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 handwritten notes
<
1 - 8
[out of range]
>
<
1 - 8
[out of range]
>
page
|<
<
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div89
"
type
="
section
"
level
="
1
"
n
="
35
">
<
p
>
<
s
xml:id
="
echoid-s1287
"
xml:space
="
preserve
">
<
pb
file
="
0056
"
n
="
56
"
rhead
="
ARCHIMEDIS
"/>
tur ex parte 1. </
s
>
<
s
xml:id
="
echoid-s1288
"
xml:space
="
preserve
">Quod ſi n o non ſecuerit ipſam ω k,
<
lb
/>
eadem nihilominus demonſtrabuntur.</
s
>
<
s
xml:id
="
echoid-s1289
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div91
"
type
="
section
"
level
="
1
"
n
="
36
">
<
head
xml:id
="
echoid-head41
"
xml:space
="
preserve
">PROPOSITIO VIII.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1290
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Recta</
emph
>
portio conoidis rectanguli, quando
<
lb
/>
axem habuerit maiorem quidem, quàm ſeſqui-
<
lb
/>
alterum eius, quæ uſque ad axem; </
s
>
<
s
xml:id
="
echoid-s1291
"
xml:space
="
preserve
">minorem ue-
<
lb
/>
ro, quàm ut ad eam, quæ uſque ad axem propor-
<
lb
/>
tionem habeat, quam quindecim ad quatuor: </
s
>
<
s
xml:id
="
echoid-s1292
"
xml:space
="
preserve
">ſi
<
lb
/>
in grauitate ad humidum habeat proportionem
<
lb
/>
minorem ea, quam quadratum, quod fit ab exceſ
<
lb
/>
ſu, quo axis maior eſt, quàm ſeſquialter eius, quæ
<
lb
/>
uſque ad axem, habet ad quadratum, quod ab
<
lb
/>
axe: </
s
>
<
s
xml:id
="
echoid-s1293
"
xml:space
="
preserve
">demiſſa in humidum, ita ut baſis ipſius humi
<
lb
/>
dum non contingat; </
s
>
<
s
xml:id
="
echoid-s1294
"
xml:space
="
preserve
">neque in rectum reſtitue-
<
lb
/>
tur, neque manebit inclinata, niſi quando axis
<
lb
/>
cum ſuperficie humidi angulum fecerit æqualẽ
<
lb
/>
ei, de quo infra dicetur.</
s
>
<
s
xml:id
="
echoid-s1295
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1296
"
xml:space
="
preserve
">SIT portio qualis dicta eſt; </
s
>
<
s
xml:id
="
echoid-s1297
"
xml:space
="
preserve
">ſitque b d æqualis axi: </
s
>
<
s
xml:id
="
echoid-s1298
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1299
"
xml:space
="
preserve
">
<
lb
/>
b k quidem dupla ipſius _K_ d: </
s
>
<
s
xml:id
="
echoid-s1300
"
xml:space
="
preserve
">r _K_ uero æqualis ei, quæ uſ-
<
lb
/>
que ad axem: </
s
>
<
s
xml:id
="
echoid-s1301
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1302
"
xml:space
="
preserve
">ſit c b ſeſquialtera b r. </
s
>
<
s
xml:id
="
echoid-s1303
"
xml:space
="
preserve
">erit & </
s
>
<
s
xml:id
="
echoid-s1304
"
xml:space
="
preserve
">c d ipſius
<
lb
/>
_k_ r ſeſquialtera. </
s
>
<
s
xml:id
="
echoid-s1305
"
xml:space
="
preserve
">Quam uero portionem habet portio ad
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0056-01
"
xlink:href
="
note-0056-01a
"
xml:space
="
preserve
">A</
note
>
humidum in grauitate, habeat quadratum f q ad quadra-
<
lb
/>
tum d b: </
s
>
<
s
xml:id
="
echoid-s1306
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1307
"
xml:space
="
preserve
">ſit f dupla ipſius q. </
s
>
<
s
xml:id
="
echoid-s1308
"
xml:space
="
preserve
">perſpicuum igitur eſt f q
<
lb
/>
ad d b proportionem minorem habere ea, quam habet
<
lb
/>
c b ad b d. </
s
>
<
s
xml:id
="
echoid-s1309
"
xml:space
="
preserve
">eſt enim c b exceſſus, quo axis maior eſt, quàm
<
lb
/>
ſeſquialter eins, quæ uſque ad axem: </
s
>
<
s
xml:id
="
echoid-s1310
"
xml:space
="
preserve
">quare f q minor eſt
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0056-02
"
xlink:href
="
note-0056-02a
"
xml:space
="
preserve
">B</
note
>
</
s
>
</
p
>
</
div
>
</
text
>
</
echo
>