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
page
|<
<
(172)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div425
"
type
="
section
"
level
="
1
"
n
="
258
">
<
p
>
<
s
xml:id
="
echoid-s4206
"
xml:space
="
preserve
">
<
pb
o
="
172
"
file
="
0192
"
n
="
192
"
rhead
="
GEOMETRIÆ
"/>
BEC, CEF, .</
s
>
<
s
xml:id
="
echoid-s4207
"
xml:space
="
preserve
">i. </
s
>
<
s
xml:id
="
echoid-s4208
"
xml:space
="
preserve
">ſunt ad illa, vt, EF, ad, {1/6}, eiuſdem, EF, ergo ex
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0192-01
"
xlink:href
="
note-0192-01a
"
xml:space
="
preserve
">Elicitur
<
lb
/>
ex.</
note
>
æquali, rectingula ſub, AE, EC, ad rectangula ſub triangulis, BE
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0192-02
"
xlink:href
="
note-0192-02a
"
xml:space
="
preserve
">24. huius.</
note
>
C, CEF, erunt vt, DE, ad, {1/6}, EF, eadem verò ad rectangula ſub,
<
lb
/>
AE, & </
s
>
<
s
xml:id
="
echoid-s4209
"
xml:space
="
preserve
">triangulo, BEC, ſiue, CEF, oſtenſa ſunt eſſe, vt, DE,
<
lb
/>
ad, {1/2}, DE, ergo, colligendo, rectangula ſub, AE, EC, ad rectan-
<
lb
/>
gula ſub, AE, & </
s
>
<
s
xml:id
="
echoid-s4210
"
xml:space
="
preserve
">triangulo, CEF, & </
s
>
<
s
xml:id
="
echoid-s4211
"
xml:space
="
preserve
">ſub triangulo, BEC, & </
s
>
<
s
xml:id
="
echoid-s4212
"
xml:space
="
preserve
">eo-
<
lb
/>
dem, CEF, .</
s
>
<
s
xml:id
="
echoid-s4213
"
xml:space
="
preserve
">i. </
s
>
<
s
xml:id
="
echoid-s4214
"
xml:space
="
preserve
">ad rectangula ſub trapezio, ADEC, & </
s
>
<
s
xml:id
="
echoid-s4215
"
xml:space
="
preserve
">triangulo,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0192-03
"
xlink:href
="
note-0192-03a
"
xml:space
="
preserve
">Per A. Co
<
lb
/>
roll. 23.
<
lb
/>
huius.</
note
>
CEF, erunt vt, DE, ad compoſitam ex, {1/2}, DE, &</
s
>
<
s
xml:id
="
echoid-s4216
"
xml:space
="
preserve
">, {1/6}, EF, quę
<
lb
/>
eſt Theorematis prima pars.</
s
>
<
s
xml:id
="
echoid-s4217
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4218
"
xml:space
="
preserve
">Dico vlterius rectangula ſub, AF, FB, ad rectangula ſub trape-
<
lb
/>
zio, ADEC, & </
s
>
<
s
xml:id
="
echoid-s4219
"
xml:space
="
preserve
">triangulo, BEC, eſſe vt, DF, ad compoſitam ex,
<
lb
/>
{1/6}, DE, &</
s
>
<
s
xml:id
="
echoid-s4220
"
xml:space
="
preserve
">, {1/3}, EF; </
s
>
<
s
xml:id
="
echoid-s4221
"
xml:space
="
preserve
">rectangula .</
s
>
<
s
xml:id
="
echoid-s4222
"
xml:space
="
preserve
">n. </
s
>
<
s
xml:id
="
echoid-s4223
"
xml:space
="
preserve
">ſub, AF, FB, ad rectangula ſub,
<
lb
/>
AE, EC, ſunt vt rectangulum, DFE, ad rectangulum, DEF, .</
s
>
<
s
xml:id
="
echoid-s4224
"
xml:space
="
preserve
">i.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4225
"
xml:space
="
preserve
">
<
note
position
="
left
"
xlink:label
="
note-0192-04
"
xlink:href
="
note-0192-04a
"
xml:space
="
preserve
">14. huius.</
note
>
vt, FD, ad, DE, rectangula vero ſub, AE, EC, ad rectangula ſub,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0192-05
"
xlink:href
="
note-0192-05a
"
xml:space
="
preserve
">3. huius.</
note
>
<
figure
xlink:label
="
fig-0192-01
"
xlink:href
="
fig-0192-01a
"
number
="
112
">
<
image
file
="
0192-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0192-01
"/>
</
figure
>
AE, & </
s
>
<
s
xml:id
="
echoid-s4226
"
xml:space
="
preserve
">triangulo, BEC, ſunt vt, B
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0192-06
"
xlink:href
="
note-0192-06a
"
xml:space
="
preserve
">Coroll. 1.
