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
41
15
42
43
16
44
45
17
46
47
18
48
49
19
50
51
20
52
53
21
54
55
22
56
57
23
58
59
24
60
61
25
62
63
26
64
65
27
66
67
22
68
69
29
70
<
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
>