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
101
43
102
103
104
105
106
107
108
109
110
111
112
113
1
114
115
2
116
117
3
118
119
4
120
121
5
122
123
6
124
125
7
126
127
8
128
129
9
130
<
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-div137
"
type
="
section
"
level
="
1
"
n
="
43
">
<
pb
file
="
0076
"
n
="
76
"
rhead
="
ARCHIMEDIS
"/>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1916
"
xml:space
="
preserve
">Ex quibus perſpicuum eſt lineas omnes ſic ductas ab
<
lb
/>
ipſis ſectionibus in eandem proportionem ſecari. </
s
>
<
s
xml:id
="
echoid-s1917
"
xml:space
="
preserve
">eſt enim
<
lb
/>
diuidendo, conuertendoque cm ad mb, & </
s
>
<
s
xml:id
="
echoid-s1918
"
xml:space
="
preserve
">cf ad fb, ut
<
lb
/>
ce ad ea.</
s
>
<
s
xml:id
="
echoid-s1919
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div139
"
type
="
section
"
level
="
1
"
n
="
44
">
<
head
xml:id
="
echoid-head49
"
xml:space
="
preserve
">LEMMA III.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1920
"
xml:space
="
preserve
">Sed & </
s
>
<
s
xml:id
="
echoid-s1921
"
xml:space
="
preserve
">illud constare potest; </
s
>
<
s
xml:id
="
echoid-s1922
"
xml:space
="
preserve
">lineas, quæ in portioni-
<
lb
/>
bus eiuſmodi ſimilibus ita ducuntur, ut cú baſibus æqua-
<
lb
/>
les angulos contineant, ab ipſis ſimiles quoque portiones
<
lb
/>
abſcindere: </
s
>
<
s
xml:id
="
echoid-s1923
"
xml:space
="
preserve
">hoc eſt, ut in propoſita figura, portiones h b c,
<
lb
/>
m f c, quas lineæ c h, c m abſcindunt, etiam inter ſe
<
lb
/>
ſimiles eſſe.</
s
>
<
s
xml:id
="
echoid-s1924
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1925
"
xml:space
="
preserve
">
<
emph
style
="
sc
">D_ividantvr_</
emph
>
enim ch, cm bifariam in punctis p q: </
s
>
<
s
xml:id
="
echoid-s1926
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1927
"
xml:space
="
preserve
">per
<
lb
/>
ipſa ducantur lineæ r p s, t q u diametris æquidiſtantes. </
s
>
<
s
xml:id
="
echoid-s1928
"
xml:space
="
preserve
">erit portio-
<
lb
/>
nis b s c diameter p s, & </
s
>
<
s
xml:id
="
echoid-s1929
"
xml:space
="
preserve
">portionis m u c diameter q u. </
s
>
<
s
xml:id
="
echoid-s1930
"
xml:space
="
preserve
">Itaque fiat
<
lb
/>
ut quadratum c r ad quadratum c p, ita linea b n ad aliam lineam,
<
lb
/>
quæ ſit s x: </
s
>
<
s
xml:id
="
echoid-s1931
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1932
"
xml:space
="
preserve
">ut quadratum c t ad quadratum c q, ita fiat f o ad
<
lb
/>
u y. </
s
>
<
s
xml:id
="
echoid-s1933
"
xml:space
="
preserve
">iam exijs
<
lb
/>
<
figure
xlink:label
="
fig-0076-01
"
xlink:href
="
fig-0076-01a
"
number
="
47
">
<
image
file
="
0076-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0076-01
"/>
</
figure
>
quæ demóſtra
<
lb
/>
uimus in com-
<
lb
/>
mentarijs in
<
lb
/>
quartam pro-
<
lb
/>
poſitioné. </
s
>
<
s
xml:id
="
echoid-s1934
"
xml:space
="
preserve
">Ar-
<
lb
/>
chrmedis de co
<
lb
/>
noidibus, & </
s
>
<
s
xml:id
="
echoid-s1935
"
xml:space
="
preserve
">
<
lb
/>
ſphæroidibus,
<
lb
/>
patet quadra-
<
lb
/>
tum c p æqua-
<
lb
/>
le eſſe rectan-
<
lb
/>
gulo p s x:</
s
>
<
s
xml:id
="
echoid-s1936
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>