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
|<
<
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div91
"
type
="
section
"
level
="
1
"
n
="
36
">
<
p
>
<
s
xml:id
="
echoid-s1341
"
xml:space
="
preserve
">
<
pb
file
="
0058
"
n
="
58
"
rhead
="
ARCHIMEDIS
"/>
& </
s
>
<
s
xml:id
="
echoid-s1342
"
xml:space
="
preserve
">quam proportionem habet quadratum e ψ ad quadra-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0058-01
"
xlink:href
="
note-0058-01a
"
xml:space
="
preserve
">G</
note
>
tum ψ b, eandem habet dimidium lineæ _k_ r ad lineã ψ b.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1343
"
xml:space
="
preserve
">quare maiorem babet proportionem _k_ r ad i y, quàm di-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0058-02
"
xlink:href
="
note-0058-02a
"
xml:space
="
preserve
">13. quin-
<
lb
/>
ti.</
note
>
midium k r ad ψ b: </
s
>
<
s
xml:id
="
echoid-s1344
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1345
"
xml:space
="
preserve
">idcirco i y minor eſt, quàm dupla
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0058-03
"
xlink:href
="
note-0058-03a
"
xml:space
="
preserve
">H</
note
>
ψ b. </
s
>
<
s
xml:id
="
echoid-s1346
"
xml:space
="
preserve
">eſt autem ipſius o i dupla. </
s
>
<
s
xml:id
="
echoid-s1347
"
xml:space
="
preserve
">ergo o i minor eſt, quàm
<
lb
/>
ψ b: </
s
>
<
s
xml:id
="
echoid-s1348
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1349
"
xml:space
="
preserve
">i ω maior, quàm ψ r. </
s
>
<
s
xml:id
="
echoid-s1350
"
xml:space
="
preserve
">ſed ψ r eſt æqualis ipſi f. </
s
>
<
s
xml:id
="
echoid-s1351
"
xml:space
="
preserve
">maior
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0058-04
"
xlink:href
="
note-0058-04a
"
xml:space
="
preserve
">K</
note
>
igitur eſt i ω, quàm f. </
s
>
<
s
xml:id
="
echoid-s1352
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1353
"
xml:space
="
preserve
">quoniam portio ad humidum in
<
lb
/>
grauitate eam ponitur habere proportionem, quam qua-
<
lb
/>
dratum f q ad quadratum b d: </
s
>
<
s
xml:id
="
echoid-s1354
"
xml:space
="
preserve
">quam uero proportionem
<
lb
/>
habet portio ad humidum in grauitate, eam habet pars ip
<
lb
/>
ſius demerſa ad totam portionem: </
s
>
<
s
xml:id
="
echoid-s1355
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1356
"
xml:space
="
preserve
">quam pars ipſius de-
<
lb
/>
merſa habet ad totam, eandem habet quadratum p m ad
<
lb
/>
quadratnm o n: </
s
>
<
s
xml:id
="
echoid-s1357
"
xml:space
="
preserve
">ſequitur quadratum p m ad quadratum
<
lb
/>
o n eam proportionem habere, quam quadratum f q ad
<
lb
/>
b d quadratum.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1358
"
xml:space
="
preserve
">
<
figure
xlink:label
="
fig-0058-01
"
xlink:href
="
fig-0058-01a
"
number
="
37
">
<
image
file
="
0058-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0058-01
"/>
</
figure
>
atque ideo ſ q æ-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0058-05
"
xlink:href
="
note-0058-05a
"
xml:space
="
preserve
">L</
note
>
qualis eſt ipſi p m.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1359
"
xml:space
="
preserve
">demõſtrata eſt au
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0058-06
"
xlink:href
="
note-0058-06a
"
xml:space
="
preserve
">M</
note
>
tem p h maior,
<
lb
/>
quàm f. </
s
>
<
s
xml:id
="
echoid-s1360
"
xml:space
="
preserve
">cõſtat igi
<
lb
/>
tur p m minorem
<
lb
/>
eſſe, quàm ſeſqui-
<
lb
/>
alterã ipſius p h:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1361
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1362
"
xml:space
="
preserve
">idcirco p h ma
<
lb
/>
iorem, quàm du-
<
lb
/>
plam h m. </
s
>
<
s
xml:id
="
echoid-s1363
"
xml:space
="
preserve
">Sit p z
<
lb
/>
ipſius z m dupla. </
s
>
<
s
xml:id
="
echoid-s1364
"
xml:space
="
preserve
">
<
lb
/>
erit t quidem cẽ-
<
lb
/>
trũ grauitatis to-
<
lb
/>
tius ſolidi: </
s
>
<
s
xml:id
="
echoid-s1365
"
xml:space
="
preserve
">centrũ
<
lb
/>
eius partis, quæ intra humidum, punctumz: </
s
>
<
s
xml:id
="
echoid-s1366
"
xml:space
="
preserve
">reliquæ uero
<
lb
/>
partis centrum erit in linea z t producta uſque ad g. </
s
>
<
s
xml:id
="
echoid-s1367
"
xml:space
="
preserve
">Eodẽ
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0058-07
"
xlink:href
="
note-0058-07a
"
xml:space
="
preserve
">N</
note
>
modo demonſtrabitur linea th perpendicularis ad ſuper-
<
lb
/>
ficiem humidi. </
s
>
<
s
xml:id
="
echoid-s1368
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1369
"
xml:space
="
preserve
">portio demerſa in humido ſeretur </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>