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
|<
<
(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
>