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
Table of Notes
<
1 - 8
[out of range]
>
[Note]
Page: 44
[Note]
Page: 44
[Note]
Page: 45
[Note]
Page: 45
[Note]
Page: 45
[Note]
Page: 45
[Note]
Page: 46
[Note]
Page: 46
[Note]
Page: 47
[Note]
Page: 47
[Note]
Page: 48
[Note]
Page: 48
[Note]
Page: 49
[Note]
Page: 49
[Note]
Page: 49
[Note]
Page: 52
[Note]
Page: 52
[Note]
Page: 52
[Note]
Page: 52
[Note]
Page: 53
[Note]
Page: 53
[Note]
Page: 55
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 57
[Note]
Page: 57
[Note]
Page: 57
[Note]
Page: 57
[Note]
Page: 58
[Note]
Page: 58
<
1 - 8
[out of range]
>
page
|<
<
(32)
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div137
"
type
="
section
"
level
="
1
"
n
="
43
">
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1859
"
xml:space
="
preserve
">
<
pb
o
="
32
"
file
="
0075
"
n
="
75
"
rhead
="
DE IIS QVAE VEH. IN AQVA.
"/>
ad ſectionem e f g ex parte e linea l m, eidem a c baſi æquidi-
<
lb
/>
stans. </
s
>
<
s
xml:id
="
echoid-s1860
"
xml:space
="
preserve
">Sit autem ſectionis a b c, linea b n iuxta quam poſſunt, quæ
<
lb
/>
à ſectione ducuntur: </
s
>
<
s
xml:id
="
echoid-s1861
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1862
"
xml:space
="
preserve
">ſectionis e f c ſit ipſa f o. </
s
>
<
s
xml:id
="
echoid-s1863
"
xml:space
="
preserve
">quoniam igi-
<
lb
/>
tur triangula c d b, c f g ſimilia ſunt, erit ut b c ad c f, ita d c
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0075-01
"
xlink:href
="
note-0075-01a
"
xml:space
="
preserve
">4. ſexti.</
note
>
ad c g; </
s
>
<
s
xml:id
="
echoid-s1864
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1865
"
xml:space
="
preserve
">b d ad f g. </
s
>
<
s
xml:id
="
echoid-s1866
"
xml:space
="
preserve
">rurſus quoniam triangula c k b, c l f etiã
<
lb
/>
inter ſe ſunt ſimilia, ut b c ad c f, boc eſt ut b d ad f g, ita erit k c
<
lb
/>
ad c l; </
s
>
<
s
xml:id
="
echoid-s1867
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1868
"
xml:space
="
preserve
">b K ad f l. </
s
>
<
s
xml:id
="
echoid-s1869
"
xml:space
="
preserve
">quare K c ad c l, & </
s
>
<
s
xml:id
="
echoid-s1870
"
xml:space
="
preserve
">b k ad f l ſunt ut d c
<
lb
/>
ad c g: </
s
>
<
s
xml:id
="
echoid-s1871
"
xml:space
="
preserve
">hoc eſt ut earum duplæ a c ad c e. </
s
>
<
s
xml:id
="
echoid-s1872
"
xml:space
="
preserve
">ſed ut b d ad f g, ita d c
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0075-02
"
xlink:href
="
note-0075-02a
"
xml:space
="
preserve
">15. quin-
<
lb
/>
ti.</
note
>
ad c g; </
s
>
<
s
xml:id
="
echoid-s1873
"
xml:space
="
preserve
">hoc ẽ a d ad e g: </
s
>
<
s
xml:id
="
echoid-s1874
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1875
"
xml:space
="
preserve
">permutãdo ut b d ad a d, ita f g ad e g.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1876
"
xml:space
="
preserve
">quadratum autem a d æquale eſt rectangulo d b n ex undecima pri
<
lb
/>
mi conicorum. </
s
>
<
s
xml:id
="
echoid-s1877
"
xml:space
="
preserve
">ergo tres lineæ b d, a d, b n inter ſe ſunt proportio
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0075-03
"
xlink:href
="
note-0075-03a
"
xml:space
="
preserve
">17. ſexti.</
note
>
nales. </
s
>
<
s
xml:id
="
echoid-s1878
"
xml:space
="
preserve
">eadem quoque ratione cum quadratum e g æquale ſit rectan
<
lb
/>
gulo g f o, tres aliæ lineæ f g, e g, f o, deinceps proportionales
<
lb
/>
erũt. </
s
>
<
s
xml:id
="
echoid-s1879
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1880
"
xml:space
="
preserve
">ut b d ad, a d, ita f g ad e g. </
s
>
<
s
xml:id
="
echoid-s1881
"
xml:space
="
preserve
">quare ut a d ad b n, ita e g
<
lb
/>
ad f o. </
s
>
<
s
xml:id
="
echoid-s1882
"
xml:space
="
preserve
">ex æquali igitur, ut d b ad b n, ita g f ad f o: </
s
>
<
s
