Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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 - 213
>
Scan
Original
151
20
152
153
21
154
155
22
156
157
23
158
159
24
160
161
25
162
163
26
164
165
27
166
167
28
168
169
29
170
171
30
172
173
31
174
175
32
176
177
33
178
179
34
180
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 213
>
page
|<
<
(34)
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div263
"
type
="
section
"
level
="
1
"
n
="
90
">
<
p
>
<
s
xml:id
="
echoid-s4455
"
xml:space
="
preserve
">
<
pb
o
="
34
"
file
="
0179
"
n
="
179
"
rhead
="
DE CENTRO GRAVIT. SOLID.
"/>
culi, uel ellipſes c d, e ſ a b ad circulum, uel ellipſim a b. </
s
>
<
s
xml:id
="
echoid-s4456
"
xml:space
="
preserve
">In-
<
lb
/>
telligatur pyramis q baſim habens æqualem tribus rectan
<
lb
/>
gulis a b, e f, c d; </
s
>
<
s
xml:id
="
echoid-s4457
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4458
"
xml:space
="
preserve
">altitudinem eãdem, quam fruſtum a d.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4459
"
xml:space
="
preserve
">intelligatur etiam conus, uel coni portio q, eadem altitudi
<
lb
/>
ne, cuius baſis ſit tribus circulis, uel tribus ellipſibus a b,
<
lb
/>
e f, c d æqualis. </
s
>
<
s
xml:id
="
echoid-s4460
"
xml:space
="
preserve
">poſtremo intelligatur pyramis a l b, cuius
<
lb
/>
baſis ſit rectangulum m n o p, & </
s
>
<
s
xml:id
="
echoid-s4461
"
xml:space
="
preserve
">altitudo eadem, quæ fru-
<
lb
/>
ſti: </
s
>
<
s
xml:id
="
echoid-s4462
"
xml:space
="
preserve
">itemq, intelligatur conus, uel coni portio a l b, cuius
<
lb
/>
baſis circulus, uel ellipſis circa diametrum a b, & </
s
>
<
s
xml:id
="
echoid-s4463
"
xml:space
="
preserve
">eadem al
<
lb
/>
titudo. </
s
>
<
s
xml:id
="
echoid-s4464
"
xml:space
="
preserve
">ut igitur rectangula a b, e f, c d ad rectangulum a b,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0179-01
"
xlink:href
="
note-0179-01a
"
xml:space
="
preserve
">6. 11. duo
<
lb
/>
decimi</
note
>
ita pyramis q ad pyramidem a l b; </
s
>
<
s
xml:id
="
echoid-s4465
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4466
"
xml:space
="
preserve
">ut circuli, uel ellip-
<
lb
/>
ſes a b, e f, c d ad a b circulum, uel ellipſim, ita conus, uel co
<
lb
/>
ni portio q ad conum, uel coni portionem a l b. </
s
>
<
s
xml:id
="
echoid-s4467
"
xml:space
="
preserve
">conus
<
lb
/>
igitur, uel coni portio q ad conum, uel coni portionem
<
lb
/>
a l b eſt, ut pyramis q ad pyramidem a l b. </
s
>
<
s
xml:id
="
echoid-s4468
"
xml:space
="
preserve
">ſed pyramis
<
lb
/>
a l b ad pyramidem a g b eſt, ut altitudo ad altitudinem, ex
<
lb
/>
20. </
s
>
<
s
xml:id
="
echoid-s4469
"
xml:space
="
preserve
">huius: </
s
>
<
s
xml:id
="
echoid-s4470
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4471
"
xml:space
="
preserve
">ita eſt conus, uel coni portio al b ad conum,
<
lb
/>
uel coni portionem a g b ex 14. </
s
>
<
s
xml:id
="
echoid-s4472
"
xml:space
="
preserve
">duodecimi elementorum,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s4473
"
xml:space
="
preserve
">ex iis, quæ nos demonſtrauimus in commentariis in un-
<
lb
/>
decimam de conoidibus, & </
s
>
<
s
xml:id
="
echoid-s4474
"
xml:space
="
preserve
">ſphæroidibus, propoſitione
<
lb
/>
quarta. </
s
>
<
s
xml:id
="
echoid-s4475
"
xml:space
="
preserve
">pyramis autem a g b ad pyramidem c g d propor-
<
lb
/>
tionem habet compoſitam ex proportione baſium & </
s
>
<
s
xml:id
="
echoid-s4476
"
xml:space
="
preserve
">pro
<
lb
/>
portione altitudinum, ex uigeſima prima huius: </
s
>
<
s
xml:id
="
echoid-s4477
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4478
"
xml:space
="
preserve
">ſimili-
<
lb
/>
ter conus, uel coni portio a g b a d conum, uel coni portio-
<
lb
/>
nem c g d proportionem habet compoſitã ex eiſdem pro-
<
lb
/>
portionibus, per ea, quæ in dictis commentariis demon-
<
lb
/>
ſtrauimus, propoſitione quinta, & </
s
>
<
s
xml:id
="
echoid-s4479
"
xml:space
="
preserve
">ſexta: </
s
>
<
s
xml:id
="
echoid-s4480
"
xml:space
="
preserve
">altitudo enim in
<
lb
/>
utriſque eadem eſt, & </
s
>
<
s
xml:id
="
echoid-s4481
"
xml:space
="
preserve
">baſes inter ſe ſe eandem habent pro-
<
lb
/>
portionem. </
s
>
<
s
xml:id
="
echoid-s4482
"
xml:space
="
preserve
">ergo ut pyramis a g b ad pyramidem c g d, ita
<
lb
/>
eſt conus, uel coni portio a g b ad a g d conum, uel coni
<
lb
/>
portionem: </
s
>
<
s
xml:id
="
echoid-s4483
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4484
"
xml:space
="
preserve
">per conuerſionẽ rationis, ut pyramis a g b
<
lb
/>
ad fruſtū à pyramide abſciſſum, ita conus uel coni portio
<
lb
/>
a g b ad fruſtum a d. </
s
>
<
s
xml:id
="
echoid-s4485
"
xml:space
="
preserve
">ex æquali igitur, ut pyramis q ad fru-
<
lb
/>
ſtum à pyramide abſciſſum, ita conus uel coni portio q </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>