<
lb
/>
26. huius.</
note
>
F, ad triangulum, BEC, .</
s
>
<
s
xml:id
="
echoid-s4227
"
xml:space
="
preserve
">i. </
s
>
<
s
xml:id
="
echoid-s4228
"
xml:space
="
preserve
">dupla .</
s
>
<
s
xml:id
="
echoid-s4229
"
xml:space
="
preserve
">i.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4230
"
xml:space
="
preserve
">vt, DE, ad, {1/2}, ipſius, DE, ergo, ex
<
lb
/>
æquali rectangula ſub, AF, FB, ad
<
lb
/>
rectangula ſub, AE, & </
s
>
<
s
xml:id
="
echoid-s4231
"
xml:space
="
preserve
">triangulo, B
<
lb
/>
EC, erunt vt, FD, ad, {1/2}, DE, quod
<
lb
/>
ſerua. </
s
>
<
s
xml:id
="
echoid-s4232
"
xml:space
="
preserve
">Item rectangula ſub, AF, FB,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0192-07
"
xlink:href
="
note-0192-07a
"
xml:space
="
preserve
">14. huius.
<
lb
/>
3. huius.
<
lb
/>
24. huius.</
note
>
ad omnia quadrata, BF, ſunt vt re-
<
lb
/>
ctangulum, DFE, ad quadratum, F
<
lb
/>
E, .</
s
>
<
s
xml:id
="
echoid-s4233
"
xml:space
="
preserve
">i. </
s
>
<
s
xml:id
="
echoid-s4234
"
xml:space
="
preserve
">vt, DF, ad, FE: </
s
>
<
s
xml:id
="
echoid-s4235
"
xml:space
="
preserve
">Omnia verò
<
lb
/>
quadrata, BF, ſunt tripla omnium
<
lb
/>
quadratorum trianguli, BEC, .</
s
>
<
s
xml:id
="
echoid-s4236
"
xml:space
="
preserve
">i. </
s
>
<
s
xml:id
="
echoid-s4237
"
xml:space
="
preserve
">ſunt vt, FE, ad, {1/3}, FE, ergo ex
<
lb
/>
æquali rectangula ſub, AF, FB, ad omnia quadrata trianguli, BE
<
lb
/>
C, ſunt vt, DF, ad, {1/3}, FE, erant autem eadem ad rectangula ſub,
<
lb
/>
AE, & </
s
>
<
s
xml:id
="
echoid-s4238
"
xml:space
="
preserve
">triangulo, BEC, vt, DF, ad, {1/2}, DE, ergo, colligendo,
<
lb
/>
rectangula ſub, AF, FB, ad rectangula ſub, AE, & </
s
>
<
s
xml:id
="
echoid-s4239
"
xml:space
="
preserve
">triangulo, BE
<
lb
/>
C, vna cum omnibus quadratis trianguli, BEC, .</
s
>
<
s
xml:id
="
echoid-s4240
"
xml:space
="
preserve
">i. </
s
>
<
s
xml:id
="
echoid-s4241
"
xml:space
="
preserve
">ad rectangula
<
lb
/>
ſub trapezio, ADEC, & </
s
>
<
s
xml:id
="
echoid-s4242
"
xml:space
="
preserve
">triangulo, BEC, erunt vt, DF, ad com-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0192-08
"
xlink:href
="
note-0192-08a
"
xml:space
="
preserve
">Per C.
<
lb
/>
Coroll.
<
lb
/>
23. huius.</
note
>
poſitam ex, {1/2}, DE, &</
s
>
<
s
xml:id
="
echoid-s4243
"
xml:space
="
preserve
">, {1/3}, EF, quę eſt Theorematis ſecunda pars;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4244
"
xml:space
="
preserve
">hæc autem erant demonſtranda.</
s
>
<
s
xml:id
="
echoid-s4245
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div429
"
type
="
section
"
level
="
1
"
n
="
259
">
<
head
xml:id
="
echoid-head274
"
xml:space
="
preserve
">COROLLARIVM.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s4246
"
xml:space
="
preserve
">_C_Olligimus autem ex hoc Theoremate rectangula ſub maximis ab-
<
lb
/>
ſciſſarum propoſitæ lineæ, adiunctis eiſdem tot vni cuidam æquali-
<
lb
/>
bus, ad rectangula ſub omnibus abſciſſis eiuſdem adiunctaiam dicta li-
<
lb
/>
nea, & </
s
>
<
s
xml:id
="
echoid-s4247
"
xml:space
="
preserve
">ſub reſiduis abſciſſarum eiuſdem, eſſe vt adiuncta ad compoſitam
<
lb
/>
ex, {1/2}, adiunctæ, & </
s
>
<
s
xml:id
="
echoid-s4248
"
xml:space
="
preserve
">{1/2}, propoſitæ lineæ, & </
s
>
<
s
xml:id
="
echoid-s4249
"
xml:space
="
preserve
">hoc ex prima parte </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>