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 figures
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 151
[out of range]
>
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 151
[out of range]
>
page
|<
<
(37)
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div157
"
type
="
section
"
level
="
1
"
n
="
51
">
<
pb
o
="
37
"
file
="
0085
"
n
="
85
"
rhead
="
DE IIS QVAE VEH. IN AQVA.
"/>
</
div
>
<
div
xml:id
="
echoid-div158
"
type
="
section
"
level
="
1
"
n
="
52
">
<
head
xml:id
="
echoid-head57
"
xml:space
="
preserve
">DEMONSTRATIO SECVNDAE PARTIS.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2176
"
xml:space
="
preserve
">ITAQVE primum habeat portio ad humidum in
<
lb
/>
grauitate proportionem quidem maiorem, quàm qua dra
<
lb
/>
tum x o ad quadratum b d; </
s
>
<
s
xml:id
="
echoid-s2177
"
xml:space
="
preserve
">minorem uero, quàm quadra
<
lb
/>
tum, quod fit ab exceſſu, quo axis eſt maior, quàm ſeſquial-
<
lb
/>
ter eius, quæ uſque ad axem, ad quadratum b d: </
s
>
<
s
xml:id
="
echoid-s2178
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2179
"
xml:space
="
preserve
">quam
<
lb
/>
proportionem habet portio ad humidum in grauitate, eã
<
lb
/>
habeat quadratum, quod fit à linea ψ ad quadratum b d:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2180
"
xml:space
="
preserve
">erit ψ maior quidem, quàm x o, minor uero, quàm exceſ-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0085-01
"
xlink:href
="
note-0085-01a
"
xml:space
="
preserve
">C</
note
>
ſus, quo axis eſt maior, quàm ſeſquialter eius, quæ uſque ad
<
lb
/>
axem. </
s
>
<
s
xml:id
="
echoid-s2181
"
xml:space
="
preserve
">aptetur quædam recta linea m n conicis ſectioni-
<
lb
/>
bus a m q l,
<
lb
/>
<
figure
xlink:label
="
fig-0085-01
"
xlink:href
="
fig-0085-01a
"
number
="
52
">
<
image
file
="
0085-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0085-01
"/>
</
figure
>
a x d interiecta,
<
lb
/>
ac media, quæ li
<
lb
/>
neæ ψ ſit æqua-
<
lb
/>
lis; </
s
>
<
s
xml:id
="
echoid-s2182
"
xml:space
="
preserve
">ſecetq; </
s
>
<
s
xml:id
="
echoid-s2183
"
xml:space
="
preserve
">reli-
<
lb
/>
quã coni ſectio
<
lb
/>
nem in pun cto
<
lb
/>
h; </
s
>
<
s
xml:id
="
echoid-s2184
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2185
"
xml:space
="
preserve
">rectam li-
<
lb
/>
neam r g in u.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2186
"
xml:space
="
preserve
">demõſtrabitur
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0085-02
"
xlink:href
="
note-0085-02a
"
xml:space
="
preserve
">D</
note
>
m h dupla ip-
<
lb
/>
ſius h n, ſicuti
<
lb
/>
demonſtratum
<
lb
/>
eſt o g ipſius g x
<
lb
/>
duplam eſſe. </
s
>
<
s
xml:id
="
echoid-s2187
"
xml:space
="
preserve
">à
<
lb
/>
puncto autẽ m
<
lb
/>
ducatur m y contingens ſectionem a m q l in m: </
s
>
<
s
xml:id
="
echoid-s2188
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2189
"
xml:space
="
preserve
">m c a d
<
lb
/>
b d perpendicularis. </
s
>
<
s
xml:id
="
echoid-s2190
"
xml:space
="
preserve
">poſtea ducta a n, & </
s
>
<
s
xml:id
="
echoid-s2191
"
xml:space
="
preserve
">producta ad q li
<
lb
/>
neæ a n, n q inter ſe æquales erunt. </
s
>
<
s
xml:id
="
echoid-s2192
"
xml:space
="
preserve
">quoniã enim in ſimi-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0085-03
"
xlink:href
="
note-0085-03a
"
xml:space
="
preserve
">E</
note
>
libus portionibus a m q l, a x d ductæ ſunt à baſibus ad
<
lb
/>
portiones lineæ a q, a n, quæ æquales angulos continent
<
lb
/>
cum ipſis baſibus, eandem proportionem habebit q a ad
<
lb
/>
an, quam la ad a d. </
s
>
<
s
xml:id
="
echoid-s2193
"
xml:space
="
preserve
">æqualis eſt ergo a n ipſi n q; </
s
>
<
s
xml:id
="
echoid-s2194
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2195
"
xml:space
="
preserve
">a q
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0085-04
"
xlink:href
="
note-0085-04a
"
xml:space
="
preserve
">F</
note
>
</
s
>
</
p
>
</
div
>
</
text
>
</
echo
>