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: 126
[Note]
Page: 126
[Note]
Page: 127
[Note]
Page: 127
[Note]
Page: 128
[Note]
Page: 128
[Note]
Page: 129
[Note]
Page: 130
[Note]
Page: 131
[Note]
Page: 132
[Note]
Page: 133
[Note]
Page: 133
[Note]
Page: 134
[Note]
Page: 134
[Note]
Page: 134
[Note]
Page: 134
[Note]
Page: 135
[Note]
Page: 136
[Note]
Page: 136
[Note]
Page: 136
[Note]
Page: 137
[Note]
Page: 138
[Note]
Page: 138
[Note]
Page: 138
[Note]
Page: 138
[Note]
Page: 138
[Note]
Page: 139
[Note]
Page: 139
[Note]
Page: 139
[Note]
Page: 139
<
1 - 8
[out of range]
>
page
|<
<
(522)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div1200
"
type
="
section
"
level
="
1
"
n
="
719
">
<
p
>
<
s
xml:id
="
echoid-s13475
"
xml:space
="
preserve
">
<
pb
o
="
522
"
file
="
0542
"
n
="
542
"
rhead
="
GEOMETRIÆ
"/>
B. </
s
>
<
s
xml:id
="
echoid-s13476
"
xml:space
="
preserve
">Dico ſolidum rectangulum ſub duobus triangulis, ABC, ACD,
<
lb
/>
contentum, regulis, BC, CF, eſſe pyramidem, cuius baſis erit pa-
<
lb
/>
rallelogrammum rectangulum ſub prædictis baſibus, BC, CD, pa-
<
lb
/>
riter contentum, dummodo alterum dictorum triangulorum ſit in
<
lb
/>
ambitu ipſius contenti ſolidi. </
s
>
<
s
xml:id
="
echoid-s13477
"
xml:space
="
preserve
">Sit enim deſcriptum ipſum ſolidum
<
lb
/>
rectangulum ſub triangulis, ABC, ACD, contentum, nempè, AE
<
lb
/>
<
figure
xlink:label
="
fig-0542-01
"
xlink:href
="
fig-0542-01a
"
number
="
356
">
<
image
file
="
0542-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0542-01
"/>
</
figure
>
BCF, ſit tamen alterum ip-
<
lb
/>
ſorum, vt, ABC, in ambitu
<
lb
/>
ipſius contenti, ſolidi, &</
s
>
<
s
xml:id
="
echoid-s13478
"
xml:space
="
preserve
">, AF
<
lb
/>
C, ſuperficies homologa ipſi,
<
lb
/>
ACD, iuxta regulam planũ,
<
lb
/>
BCF, erit ergo, ACF, trian-
<
lb
/>
gulum, eſto enim, quod vnũ
<
lb
/>
parallelorum ipſi, BF, plano-
<
lb
/>
rum, ſolidum, AEC, ſecanti-
<
lb
/>
um, in eo effecerit parallelo
<
lb
/>
grammum rectangulũ, GMIH, & </
s
>
<
s
xml:id
="
echoid-s13479
"
xml:space
="
preserve
">intriangulo, ACD, rectam, IY,
<
lb
/>
iam ſcimus, quod, HI, eſt in eodem plano cum, FC, cui eſt paral-
<
lb
/>
lela, & </
s
>
<
s
xml:id
="
echoid-s13480
"
xml:space
="
preserve
">ambo ſunt in eodem plano cum, AC, quod etiam de reli-
<
lb
/>
quis in ſuperficie, ACF, ipſi, FC, parallelis exiſtentibus eodem mo-
<
lb
/>
do oſtendetur, ergo iacent omnes in plano ipſarum, AC, CF, ergo,
<
lb
/>
ACF, eſt ſuperficies plana cum vero vt, CD, ad, IY, ita ſit, CA, ad,
<
lb
/>
AI, & </
s
>
<
s
xml:id
="
echoid-s13481
"
xml:space
="
preserve
">ita etiam, CF, ad, IH, erit, CF, ad, IH, vt, CA, ad, AI, er-
<
lb
/>
gotria puncta, FHA, erunt in recta linea, in eadem autem eſſe
<
lb
/>
oſtendemus etiam reliquarum ipſi, CF, parallelarum extrema pun-
<
lb
/>
cta ex hac parte, ergo, ACF, erit triangulum: </
s
>
<
s
xml:id
="
echoid-s13482
"
xml:space
="
preserve
">Conſimili autem
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0542-01
"
xlink:href
="
note-0542-01a
"
xml:space
="
preserve
">Lemwa 1.
<
lb
/>
22. l. 1.</
note
>
modo pariter demonſtrabimus, ABE, AEF, eſſe triangula, & </
s
>
<
s
xml:id
="
echoid-s13483
"
xml:space
="
preserve
">eſt,
<
lb
/>
BF, parallelogrammum rectangulum, ergo ſolidum, ABF, eſt py-
<
lb
/>
ramis, & </
s
>
<
s
xml:id
="
echoid-s13484
"
xml:space
="
preserve
">eius baſis parallelogrammum, BF, quod oſtendere opus
<
lb
/>
erat.</
s
>
<
s
xml:id
="
echoid-s13485
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div1202
"
type
="
section
"
level
="
1
"
n
="
720
">
<
head
xml:id
="
echoid-head753
"
xml:space
="
preserve
">COROLLARIVM I.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s13486
"
xml:space
="
preserve
">_E_X hoc pariter intelligipoteſt, quod ſolidum rectang. </
s
>
<
s
xml:id
="
echoid-s13487
"
xml:space
="
preserve
">contentum
<
lb
/>
ſub trapezijs ex.</
s
>
<
s
xml:id
="
echoid-s13488
"
xml:space
="
preserve
">g.</
s
>
<
s
xml:id
="
echoid-s13489
"
xml:space
="
preserve
">MBCI, ICDγ, in eiſdem parallelis, Sγ, ND,
<
lb
/>
exiſtentibus, regulis ijſdem, BC, CF, eſt fruſtum pyramidis abſciſſæ per
<
lb
/>
planum baſi, BF, æquidiſtans, vt, GECI, dummodo alterum dictorum
<
lb
/>
trapeziorum in ambitu contenti ſolidi conſiſtat.</
s
>
<
s
xml:id
="
echoid-s13490
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>