xml:id
="
echoid-s1883
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1884
"
xml:space
="
preserve
">permu-
<
lb
/>
tando ut d b ad g f, ita b n ad f o. </
s
>
<
s
xml:id
="
echoid-s1885
"
xml:space
="
preserve
">ut autem d b ad g f, ita b k
<
lb
/>
ad f l. </
s
>
<
s
xml:id
="
echoid-s1886
"
xml:space
="
preserve
">ergo b k ad f l, ut b n ad f o: </
s
>
<
s
xml:id
="
echoid-s1887
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1888
"
xml:space
="
preserve
">permutando, ut b k ad
<
lb
/>
bn, ita f l ad f o. </
s
>
<
s
xml:id
="
echoid-s1889
"
xml:space
="
preserve
">Rurſus quoniá quadratú h K æquale eſt rectan
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0075-04
"
xlink:href
="
note-0075-04a
"
xml:space
="
preserve
">11. primi
<
lb
/>
conicorũ</
note
>
gulo k b n: </
s
>
<
s
xml:id
="
echoid-s1890
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1891
"
xml:space
="
preserve
">quadratum m l rectangulo l f o æquale: </
s
>
<
s
xml:id
="
echoid-s1892
"
xml:space
="
preserve
">erunt tres
<
lb
/>
lineæ b k, k h, b n proportionales: </
s
>
<
s
xml:id
="
echoid-s1893
"
xml:space
="
preserve
">itémq; </
s
>
<
s
xml:id
="
echoid-s1894
"
xml:space
="
preserve
">proportionales inter ſe
<
lb
/>
f l, l m, f o. </
s
>
<
s
xml:id
="
echoid-s1895
"
xml:space
="
preserve
">quare ut linea b K ad lineam b n, ita quadratum b K
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0075-05
"
xlink:href
="
note-0075-05a
"
xml:space
="
preserve
">cor. 20. ſe
<
lb
/>
xti.</
note
>
ad quadratum h k: </
s
>
<
s
xml:id
="
echoid-s1896
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1897
"
xml:space
="
preserve
">ut linea f l ad ipſam f o, ita quadratú f l
<
lb
/>
ad quadratum l m. </
s
>
<
s
xml:id
="
echoid-s1898
"
xml:space
="
preserve
">Itaque quoniam, ut b K ad b n, ita eſt f l ad
<
lb
/>
f o; </
s
>
<
s
xml:id
="
echoid-s1899
"
xml:space
="
preserve
">erit ut quadratum b K ad quadratum k h, ita quadratum f l
<
lb
/>
ad l m quadratum. </
s
>
<
s
xml:id
="
echoid-s1900
"
xml:space
="
preserve
">ergo ut linea b k, ad lineam K h, ita linea f l
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0075-06
"
xlink:href
="
note-0075-06a
"
xml:space
="
preserve
">22. ſexti</
note
>
ad ipsã lm: </
s
>
<
s
xml:id
="
echoid-s1901
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1902
"
xml:space
="
preserve
">permutãdo ut b k ad f l, ita k h ad lm. </
s
>
<
s
xml:id
="
echoid-s1903
"
xml:space
="
preserve
">ſed b k ad
<
lb
/>
f l erat ut k c ad c l. </
s
>
<
s
xml:id
="
echoid-s1904
"
xml:space
="
preserve
">ergo k h ad lm, ut K c ad c l. </
s
>
<
s
xml:id
="
echoid-s1905
"
xml:space
="
preserve
">quare ex eo
<
lb
/>
dem lemmate patet lineam h c, & </
s
>
<
s
xml:id
="
echoid-s1906
"
xml:space
="
preserve
">per m punctum tranſire. </
s
>
<
s
xml:id
="
echoid-s1907
"
xml:space
="
preserve
">ut igi-
<
lb
/>
tur K c ad c l: </
s
>
<
s
xml:id
="
echoid-s1908
"
xml:space
="
preserve
">hoc eſt ut a c ad c e, ita h c ad c m; </
s
>
<
s
xml:id
="
echoid-s1909
"
xml:space
="
preserve
">hoc eſt ad eam
<
lb
/>
ipſius partem, quæ inter c, & </
s
>
<
s
xml:id
="
echoid-s1910
"
xml:space
="
preserve
">e g c ſectionem interyeitur. </
s
>
<
s
xml:id
="
echoid-s1911
"
xml:space
="
preserve
">ſimiliter
<
lb
/>
demonſtrabimus idem contingere in alijs lineis, quæ à puncto c ad
<
lb
/>
a b c ſectionem perducuntur. </
s
>
<
s
xml:id
="
echoid-s1912
"
xml:space
="
preserve
">At uero b c ad e f eandern propor-
<
lb
/>
tionem habere, liquido apparet; </
s
>
<
s
xml:id
="
echoid-s1913
"
xml:space
="
preserve
">nam b c ad c f, eſt ut d c ad c g;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1914
"
xml:space
="
preserve
">uidelicet ut earum duplæ, a c ad c e.</
s
>
<
s
xml:id
="
echoid-s1915
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>