Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of Notes
<
1 - 8
[out of range]
>
[Note]
Page: 31
[Note]
Page: 31
[Note]
Page: 31
[Note]
Page: 33
[Note]
Page: 33
[Note]
Page: 33
[Note]
Page: 34
[Note]
Page: 34
[Note]
Page: 35
[Note]
Page: 35
[Note]
Page: 35
[Note]
Page: 35
[Note]
Page: 35
[Note]
Page: 35
[Note]
Page: 35
[Note]
Page: 35
[Note]
Page: 36
[Note]
Page: 36
[Note]
Page: 36
[Note]
Page: 36
[Note]
Page: 36
[Note]
Page: 37
[Note]
Page: 37
[Note]
Page: 38
[Note]
Page: 38
[Note]
Page: 38
[Note]
Page: 40
[Note]
Page: 40
[Note]
Page: 40
[Note]
Page: 41
<
1 - 8
[out of range]
>
page
|<
<
(152)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div374
"
type
="
section
"
level
="
1
"
n
="
227
">
<
p
>
<
s
xml:id
="
echoid-s3588
"
xml:space
="
preserve
">
<
pb
o
="
152
"
file
="
0172
"
n
="
172
"
rhead
="
GEOMETRIÆ
"/>
& </
s
>
<
s
xml:id
="
echoid-s3589
"
xml:space
="
preserve
">rectangulis bis ſub, GN, NP, fient omnia quadrata, GQ, hęc
<
lb
/>
ſi iunxeris omnibus quadratis, FK, cum rectangulis bis ſub, FK, K
<
lb
/>
Q, fient omnia quadrata, FR, quę tandem ſi iunxeris omnibus qua-
<
lb
/>
dratis, DM, cum rectangulis bis ſub, DM, MR, fient omnia qua-
<
lb
/>
drata, DS, quę cum ſint minora omnibus quadratis figurę, Ω, hinc
<
lb
/>
figuræ circumſcriptæ omnia quadrata excedunt omnia quadrata in-
<
lb
/>
ſcriptę minori quantitate, quam ſint omnia quadrata, Ω, & </
s
>
<
s
xml:id
="
echoid-s3590
"
xml:space
="
preserve
">ideò ex-
<
lb
/>
cedunt omnia quadrata trianguli, OES, multò minon quantitate:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3591
"
xml:space
="
preserve
">Quia ergo omnia quadrata, AS, ad omnia quadrata trianguli, OE
<
lb
/>
S, cum omnibus quadratis, Ω, erant vt omnia quadrata, Τ β, ad om-
<
lb
/>
nia quadrata trianguli, & </
s
>
<
s
xml:id
="
echoid-s3592
"
xml:space
="
preserve
">Ζ β, hinc omnia quadrata, AS, ad om-
<
lb
/>
nia quadrata figurę circumſcriptę triangulo, OES, habebunt maio-
<
lb
/>
rem rationem, quam omnia quadrata, Τ β, ad omnia quadrata tri-
<
lb
/>
anguli, & </
s
>
<
s
xml:id
="
echoid-s3593
"
xml:space
="
preserve
">Ζ β.</
s
>
<
s
xml:id
="
echoid-s3594
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3595
"
xml:space
="
preserve
">Nunc diuidatur ſimiliter, & </
s
>
<
s
xml:id
="
echoid-s3596
"
xml:space
="
preserve
">β in punctis, ℟, Δ Σ, ac, OS, in
<
lb
/>
punctis, P, Q, R, & </
s
>
<
s
xml:id
="
echoid-s3597
"
xml:space
="
preserve
">per puncta, ℟ Δ Σ, parallelæ ipſi, Ζ β, du-
<
lb
/>
cantur, ℟ V, Δ Χ, Σ Υ, ſecantes, & </
s
>
<
s
xml:id
="
echoid-s3598
"
xml:space
="
preserve
">Ζ, in punctis, r, 3, 6, per quę
<
lb
/>
vſque ad proximas parallelas ipſis, & </
s
>
<
s
xml:id
="
echoid-s3599
"
xml:space
="
preserve
">β, ΤΖ, æquidiſtantes ducan-
<
lb
/>
tur, Φ Γ, Λ 3, 46, vt triangulo, & </
s
>
<
s
xml:id
="
echoid-s3600
"
xml:space
="
preserve
">Ζ β, ſit circumſcripta figura ex
<
lb
/>
<
figure
xlink:label
="
fig-0172-01
"
xlink:href
="
fig-0172-01a
"
number
="
100
">
<
image
file
="
0172-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0172-01
"/>
</
figure
>
parallelogrãmis,
<
lb
/>
Φ ℟, Δ Δ, 4 Σ, Υ
<
lb
/>
β, cõpoſita, quia
<
lb
/>
ergo, vt, OS, ad,
<
lb
/>
SR, ita eſt, & </
s
>
<
s
xml:id
="
echoid-s3601
"
xml:space
="
preserve
">β,
<
lb
/>
ad, β Σ, vt au-
<
lb
/>
tem, OS, ad, S
<
lb
/>
R, ita ſunt om-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0172-01
"
xlink:href
="
note-0172-01a
"
xml:space
="
preserve
">10. huius.</
note
>
nia quadrata, A
<
lb
/>
S, ad omnia qua-
<
lb
/>
drata, DS, & </
s
>
<
s
xml:id
="
echoid-s3602
"
xml:space
="
preserve
">
<
lb
/>
vt, & </
s
>
<
s
xml:id
="
echoid-s3603
"
xml:space
="
preserve
">β, ad, β
<
lb
/>
Σ, rta ſunt omnia
<
lb
/>
quadrata, Τ β, ad
<
lb
/>
omnia quadrata,
<
lb
/>
Υ β, ergo omnia
<
lb
/>
quadrata, AS, ad omnia quadrata, DS, ſunt vt omnia quadrata,
<
lb
/>
Τ β, ad omnia quadrata, Υ β, quia verò omnia quadrata, Υ β, ad
<
lb
/>
omnia quadrata, 6 β, .</
s
>
<
s
xml:id
="
echoid-s3604
"
xml:space
="
preserve
">@. </
s
>
<
s
xml:id
="
echoid-s3605
"
xml:space
="
preserve
">ad omnia quadrata, 4 Σ, ſunt vt quadra-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0172-02
"
xlink:href
="
note-0172-02a
"
xml:space
="
preserve
">9. huius.</
note
>
tum, Ζ β, ad quadratum, 7 β, .</
s
>
<
s
xml:id
="
echoid-s3606
"
xml:space
="
preserve
">@. </
s
>
<
s
xml:id
="
echoid-s3607
"
xml:space
="
preserve
">ad quadratum, 6 Σ, .</
s
>
<
s
xml:id
="
echoid-s3608
"
xml:space
="
preserve
">@. </
s
>
<
s
xml:id
="
echoid-s3609
"
xml:space
="
preserve
">vt quadra-
<
lb
/>
tum, β &</
s
>
<
s
xml:id
="
echoid-s3610
"
xml:space
="
preserve
">, ad quadratum, & </
s
>
<
s
xml:id
="
echoid-s3611
"
xml:space
="
preserve
">Σ, .</
s
>
<
s
xml:id
="
echoid-s3612
"
xml:space
="
preserve
">@. </
s
>
<
s
xml:id
="
echoid-s3613
"
xml:space
="
preserve
">vt quadrarum, SO, ad quadra-
<
lb
/>
tum, OR, ideſt vt quadratum, ES, ad quadratum, HR, ideſt, vt
<
lb
/>
omnia quadrata, DS, ad omnia quadrata, FR, ergo ex æquali </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>