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
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 213
>
51
(20)
52
53
(21)
54
55
(22)
56
57
(23)
58
59
(24)
60
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 213
>
page
|<
<
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div268
"
type
="
section
"
level
="
1
"
n
="
91
">
<
p
>
<
s
xml:id
="
echoid-s4528
"
xml:space
="
preserve
">
<
pb
file
="
0182
"
n
="
182
"
rhead
="
FED. COMMANDINI
"/>
nis, quouſque in unum punctum r conueniant; </
s
>
<
s
xml:id
="
echoid-s4529
"
xml:space
="
preserve
">erit pyra-
<
lb
/>
midis a b c r, & </
s
>
<
s
xml:id
="
echoid-s4530
"
xml:space
="
preserve
">pyramidis d e f r grauitatis centrum in li-
<
lb
/>
nea r h. </
s
>
<
s
xml:id
="
echoid-s4531
"
xml:space
="
preserve
">ergo & </
s
>
<
s
xml:id
="
echoid-s4532
"
xml:space
="
preserve
">reliquæ magnitudinis, uidelicet fruſti cen-
<
lb
/>
trum in eadem linea neceſſario comperietur. </
s
>
<
s
xml:id
="
echoid-s4533
"
xml:space
="
preserve
">Iungantur
<
lb
/>
d b, d c, d h, d m: </
s
>
<
s
xml:id
="
echoid-s4534
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4535
"
xml:space
="
preserve
">per lineas d b, d c ducto altero plano
<
lb
/>
intelligatur fruſtum in duas pyramides diuiſum: </
s
>
<
s
xml:id
="
echoid-s4536
"
xml:space
="
preserve
">in pyra-
<
lb
/>
midem quidem, cuius baſis eſt triangulum a b c, uertex d:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4537
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4538
"
xml:space
="
preserve
">in eam, cuius idem uertex, & </
s
>
<
s
xml:id
="
echoid-s4539
"
xml:space
="
preserve
">baſis trapezium b c f e. </
s
>
<
s
xml:id
="
echoid-s4540
"
xml:space
="
preserve
">erit
<
lb
/>
igitur pyramidis a b c d axis d h, & </
s
>
<
s
xml:id
="
echoid-s4541
"
xml:space
="
preserve
">pyramidis b c f e d axis
<
lb
/>
d m: </
s
>
<
s
xml:id
="
echoid-s4542
"
xml:space
="
preserve
">atque erunt tres axes g h, d h, d m in eodem plano
<
lb
/>
d a K l. </
s
>
<
s
xml:id
="
echoid-s4543
"
xml:space
="
preserve
">ducatur præterea per o linea ſt ip ſi a K æquidiſtãs,
<
lb
/>
quæ lineam d h in u ſecet: </
s
>
<
s
xml:id
="
echoid-s4544
"
xml:space
="
preserve
">per p uero ducatur x y æquidi-
<
lb
/>
ſtans eidem, ſecansque d m in
<
lb
/>
<
figure
xlink:label
="
fig-0182-01
"
xlink:href
="
fig-0182-01a
"
number
="
135
">
<
image
file
="
0182-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0182-01
"/>
</
figure
>
z: </
s
>
<
s
xml:id
="
echoid-s4545
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4546
"
xml:space
="
preserve
">iungatur z u, quæ ſecet
<
lb
/>
g h in φ. </
s
>
<
s
xml:id
="
echoid-s4547
"
xml:space
="
preserve
">tranſibit ea per q: </
s
>
<
s
xml:id
="
echoid-s4548
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4549
"
xml:space
="
preserve
">
<
lb
/>
erunt φ q unum, atque idem
<
lb
/>
pun ctum; </
s
>
<
s
xml:id
="
echoid-s4550
"
xml:space
="
preserve
">ut inferius appare-
<
lb
/>
bit. </
s
>
<
s
xml:id
="
echoid-s4551
"
xml:space
="
preserve
">Quoniam igitur linea u o
<
lb
/>
æ quidiſtat ipſi d g, erit d u ad
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0182-01
"
xlink:href
="
note-0182-01a
"
xml:space
="
preserve
">2. ſexti.</
note
>
u h, ut g o ad o h. </
s
>
<
s
xml:id
="
echoid-s4552
"
xml:space
="
preserve
">Sed g o tri-
<
lb
/>
pla eſt o h. </
s
>
<
s
xml:id
="
echoid-s4553
"
xml:space
="
preserve
">quare & </
s
>
<
s
xml:id
="
echoid-s4554
"
xml:space
="
preserve
">d u ipſius
<
lb
/>
u h eſt tripla: </
s
>
<
s
xml:id
="
echoid-s4555
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4556
"
xml:space
="
preserve
">ideo pyrami-
<
lb
/>
dis a b c d centrum grauitatis
<
lb
/>
erit punctum 11. </
s
>
<
s
xml:id
="
echoid-s4557
"
xml:space
="
preserve
">Rurſus quo-
<
lb
/>
niam z y ipſi d l æquidiſtat, d z
<
lb
/>
a d z m eſt, utly ad y m: </
s
>
<
s
xml:id
="
echoid-s4558
"
xml:space
="
preserve
">eſtque
<
lb
/>
ly ad y m, ut g p ad p n. </
s
>
<
s
xml:id
="
echoid-s4559
"
xml:space
="
preserve
">ergo
<
lb
/>
d z ad z m eſt, ut g p ad p n.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4560
"
xml:space
="
preserve
">Quòd cum g p ſit tripla p n; </
s
>
<
s
xml:id
="
echoid-s4561
"
xml:space
="
preserve
">
<
lb
/>
erit etiam d z ipſius z m tri-
<
lb
/>
pla. </
s
>
<
s
xml:id
="
echoid-s4562
"
xml:space
="
preserve
">atque ob eandem cauſ-
<
lb
/>
ſam punctum z eſt centrũ gra-
<
lb
/>
uitatis pyramidis b c f e d. </
s
>
<
s
xml:id
="
echoid-s4563
"
xml:space
="
preserve
">iun
<
lb
/>
ctaigitur z u, in ea erit </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>