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
181
35
182
183
36
184
185
37
186
187
38
188
189
39
190
191
40
192
193
41
194
195
42
196
197
43
198
199
44
200
201
45
202
203
46
204
205
47
206
207
208
209
210
<
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-div146
"
type
="
section
"
level
="
1
"
n
="
47
">
<
pb
file
="
0082
"
n
="
82
"
rhead
="
ARCHIMEDIS
"/>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s2098
"
xml:space
="
preserve
">_Etenim c b ad b d eſt ut ſex ad quindecim.</
s
>
<
s
xml:id
="
echoid-s2099
"
xml:space
="
preserve
">]_ Poſuimus
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0082-01
"
xlink:href
="
note-0082-01a
"
xml:space
="
preserve
">N</
note
>
enim b K duplam eſſe ipſius K d. </
s
>
<
s
xml:id
="
echoid-s2100
"
xml:space
="
preserve
">quare componendo b d ad k d erit,
<
lb
/>
ut tria ad unum; </
s
>
<
s
xml:id
="
echoid-s2101
"
xml:space
="
preserve
">hoc eſt ut quindecim ad quinque. </
s
>
<
s
xml:id
="
echoid-s2102
"
xml:space
="
preserve
">ſed b d ad K c
<
lb
/>
erat ut quídecim
<
lb
/>
<
figure
xlink:label
="
fig-0082-01
"
xlink:href
="
fig-0082-01a
"
number
="
51
">
<
image
file
="
0082-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0082-01
"/>
</
figure
>
ad quatuor. </
s
>
<
s
xml:id
="
echoid-s2103
"
xml:space
="
preserve
">ergo
<
lb
/>
b d ad d c, ut quin
<
lb
/>
decim ad nouem:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2104
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2105
"
xml:space
="
preserve
">per conuerſio
<
lb
/>
nem rationis, con
<
lb
/>
uertendôq; </
s
>
<
s
xml:id
="
echoid-s2106
"
xml:space
="
preserve
">c b ad
<
lb
/>
b d, ut ſex ad quí
<
lb
/>
decim.</
s
>
<
s
xml:id
="
echoid-s2107
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2108
"
xml:space
="
preserve
">Etut c b ad
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0082-02
"
xlink:href
="
note-0082-02a
"
xml:space
="
preserve
">O</
note
>
b d, ita e b ad
<
lb
/>
b a, & </
s
>
<
s
xml:id
="
echoid-s2109
"
xml:space
="
preserve
">d z ad
<
lb
/>
d a.</
s
>
<
s
xml:id
="
echoid-s2110
"
xml:space
="
preserve
">] _Nam cum_
<
lb
/>
_triangula c b e,_
<
lb
/>
_d b a ſint ſimilia,_
<
lb
/>
_erit ut c b ad b e,_
<
lb
/>
_ita d b, ad b a & </
s
>
<
s
xml:id
="
echoid-s2111
"
xml:space
="
preserve
">permutando, ut c b ad b d; </
s
>
<
s
xml:id
="
echoid-s2112
"
xml:space
="
preserve
">ita e b ad b a. </
s
>
<
s
xml:id
="
echoid-s2113
"
xml:space
="
preserve
">Rurſus_
<
lb
/>
_ut b c ad c e, ita b d ad d a: </
s
>
<
s
xml:id
="
echoid-s2114
"
xml:space
="
preserve
">permutandôq; </
s
>
<
s
xml:id
="
echoid-s2115
"
xml:space
="
preserve
">ut c b ad b d, ita c e, hoc_
<
lb
/>
_eſt d z ei æqualis ad d a._</
s
>
<
s
xml:id
="
echoid-s2116
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2117
"
xml:space
="
preserve
">Harum autem d z d a duplæ ſuntipſæ l i, la.</
s
>
<
s
xml:id
="
echoid-s2118
"
xml:space
="
preserve
">] _Lineam_
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0082-03
"
xlink:href
="
note-0082-03a
"
xml:space
="
preserve
">P</
note
>
_quidem l a duplam eſſe ipſius d a, cum b d ſit portionis diameter,_
<
lb
/>
_manifeſte conſtat. </
s
>
<
s
xml:id
="
echoid-s2119
"
xml:space
="
preserve
">At uero l i ipſius d z dupla hoc pacto demon-_
<
lb
/>
_ſtrabitur. </
s
>
<
s
xml:id
="
echoid-s2120
"
xml:space
="
preserve
">Quoniam enim z d ad d a eſt, ut duo ad quinque; </
s
>
<
s
xml:id
="
echoid-s2121
"
xml:space
="
preserve
">erit có_
<
lb
/>
_uertendo, diuidendôq; </
s
>
<
s
xml:id
="
echoid-s2122
"
xml:space
="
preserve
">a z, hoc eſt i z ad z d, ut tria ad duo: </
s
>
<
s
xml:id
="
echoid-s2123
"
xml:space
="
preserve
">&_</
s
>
<
s
xml:id
="
echoid-s2124
"
xml:space
="
preserve
">
<
lb
/>
_rurſus diuidendo i d ad d z, ut
<
gap
/>
m ad duo. </
s
>
<
s
xml:id
="
echoid-s2125
"
xml:space
="
preserve
">erat autem z d ad_
<
lb
/>
_d a, hoc eſt ad d l, ut duo ad quinque. </
s
>
<
s
xml:id
="
echoid-s2126
"
xml:space
="
preserve
">ergo ex æquali, conuertendóq;_
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2127
"
xml:space
="
preserve
">_l d ad d i, ut quinque ad unum: </
s
>
<
s
xml:id
="
echoid-s2128
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2129
"
xml:space
="
preserve
">per conuerſionem rationis d l ad_
<
lb
/>
_li, ut quinque ad quatuor. </
s
>
<
s
xml:id
="
echoid-s2130
"
xml:space
="
preserve
">ſed d z ad d l erat, ut duo ad quinque._ </
s
>
<
s
xml:id
="
echoid-s2131
"
xml:space
="
preserve
">
<
lb
/>
_ergo rurſus ex æquali d z ad l i, ut duo ad quatuor. </
s
>
<
s
xml:id
="
echoid-s2132
"
xml:space
="
preserve
">dupla eſt igitur_
<
lb
/>
_l i ipſius d z. </
s
>
<
s
xml:id
="
echoid-s2133
"
xml:space
="
preserve
">quod demonſtrandum fuerat._</
s
>
<
s
xml:id
="
echoid-s2134
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2135
"
xml:space
="
preserve
">Et a d ad d i eam proportionem habet, quã quinque
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0082-04
"
xlink:href
="
note-0082-04a
"
xml:space
="
preserve
">Q</
note
>
</
s
>
</
p
>
</
div
>
</
text
>
</
echo
>