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]
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Page concordance
<
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
>
Scan
Original
421
409
422
410
423
411
424
412
425
413
426
414
427
415
428
416
429
417
430
418
431
419
432
420
433
421
434
422
435
423
436
424
437
425
438
426
439
440
441
442
443
444
<
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
>
page
|<
<
(386)
of 445
>
>|
<
echo
version
="
1.0
">
<
text
type
="
book
"
xml:lang
="
la
">
<
div
xml:id
="
echoid-div7
"
type
="
body
"
level
="
1
"
n
="
1
">
<
div
xml:id
="
echoid-div477
"
type
="
chapter
"
level
="
2
"
n
="
6
">
<
div
xml:id
="
echoid-div737
"
type
="
section
"
level
="
3
"
n
="
42
">
<
div
xml:id
="
echoid-div737
"
type
="
letter
"
level
="
4
"
n
="
1
">
<
p
>
<
s
xml:id
="
echoid-s4580
"
xml:space
="
preserve
">
<
pb
o
="
386
"
rhead
="
IO. BAPT. BENED.
"
n
="
398
"
file
="
0398
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0398
"/>
ipſius
<
var
>.b.e.</
var
>
ad compoſitum quintupli ipſius
<
var
>.a.b.</
var
>
cum decuplo ipſius
<
var
>.c.b.</
var
>
cum decuplo
<
lb
/>
ipſius
<
var
>.b.d.</
var
>
cum quintuplo ipſius
<
var
>.b.e.</
var
>
eadem ſit quæ ipſius
<
var
>.g.h.</
var
>
ad
<
var
>.a.d.</
var
>
& vult proba-
<
lb
/>
re
<
var
>.f.h.</
var
>
eſſe duas quintas ipſius
<
var
>.a.b</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4581
"
xml:space
="
preserve
">Cum autem dicit proportionem ipſius
<
var
>.a.c.</
var
>
ad
<
var
>.c.d.</
var
>
& ipſius
<
var
>.c.d.</
var
>
ad
<
var
>.d.e.</
var
>
eſſe vt ipſius
<
lb
/>
<
var
>a.b.</
var
>
a
<
unsure
/>
d.b.c. & cętera, verum dicit ex .19. quinti Eucli. eo quod cum ex hypotheſi ſit
<
lb
/>
ipſius,
<
var
>a.b.</
var
>
totalis ad
<
var
>.c.b.</
var
>
totalom vt ipſius
<
var
>.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
<
lb
/>
ex
<
var
>.a.b.</
var
>
) ad
<
var
>.c.d.</
var
>
(reſiduum ex
<
var
>.c.b.</
var
>
) vt ipſius
<
var
>.a.b.</
var
>
ad
<
var
>.c.b.</
var
>
& ita probabitur de pro-
<
lb
/>
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
<
var
>.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.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4583
"
xml:space
="
preserve
">Verum etiam erit (ex .13. quinti) cum dicit eandem proportionem eſſe ipſius
<
var
>.a.d.</
var
>
<
lb
/>
ad
<
var
>.d.e.</
var
>
quę dupli primi antecedentis cum ſimplo ſecundi antecedentis ad duplum
<
lb
/>
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
="
echoid-s4584
"
xml:space
="
preserve
">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
"
xlink:href
="
note-0398-01a
"
position
="
left
"
xml:space
="
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
="
echoid-s4585
"
xml:space
="
preserve
">Inquit nunc Archimedes, ſi quis ſumeret aliquod maius antecedens æquale ſci-
<
lb
/>
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
<
lb
/>
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
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4586
"
xml:space
="
preserve
">Nunc ſi ſumpta fuerit aliqua linea, puta
<
var
>.d.o.</
var
>
cui
<
var
>.a.d.</
var
>
<
reg
norm
="
dictam
"
type
="
context
">dictã</
reg
>
habeat proportionem
<
lb
/>
maiorem, larum erit ex ſecunda parte decimę quinti quod
<
var
>.d.o.</
var
>
minor erit ipſa
<
var
>.d.e.</
var
>
<
lb
/>
Corrige igitur impreſſionem Baſileę locando characterem
<
var
>.o.</
var
>
inter
<
var
>.d.</
var
>
et
<
var
>.e.</
var
>
eo quod
<
lb
/>
ibi poſitum non fuit.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4587
"
xml:space
="
preserve
">Volo nunc quod dictum maius antecedens æquale ſcilicet duplo ipſius
<
var
>.a.b.</
var
>
cum
<
lb
/>
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
="
echoid-s4588
"
xml:space
="
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
="
left
"
xml:space
="
preserve
">β</
note
>
<
p
>
<
s
xml:id
="
echoid-s4589
"
xml:space
="
preserve
">Ex .18. quinti poſtea habebimus
<
var
>.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
="
echoid-s4590
"
xml:space
="
preserve
">Sed hoc vltimum antecedens in
<
lb
/>
<
note
xlink:label
="
note-0398-03
"
xlink:href
="
note-0398-03a
"
position
="
left
"
xml:space
="
preserve
">T</
note
>
ſe continet id quod Archimedes ſcribit, hoc eſt duplum ipſius
<
var
>.a.b.</
var
>
<
reg
norm
="
quadruplum
"
type
="
context
">quadruplũ</
reg
>
ipſius
<
lb
/>
<
var
>b.c.</
var
>
ſexcuplum ipſius
<
var
>.b.d.</
var
>
& triplum ipſius
<
var
>.b.e</
var
>
. </
s
>
<
s
xml:id
="
echoid-s4591
"
xml:space
="
preserve
">Conſequens verò
<
var
>.A.</
var
>
continet du
<
lb
/>
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
xml:id
="
echoid-s4592
"
xml:space
="
preserve
">Ex ſuppoſito deinde ipſius Archimedis & ex conuerſa proportionalitate in .19.
<
lb
/>
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
="
echoid-s4594
"
xml:space
="
preserve
">Ergò ex .23. quinti Archime
<
lb
/>
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
="
echoid-s4595
"
xml:space
="
preserve
">Clarum per ſe etiam eſt, id quod Archimed. dicit hoc eſt quod
<
var
>.V.</
var
>
ad
<
var
>.A.</
var
>
eſt vt
<
lb
/>
<
note
xlink:label
="
note-0398-04
"
xlink:href
="
note-0398-04a
"
position
="
left
"
xml:space
="
preserve
">ω</
note
>
</
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>