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
91
40
92
93
41
94
95
42
96
97
43
98
99
44
100
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
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 213
>
page
|<
<
(25)
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div139
"
type
="
section
"
level
="
1
"
n
="
44
">
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1936
"
xml:space
="
preserve
">
<
pb
o
="
25
"
file
="
0077
"
n
="
77
"
rhead
="
DE IIS QVAE VEH. IN AQVA.
"/>
itêmq; </
s
>
<
s
xml:id
="
echoid-s1937
"
xml:space
="
preserve
">quadratum c q æquale rectangulo q u y, hoc eſt ſectionum
<
lb
/>
h s c, m u c lineas s x, u y, eas eſſe, iuxta quas poſſunt, quæ à ſectio-
<
lb
/>
ne ad diametrum ducuntur. </
s
>
<
s
xml:id
="
echoid-s1938
"
xml:space
="
preserve
">ſed cú triangula c p r, c q t ſimilia ſint,
<
lb
/>
habebit c r ad c p eandem proportionem, quam c t ad c q: </
s
>
<
s
xml:id
="
echoid-s1939
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1940
"
xml:space
="
preserve
">id-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0077-01
"
xlink:href
="
note-0077-01a
"
xml:space
="
preserve
">22. fexti</
note
>
circo quadratum c r ad quadratum c p eandem habebit, quam
<
lb
/>
quadratum c t ad quadratum c q. </
s
>
<
s
xml:id
="
echoid-s1941
"
xml:space
="
preserve
">ergo & </
s
>
<
s
xml:id
="
echoid-s1942
"
xml:space
="
preserve
">linea b n, ad lineam
<
lb
/>
ſ x ita erit, ut linea fo ad ipſam u y. </
s
>
<
s
xml:id
="
echoid-s1943
"
xml:space
="
preserve
">erat autem b c ad c m, ut a c
<
lb
/>
ad c e. </
s
>
<
s
xml:id
="
echoid-s1944
"
xml:space
="
preserve
">quare & </
s
>
<
s
xml:id
="
echoid-s1945
"
xml:space
="
preserve
">earum dimidiæ c p ad c q, ut a d ad e g: </
s
>
<
s
xml:id
="
echoid-s1946
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1947
"
xml:space
="
preserve
">
<
lb
/>
permutando c p ad a d, ut c q ad e g. </
s
>
<
s
xml:id
="
echoid-s1948
"
xml:space
="
preserve
">Sed oſtenſum est a d ad b n
<
lb
/>
ita eſſe, ut e g ad f o: </
s
>
<
s
xml:id
="
echoid-s1949
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1950
"
xml:space
="
preserve
">b n ad s x, ut f o ad u y. </
s
>
<
s
xml:id
="
echoid-s1951
"
xml:space
="
preserve
">ergo ex
<
lb
/>
æquali c p ad ſ x erit, ut c q ad u y. </
s
>
<
s
xml:id
="
echoid-s1952
"
xml:space
="
preserve
">Quòd cum quadratú c p æqua
<
lb
/>
le ſit rectangulo p s x & </
s
>
<
s
xml:id
="
echoid-s1953
"
xml:space
="
preserve
">quadratum c q rectangulo q u y, erunt
<
lb
/>
tres lineæ ſ p, p c, ſ x proportionales; </
s
>
<
s
xml:id
="
echoid-s1954
"
xml:space
="
preserve
">itemq; </
s
>
<
s
xml:id
="
echoid-s1955
"
xml:space
="
preserve
">proportionales ip-
<
lb
/>
ſæ u q, q c, u y. </
s
>
<
s
xml:id
="
echoid-s1956
"
xml:space
="
preserve
">quare & </
s
>
<
s
xml:id
="
echoid-s1957
"
xml:space
="
preserve
">ſ p ad p c, ut u q ad q c: </
s
>
<
s
xml:id
="
echoid-s1958
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1959
"
xml:space
="
preserve
">ut p c ad
<
lb
/>
c h, ita q c ad c m. </
s
>
<
s
xml:id
="
echoid-s1960
"
xml:space
="
preserve
">ex æquali igitur ut portionis h ſ c diameter ſ p
<
lb
/>
ad eius baſim c h, ita portionis m u s diameter u q ad baſim c m.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1961
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1962
"
xml:space
="
preserve
">anguli, quos diametri cum baſibus continent, ſunt æquales, quòd
<
lb
/>
lineæ ſ p, u q ſibi ipſis æquidiſtent, ergo & </
s
>
<
s
xml:id
="
echoid-s1963
"
xml:space
="
preserve
">portiones h ſ c, m u c
<
lb
/>
inter ſe ſimiles erunt. </
s
>
<
s
xml:id
="
echoid-s1964
"
xml:space
="
preserve
">id quod demonstrandum proponebatur.</
s
>
<
s
xml:id
="
echoid-s1965
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div141
"
type
="
section
"
level
="
1
"
n
="
45
">
<
head
xml:id
="
echoid-head50
"
xml:space
="
preserve
">LEMMA IIII.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1966
"
xml:space
="
preserve
">Sint duæ lineæ a b, c d, quæ ſecentur in punctis e f,
<
lb
/>
ita ut quam proportionem habet a e ad e b, habeat c f
<
lb
/>
ad f d: </
s
>
<
s
xml:id
="
echoid-s1967
"
xml:space
="
preserve
">rurſus ſecentur in aliis duobus punctis g h; </
s
>
<
s
xml:id
="
echoid-s1968
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1969
"
xml:space
="
preserve
">
<
lb
/>
habeat c h ad h d eandem proportionem, quam a g ad
<
lb
/>
g b. </
s
>
<
s
xml:id
="
echoid-s1970
"
xml:space
="
preserve
">Dico c f ad f h ita eſſe, ut a e ad e g.</
s
>
<
s
xml:id
="
echoid-s1971
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1972
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Q_voniam_</
emph
>
enim ut a e ad e b, ita c f ad f d, erit componen
<
lb
/>
do ut a b ad e b, ita c d ad f d. </
s
>
<
s
xml:id
="
echoid-s1973
"
xml:space
="
preserve
">Rurſus cum ſit ut a g ad g b, ita
<
lb
/>
c h ad h d; </
s
>
<
s
xml:id
="
echoid-s1974
"
xml:space
="
preserve
">componendo, conuertendoq; </
s
>
<
s
xml:id
="
echoid-s1975
"
xml:space
="
preserve
">ut g b ad a b, ita erit h d
<
lb
/>
ad c d. </
s
>
<
s
xml:id
="
echoid-s1976
"
xml:space
="
preserve
">ergo ex æquali, conuertendoq; </
s
>
<
s
xml:id
="
echoid-s1977
"
xml:space
="
preserve
">ut e b ad g b, ita f d ad h d:</
s
>
<
s
xml:id
="
echoid-s1978
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>