xml:id
="
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xml:space
="
preserve
">Sed hoc vltimum antecedens in
<
lb
/>
<
note
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="
note-0398-03
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xlink:href
="
note-0398-03a
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position
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">T</
note
>
ſe continet id quod Archimedes ſcribit, hoc eſt duplum ipſius
<
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>.a.b.</
var
>
<
reg
norm
="
quadruplum
"
type
="
context
">quadruplũ</
reg
>
ipſius
<
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/>
<
var
>b.c.</
var
>
ſexcuplum ipſius
<
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>.b.d.</
var
>
& triplum ipſius
<
var
>.b.e</
var
>
. </
s
>
<
s
xml:id
="
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xml:space
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">Conſequens verò
<
var
>.A.</
var
>
continet du
<
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/>
plum ipſius
<
var
>.a.b.</
var
>
quadruplum ipſius
<
var
>.b.c.</
var
>
quadruplum ipſius
<
var
>.b.d.</
var
>
& duplum ipſius
<
var
>.b.e</
var
>
.</
s
>
</
p
>
<
p
>
<
s
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xml:space
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">Ex ſuppoſito deinde ipſius Archimedis & ex conuerſa proportionalitate in .19.
<
lb
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dicta, verum eſt id quod dicit Archimedes, videlicet quod eadem proportio eſt
<
lb
/>
ipſius
<
var
>.a.d.</
var
>
ad
<
var
>.g.h.</
var
>
quod quintupli ipſius
<
var
>.a.b.</
var
>
cum quintuplo ipſius
<
var
>.b.e.</
var
>
cum decuplo
<
lb
/>
ipſius
<
var
>.b.c.</
var
>
cum decuplo ipſius
<
var
>.b.d.</
var
>
(quod quidem antecedens ſignificetur per
<
var
>.V.</
var
>
)
<
lb
/>
ad duplum ipſius
<
var
>.a.b.</
var
>
cum quadruplo ipſius
<
var
>.b.c.</
var
>
cum ſexcuplo ipſius
<
var
>.b.d.</
var
>
cum triplo
<
lb
/>
ipſius
<
var
>.b.e.</
var
>
hoc eſt ad
<
var
>.A.B</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4593
"
xml:space
="
preserve
">Erit igitur
<
var
>.V.</
var
>
ad
<
var
>.A.B.</
var
>
vt ipſius
<
var
>.a.d.</
var
>
ad
<
var
>.g.h.</
var
>
ſed ſuperius vbi ſignatum eſt
<
var
>.T.</
var
>
iam
<
lb
/>
probatum fuit ita eſſe
<
var
>.A.B.</
var
>
ad
<
var
>.A.</
var
>
vt ipſius
<
var
>.a.o.</
var
>
ad
<
var
>.a.d</
var
>
. </
s
>
<
s
xml:id
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echoid-s4594
"
xml:space
="
preserve
">Ergò ex .23. quinti Archime
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des verum ſcribit, hoc eſt quod ita erit ipſius
<
var
>.V.</
var
>
ad
<
var
>.A.</
var
>
vt ipſius
<
var
>.a.o.</
var
>
ad
<
var
>.g.h</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
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echoid-s4595
"
xml:space
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preserve
">Clarum per ſe etiam eſt, id quod Archimed. dicit hoc eſt quod
<
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>.V.</
var
>
ad
<
var
>.A.</
var
>
eſt vt
<
lb
/>
<
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note-0398-04
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xlink:href
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note-0398-04a
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position
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xml:space
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