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 concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 213
>
Scan
Original
151
20
152
153
21
154
155
22
156
157
23
158
159
24
160
161
25
162
163
26
164
165
27
166
167
28
168
169
29
170
171
30
172
173
31
174
175
32
176
177
33
178
179
34
180
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 213
>
page
|<
<
(25)
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div94
"
type
="
section
"
level
="
1
"
n
="
37
">
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1428
"
xml:space
="
preserve
">
<
pb
o
="
25
"
file
="
0061
"
n
="
61
"
rhead
="
DE IIS QVAE VEH. IN AQVA.
"/>
b ψ dupla ſit ψ d, erit d b ipſius b ψ ſeſquialtera. </
s
>
<
s
xml:id
="
echoid-s1429
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1430
"
xml:space
="
preserve
">quoniam e b ſeſ
<
lb
/>
quialtera est b r, ſequitur reliquam c d ipſius ψ r, boc est eius, quæ
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0061-01
"
xlink:href
="
note-0061-01a
"
xml:space
="
preserve
">12. quinti</
note
>
uſque ad axem ſeſquialteram eſſe. </
s
>
<
s
xml:id
="
echoid-s1431
"
xml:space
="
preserve
">quare b c erit exceſſus, quo axis
<
lb
/>
maior est, quàm ſeſquialter eius, quæ uſque ad axem.</
s
>
<
s
xml:id
="
echoid-s1432
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1433
"
xml:space
="
preserve
">_Quare f q minor éſtipſa b c.</
s
>
<
s
xml:id
="
echoid-s1434
"
xml:space
="
preserve
">]_ Nam cum portio ad bumi-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0061-02
"
xlink:href
="
note-0061-02a
"
xml:space
="
preserve
">B</
note
>
dum in grauitate proportionem habeat eandem, quàm quadratum
<
lb
/>
f q ad quadratum d b: </
s
>
<
s
xml:id
="
echoid-s1435
"
xml:space
="
preserve
">habeatq, minorem proportionem, quàm qua
<
lb
/>
dratum factum ab exceſſu, quo axis maior eſt, quàm ſeſquialter eius,
<
lb
/>
quæ uſque ad axem, ad quadratum ab axe; </
s
>
<
s
xml:id
="
echoid-s1436
"
xml:space
="
preserve
">boc eſt minorem, quàm
<
lb
/>
quadratum c b ad quadratum b d: </
s
>
<
s
xml:id
="
echoid-s1437
"
xml:space
="
preserve
">ponitur enim linea b d æqualis
<
lb
/>
axi: </
s
>
<
s
xml:id
="
echoid-s1438
"
xml:space
="
preserve
">quadratum f q ad quadratum d b proportionem minorem ha-
<
lb
/>
bebit, quàm quadratum c b ad idem b d quadratum. </
s
>
<
s
xml:id
="
echoid-s1439
"
xml:space
="
preserve
">ergo quadra-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0061-03
"
xlink:href
="
note-0061-03a
"
xml:space
="
preserve
">8. quinti.</
note
>
tum f q minus erit quadrato c b: </
s
>
<
s
xml:id
="
echoid-s1440
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1441
"
xml:space
="
preserve
">propterea linea f q ipſa b c
<
lb
/>
minor.</
s
>
<
s
xml:id
="
echoid-s1442
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1443
"
xml:space
="
preserve
">_Etidcirco f minor ipſa b r.</
s
>
<
s
xml:id
="
echoid-s1444
"
xml:space
="
preserve
">]_ Quoniam enim c b ſeſquial-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0061-04
"
xlink:href
="
note-0061-04a
"
xml:space
="
preserve
">C</
note
>
tera eſt b r, & </
s
>
<
s
xml:id
="
echoid-s1445
"
xml:space
="
preserve
">f q ipſius f ſeſquialtera: </
s
>
<
s
xml:id
="
echoid-s1446
"
xml:space
="
preserve
">estq; </
s
>
<
s
xml:id
="
echoid-s1447
"
xml:space
="
preserve
">f q minor b c; </
s
>
<
s
xml:id
="
echoid-s1448
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1449
