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
71
30
72
73
37
74
75
32
76
77
25
78
79
34
80
81
35
82
83
36
84
85
37
86
87
38
88
89
39
90
91
40
92
93
41
94
95
42
96
97
43
98
99
44
100
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 213
>
page
|<
<
(37)
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div123
"
type
="
section
"
level
="
1
"
n
="
41
">
<
pb
o
="
37
"
file
="
0073
"
n
="
73
"
rhead
="
DE IIS QVAE VEH. IN AQVA.
"/>
<
p
>
<
s
xml:id
="
echoid-s1813
"
xml:space
="
preserve
">Cum ergo tres portiones ſint a p o i, a ei, atd, con-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0073-01
"
xlink:href
="
note-0073-01a
"
xml:space
="
preserve
">M</
note
>
tentæ rectis lineis, & </
s
>
<
s
xml:id
="
echoid-s1814
"
xml:space
="
preserve
">rectãgulorum conorum ſectionibus;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1815
"
xml:space
="
preserve
">rectæq;</
s
>
<
s
xml:id
="
echoid-s1816
"
xml:space
="
preserve
">, ſimiles, & </
s
>
<
s
xml:id
="
echoid-s1817
"
xml:space
="
preserve
">inæquales, quæ contingunt ſe ſe ſuper
<
lb
/>
unam quamque baſim.</
s
>
<
s
xml:id
="
echoid-s1818
"
xml:space
="
preserve
">] _Poſt ea uerba, ſuper unamquanque_
<
lb
/>
_baſim, in trans latione aliqua deſiderari uidentur. </
s
>
<
s
xml:id
="
echoid-s1819
"
xml:space
="
preserve
">Ad borum autem_
<
lb
/>
_demonſtrationem non nulla præmittere oportet, quæ etiam ad alia,_
<
lb
/>
_quæ ſequuntur, neceſſaria erunt._</
s
>
<
s
xml:id
="
echoid-s1820
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div135
"
type
="
section
"
level
="
1
"
n
="
42
">
<
head
xml:id
="
echoid-head47
"
xml:space
="
preserve
">LEMMA I.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1821
"
xml:space
="
preserve
">Sit recta linea a b, quam ſecent duæ lineæ inter ſeſe
<
lb
/>
æquidiſtantes a c, d e, ita ut quam proportionem ba-
<
lb
/>
bet a b ad b d, eandern haheat a c ad de. </
s
>
<
s
xml:id
="
echoid-s1822
"
xml:space
="
preserve
">Dico li-
<
lb
/>
neam, quæ c b puncta coniungit, etiam per ipſum e
<
lb
/>
tr anſire.</
s
>
<
s
xml:id
="
echoid-s1823
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1824
"
xml:space
="
preserve
">SI enim fieri poteſt, non tranſeat pere, ſed nel ſupra, uel infra.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1825
"
xml:space
="
preserve
">tranſeat primum infra, ut per f. </
s
>
<
s
xml:id
="
echoid-s1826
"
xml:space
="
preserve
">erunt triangula a b c, d b f inter ſe
<
lb
/>
ſimilia. </
s
>
<
s
xml:id
="
echoid-s1827
"
xml:space
="
preserve
">quare ut a b ad b d, ita a c ad d f. </
s
>
<
s
xml:id
="
echoid-s1828
"
xml:space
="
preserve
">ſed ut a b ad bd, ita
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0073-02
"
xlink:href
="
note-0073-02a
"
xml:space
="
preserve
">4. ſexti.</
note
>
erat a c ad d e. </
s
>
<
s
xml:id
="
echoid-s1829
"
xml:space
="
preserve
">ergo d f ipſi d e æqualis erit, uidelicet pars to-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0073-03
"
xlink:href
="
note-0073-03a
"
xml:space
="
preserve
">9. quinti.</
note
>
ti, quod eſt
<
lb
/>
<
figure
xlink:label
="
fig-0073-01
"
xlink:href
="
fig-0073-01a
"
number
="
45
">
<
image
file
="
0073-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0073-01
"/>
</
figure
>
cbſurdum.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1830
"
xml:space
="
preserve
">Idem ab-
<
lb
/>
ſurdum ſe
<
lb
/>
quetur, ſi
<
lb
/>
linea c b
<
lb
/>
ſupra e pú
<
lb
/>
ctum tran
<
lb
/>
ſire pona-
<
lb
/>
tur. </
s
>
<
s
xml:id
="
echoid-s1831
"
xml:space
="
preserve
">quare
<
lb
/>
c b etiam
<
lb
/>
per e ne-
<
lb
/>
ceſſario tranſibit. </
s
>
<
s
xml:id
="
echoid-s1832
"
xml:space
="
preserve
">quod oportebat demonſtrare.</
s
>
<
s
xml:id
="
echoid-s1833
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>