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
|<
<
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div120
"
type
="
section
"
level
="
1
"
n
="
40
">
<
p
>
<
s
xml:id
="
echoid-s1694
"
xml:space
="
preserve
">
<
pb
file
="
0070
"
n
="
70
"
rhead
="
ARCHIMEDIS
"/>
dem circa e z diametrum; </
s
>
<
s
xml:id
="
echoid-s1695
"
xml:space
="
preserve
">a t d uero circa diametrum t h;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1696
"
xml:space
="
preserve
">
<
note
position
="
left
"
xlink:label
="
note-0070-01
"
xlink:href
="
note-0070-01a
"
xml:space
="
preserve
">K</
note
>
quæ ſimiles ſint portioni a b l. </
s
>
<
s
xml:id
="
echoid-s1697
"
xml:space
="
preserve
">tranſibit igitur a e i coni
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0070-02
"
xlink:href
="
note-0070-02a
"
xml:space
="
preserve
">L</
note
>
ſectio per _K_: </
s
>
<
s
xml:id
="
echoid-s1698
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1699
"
xml:space
="
preserve
">quæ ab r ducta eſt perpendicularis ad b d,
<
lb
/>
ipſam a e i ſecabit. </
s
>
<
s
xml:id
="
echoid-s1700
"
xml:space
="
preserve
">ſecet in punctis y g: </
s
>
<
s
xml:id
="
echoid-s1701
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1702
"
xml:space
="
preserve
">per y g ducan
<
lb
/>
tur ipſi b d æquidiſtantes p y q, o g n, quæ ſecent a t d in
<
lb
/>
f x. </
s
>
<
s
xml:id
="
echoid-s1703
"
xml:space
="
preserve
">ducantur poſtremo, & </
s
>
<
s
xml:id
="
echoid-s1704
"
xml:space
="
preserve
">p χ, o φ contingentes ſectionẽ
<
lb
/>
a p o l in punctis p o. </
s
>
<
s
xml:id
="
echoid-s1705
"
xml:space
="
preserve
">cũ
<
unsure
/>
ergo tres portiones ſint a p o l,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0070-03
"
xlink:href
="
note-0070-03a
"
xml:space
="
preserve
">M</
note
>
a e i, a t d, contentæ rectis lineis, & </
s
>
<
s
xml:id
="
echoid-s1706
"
xml:space
="
preserve
">rectangulorum cono-
<
lb
/>
rum ſectionibus; </
s
>
<
s
xml:id
="
echoid-s1707
"
xml:space
="
preserve
">rectæq, ſimiles, & </
s
>
<
s
xml:id
="
echoid-s1708
"
xml:space
="
preserve
">inæquales, quæ contin
<
lb
/>
gunt ſe ſe ſuper unamquanque baſim: </
s
>
<
s
xml:id
="
echoid-s1709
"
xml:space
="
preserve
">à puncto autem n
<
lb
/>
ſurſum ducta ſit n x g o; </
s
>
<
s
xml:id
="
echoid-s1710
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1711
"
xml:space
="
preserve
">à q ipſa q fy p: </
s
>
<
s
xml:id
="
echoid-s1712
"
xml:space
="
preserve
">habebit o g ad
<
lb
/>
g x proportionem compoſitam ex proportione, quam ha
<
lb
/>
bet i l ad l a; </
s
>
<
s
xml:id
="
echoid-s1713
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1714
"
xml:space
="
preserve
">ex proportione, quam a d habet ad d i.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1715
"
xml:space
="
preserve
">Sed i l ad l a
<
lb
/>
<
figure
xlink:label
="
fig-0070-01
"
xlink:href
="
fig-0070-01a
"
number
="
44
">
<
image
file
="
0070-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0070-01
"/>
</
figure
>
habet eandem,
<
lb
/>
quam duo ad
<
lb
/>
quinque. </
s
>
<
s
xml:id
="
echoid-s1716
"
xml:space
="
preserve
">ete-
<
lb
/>
nim c b ad b d
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0070-04
"
xlink:href
="
note-0070-04a
"
xml:space
="
preserve
">N</
note
>
eſt, ut ſex ad
<
lb
/>
quĩdecim; </
s
>
<
s
xml:id
="
echoid-s1717
"
xml:space
="
preserve
">hoc
<
lb
/>
eſt ut duo ad
<
lb
/>
quinque: </
s
>
<
s
xml:id
="
echoid-s1718
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1719
"
xml:space
="
preserve
">ut
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0070-05
"
xlink:href
="
note-0070-05a
"
xml:space
="
preserve
">O</
note
>
c b ad b d, ita
<
lb
/>
e b ad b a: </
s
>
<
s
xml:id
="
echoid-s1720
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1721
"
xml:space
="
preserve
">
<
lb
/>
d z ad d a. </
s
>
<
s
xml:id
="
echoid-s1722
"
xml:space
="
preserve
">ha-
<
lb
/>
rum autẽ d z,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0070-06
"
xlink:href
="
note-0070-06a
"
xml:space
="
preserve
">P</
note
>
d a duplæ ſunt
<
lb
/>
ipſæ l i, l a: </
s
>
<
s
xml:id
="
echoid-s1723
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1724
"
xml:space
="
preserve
">
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0070-07
"
xlink:href
="
note-0070-07a
"
xml:space
="
preserve
">Q</
note
>
a d ad d i eã pro
<
lb
/>
portionem habet, quam quinque ad unum. </
s
>
<
s
xml:id
="
echoid-s1725
"
xml:space
="
preserve
">ſed proportio
<
lb
/>
compoſita ex proportione, quam habet duo ad quinque;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1726
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1727
"
xml:space
="
preserve
">ex proportione, quam quinque ad unum; </
s
>
<
s
xml:id
="
echoid-s1728
"
xml:space
="
preserve
">eſt eadem,
<
lb
/>
quam habent duo ad unum: </
s
>
<
s
xml:id
="
echoid-s1729
"
xml:space
="
preserve
">duo autem ad unum duplam
<
lb
/>
proportionem habent. </
s
>
<
s
xml:id
="
echoid-s1730
"
xml:space
="
preserve
">dupla eſt igitur g b ipſius g x: </
s
>
<
s
xml:id
="
echoid-s1731
"
xml:space
="
preserve
">&</
s
>
<
s
xml:id
="
echoid-s1732
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>