"
xml:space
="
preserve
">f
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0061-05
"
xlink:href
="
note-0061-05a
"
xml:space
="
preserve
">14. quin-
<
lb
/>
ti.</
note
>
ipſa b r minor erit.</
s
>
<
s
xml:id
="
echoid-s1450
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1451
"
xml:space
="
preserve
">_Itaque quoniam ponitur axis portionis cum ſuperficie_
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0061-06
"
xlink:href
="
note-0061-06a
"
xml:space
="
preserve
">D</
note
>
_humidi facere angulum maiorem angulo b: </
s
>
<
s
xml:id
="
echoid-s1452
"
xml:space
="
preserve
">erit angulus_
<
lb
/>
_p y i angulo b maior.</
s
>
<
s
xml:id
="
echoid-s1453
"
xml:space
="
preserve
">]_ Nam cum linea p y ſuperficiei bumidi
<
lb
/>
æ quidistet; </
s
>
<
s
xml:id
="
echoid-s1454
"
xml:space
="
preserve
">uidelicet ipſi x s: </
s
>
<
s
xml:id
="
echoid-s1455
"
xml:space
="
preserve
">angulus p y i æqualis erit angulo, qui
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0061-07
"
xlink:href
="
note-0061-07a
"
xml:space
="
preserve
">29. primi</
note
>
diametro portionis n o, & </
s
>
<
s
xml:id
="
echoid-s1456
"
xml:space
="
preserve
">linea x s continetur. </
s
>
<
s
xml:id
="
echoid-s1457
"
xml:space
="
preserve
">quare & </
s
>
<
s
xml:id
="
echoid-s1458
"
xml:space
="
preserve
">angulo
<
lb
/>
b maior erit.</
s
>
<
s
xml:id
="
echoid-s1459
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1460
"
xml:space
="
preserve
">_Maiorem igitur proportionem habet quadratum p i ad_
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0061-08
"
xlink:href
="
note-0061-08a
"
xml:space
="
preserve
">E</
note
>
_quadratum i y, quàm quadratum e ψ ad ψ b quadratu.</
s
>
<
s
xml:id
="
echoid-s1461
"
xml:space
="
preserve
">]_
<
lb
/>
Deſcribantur ſeorſum triangula p i y, e ψ b. </
s
>
<
s
xml:id
="
echoid-s1462
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1463
"
xml:space
="
preserve
">cum angulus p y i
<
lb
/>
maior ſit angulo e b ψ, ad lineam i y, atque ad punctum y in ea da-
<
lb
/>
tum fiat angulus u y i æqualis angulo e b ψ. </
s
>
<
s
xml:id
="
echoid-s1464
"
xml:space
="
preserve
">est autem angulus ad
<
lb
/>
i rectus æqualis recto ad ψ. </
s
>
<
s
xml:id
="
echoid-s1465
"
xml:space
="
preserve
">reliquus igitur y u i reliquo b c ψ est
<
lb
/>
æqualis. </
s
>
<
s
xml:id
="
echoid-s1466
"
xml:space
="
preserve
">quare linea u i ad lineam i y eandem proportionem ha-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0061-09
"
xlink:href
="
note-0061-09a
"
xml:space
="
preserve
">4. ſexti.</
note
>
bet, quam linea e ψ ad ψ b. </
s
>
<
s
xml:id
="
echoid-s1467
"
xml:space
="
preserve
">Sed linea p i, quæ maior est ipſa u i ad
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0061-10
"
xlink:href
="
note-0061-10a
"
xml:space
="
preserve
">8. quinti.</
note
>
lineam in maiorem habet proportionem quam u i ad eandem. </
s
>
<
s
xml:id
="
echoid-s1468
"
xml:space
="
preserve
">ergo
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0061-11
"
xlink:href
="
note-0061-11a
"
xml:space
="
preserve
">13. quin-
<
lb
/>
ti.</
note
>
p i ad i y maiorem proportionem habebit, quàm e ψ ad ψ b: </
s
>
<
s
xml:id
="
echoid-s1469
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1470
"
xml:space
="
preserve
">
<
lb
/>
propterea quadratum p i ad quadratum i y maiorem habebit, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>