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
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
191
40
192
193
41
194
195
42
196
197
43
198
199
44
200
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 213
>
page
|<
<
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div260
"
type
="
section
"
level
="
1
"
n
="
89
">
<
p
>
<
s
xml:id
="
echoid-s4353
"
xml:space
="
preserve
">
<
pb
file
="
0174
"
n
="
174
"
rhead
="
FED. COMMANDINI
"/>
per f planum baſibus æquidiſtans ducatur, ut ſit ſectio cir
<
lb
/>
culus, uel ellipſis circa diametrum f g. </
s
>
<
s
xml:id
="
echoid-s4354
"
xml:space
="
preserve
">Dico ſectionem a b
<
lb
/>
ad ſectionem f g eandem proportionem habere, quam f g
<
lb
/>
ad ipſam c d. </
s
>
<
s
xml:id
="
echoid-s4355
"
xml:space
="
preserve
">Simili enim ratione, qua ſupra, demonſtrabi-
<
lb
/>
tur quadratum a b ad quadratum f g ita eſſe, ut quadratũ
<
lb
/>
f g ad c d quadratum. </
s
>
<
s
xml:id
="
echoid-s4356
"
xml:space
="
preserve
">Sed circuli inter ſe eandem propor-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0174-01
"
xlink:href
="
note-0174-01a
"
xml:space
="
preserve
">2. duode
<
lb
/>
cimi</
note
>
tionem habent, quam diametrorum quadrata. </
s
>
<
s
xml:id
="
echoid-s4357
"
xml:space
="
preserve
">ellipſes au-
<
lb
/>
tem circa a b, f g, c d, quæ ſimiles ſunt, ut oſten dimus in cõ-
<
lb
/>
mentariis in principium libri Archimedis de conoidibus,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s4358
"
xml:space
="
preserve
">ſphæroidibus, eam habẽt proportionem, quam quadrar
<
lb
/>
ta diametrorum, quæ eiuſdem rationis ſunt, ex corollaio-
<
lb
/>
ſeptimæ propoſitionis eiuſdem li-
<
lb
/>
<
figure
xlink:label
="
fig-0174-01
"
xlink:href
="
fig-0174-01a
"
number
="
128
">
<
image
file
="
0174-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0174-01
"/>
</
figure
>
bri. </
s
>
<
s
xml:id
="
echoid-s4359
"
xml:space
="
preserve
">ellipſes enim nunc appello ip-
<
lb
/>
ſa ſpacia ellipſibus contenta. </
s
>
<
s
xml:id
="
echoid-s4360
"
xml:space
="
preserve
">ergo
<
lb
/>
circulus, uel ellipſis a b ad circulũ,
<
lb
/>
uel ellipſim f g eam proportionem
<
lb
/>
habet, quam circulus, uel ellipſis
<
lb
/>
f g ad circulum uel ellipſim c d.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4361
"
xml:space
="
preserve
">quod quidem facienduni propo-
<
lb
/>
ſuimus.</
s
>
<
s
xml:id
="
echoid-s4362
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div263
"
type
="
section
"
level
="
1
"
n
="
90
">
<
head
xml:id
="
echoid-head97
"
xml:space
="
preserve
">THEOREMA XX. PROPOSITIO XXV.</
head
>
<
p
>
<
s
xml:id
="
echoid-s4363
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Qvodlibet</
emph
>
fruſtum pyramidis, uel coni,
<
lb
/>
uel coni portionis ad pyramidem, uel conum, uel
<
lb
/>
coni portionem, cuius baſis eadem eſt, & </
s
>
<
s
xml:id
="
echoid-s4364
"
xml:space
="
preserve
">æqualis
<
lb
/>
altitudo, eandem proportionