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
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
181
35
182
183
36
184
185
37
186
187
38
188
189
39
190
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 213
>
page
|<
<
(38)
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div158
"
type
="
section
"
level
="
1
"
n
="
52
">
<
p
>
<
s
xml:id
="
echoid-s2222
"
xml:space
="
preserve
">
<
pb
o
="
38
"
file
="
0087
"
n
="
87
"
rhead
="
DE IIS QVAE VEH. IN AQVA.
"/>
æqualibus, & </
s
>
<
s
xml:id
="
echoid-s2223
"
xml:space
="
preserve
">ſimilibus, a p o l, a m q l ab extremitati-
<
lb
/>
bus baſium ductæ ſint a o, a q ita, ut portiones ablatæ
<
lb
/>
faciant cum diametris angulos æquales; </
s
>
<
s
xml:id
="
echoid-s2224
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2225
"
xml:space
="
preserve
">anguli, qui
<
lb
/>
ad y g: </
s
>
<
s
xml:id
="
echoid-s2226
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2227
"
xml:space
="
preserve
">lineæ y b, g b, & </
s
>
<
s
xml:id
="
echoid-s2228
"
xml:space
="
preserve
">b c, b s inter ſe æquales erunt.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2229
"
xml:space
="
preserve
">quare & </
s
>
<
s
xml:id
="
echoid-s2230
"
xml:space
="
preserve
">ipſæ c r, s r: </
s
>
<
s
xml:id
="
echoid-s2231
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2232
"
xml:space
="
preserve
">m u, p z: </
s
>
<
s
xml:id
="
echoid-s2233
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2234
"
xml:space
="
preserve
">u n, z t. </
s
>
<
s
xml:id
="
echoid-s2235
"
xml:space
="
preserve
">Quo-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0087-01
"
xlink:href
="
note-0087-01a
"
xml:space
="
preserve
">L</
note
>
niam igitur m u minor eſt, quàm dupla u n; </
s
>
<
s
xml:id
="
echoid-s2236
"
xml:space
="
preserve
">conſtat p z ip-
<
lb
/>
ſius z t minorem eſſe, quàm duplam. </
s
>
<
s
xml:id
="
echoid-s2237
"
xml:space
="
preserve
">Sit p α dupla ipſius
<
lb
/>
ω t: </
s
>
<
s
xml:id
="
echoid-s2238
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2239
"
xml:space
="
preserve
">iuncta α k ad e producatur. </
s
>
<
s
xml:id
="
echoid-s2240
"
xml:space
="
preserve
">ergo totius quidem por
<
lb
/>
tionis centrum grauitatis erit puntum κ; </
s
>
<
s
xml:id
="
echoid-s2241
"
xml:space
="
preserve
">partis eius, quæ
<
lb
/>
in humido eſt, centrum ω; </
s
>
<
s
xml:id
="
echoid-s2242
"
xml:space
="
preserve
">eius uero, quæ extra humidum
<
lb
/>
in linea k e, quod ſit e. </
s
>
<
s
xml:id
="
echoid-s2243
"
xml:space
="
preserve
">Sed linea k z perpendicularis erit
<
lb
/>
ad ſuperficiem humidi. </
s
>
<
s
xml:id
="
echoid-s2244
"
xml:space
="
preserve
">quare & </
s
>
<
s
xml:id
="
echoid-s2245
"
xml:space
="
preserve
">lineæ quæ per puncta e,
<
lb
/>
ω, æ quidiſtantes ipſi κ z ducuntur. </
s
>
<
s
xml:id
="
echoid-s2246
"
xml:space
="
preserve
">non ergo manebit por-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0087-02
"
xlink:href
="
note-0087-02a
"
xml:space
="
preserve
">M</
note
>
tio, ſed reuoluetur ita, ut baſis ipſius ſuperficiem humidi
<
lb
/>
nullo modo contingat: </
s
>
<
s
xml:id
="
echoid-s2247
"
xml:space
="
preserve
">quoniã nuncin uno puncto contin
<
lb
/>
gens, ſurſum fertur ex parte a. </
s
>
<
s
xml:id
="
echoid-s2248
"
xml:space
="
preserve
">perſpicuum eſt igitur por-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0087-03
"
xlink:href
="
note-0087-03a
"
xml:space
="
preserve
">N</
note
>
tionem conſiſt ere ita, ut axis cum ſuperſicie humidi faciat
<
lb
/>
angulum maiorem angulo χ.</
s
>
<
s
xml:id
="
echoid-s2249
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div160
"
type
="
section
"
level
="
1
"
n
="
53
">
<
head
xml:id
="
echoid-head58
"
xml:space
="
preserve
">COMMENTARIVS.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2250
"
xml:space
="
preserve
">Siportio ad humidum in grauitate minorẽ proportio-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0087-04
"
xlink:href
="
note-0087-04a
"
xml:space
="
preserve
">A</
note
>
nem habeat; </
s
>
<
s
xml:id
="
echoid-s2251
"
xml:space
="
preserve
">quàm quadratum s b ad quadratum b d; </
s
>
<
s
xml:id
="
echoid-s2252
"
xml:space
="
preserve
">ma-
<
lb
/>
iorem uero, quàm quadratum x o ad b d quadratum.</
s
>
<
s
xml:id
="
echoid-s2253
"
xml:space
="
preserve
">] _Hæc_
<
lb
/>
_eſt ſecunda pars propoſitionis, quam aliæ deinceps, postea ipſarum_
<
lb
/>
_demonstrationes eodem ordine ſequuntur_.</
s
>
<
s
xml:id
="
echoid-s2254
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2255
"
xml:space
="
preserve
">SI portio ad humidum in grauitate maiorem quidem
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0087-05
"
xlink:href
="
note-0087-05a
"
xml:space
="
preserve
">B</
note
>
proportionẽ habeat, quàm quadratũ f p ad quadratũb d.</
s
>
<
s
xml:id
="
echoid-s2256
"
xml:space
="
preserve
">]
<
lb
/>
_Hãc quartá parté nos reſtituimus, quæ ĩ trãſlatione deſiderabatur_.</
s
>
<
s
xml:id
="
echoid-s2257
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2258
"
xml:space
="
preserve
">Erit ψ maior quidem, quàm x o, minor uero, quàm ex-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0087-06
"
xlink:href
="
note-0087-06a
"
xml:space
="
preserve
">C</
note
>
ceſſus, quo axis eſt maior, quam ſeſquialter eius, quæ uſque
<
lb
/>
ad axem,] _Sequitur illud ex decima quinti libri elementornm_.</
s
>
<
s
xml:id
="
echoid-s2259
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2260
"
xml:space
="
preserve
">Demonſtrabitur m h duplaipſius h n, ſicuti demonſtra
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0087-07
"
xlink:href
="
note-0087-07a
"
xml:space
="
preserve
">D</
note
>
tũ eſt o gipſius g x duplam eſſe.</
s
>
<
s
xml:id
="
echoid-s2261
"
xml:space
="
preserve
">] _Vt in prima parte huius, &_</
s
>
<
s
xml:id
="
echoid-s2262
"
xml:space
="
preserve
">
<
lb
/>
_exijs, quæ nos proxime in ipſam conſcripſimus_.</
s
>
<
s
xml:id
="
echoid-s2263
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2264
"
xml:space
="
preserve
">Quoniam enim in ſimilibus portionibus a p o l, a x d,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0087-08
"
xlink:href
="
note-0087-08a
"
xml:space
="
preserve
">E</
note
>
</
s
>
</
p
>
</
div
>
</
text
>
</
echo
>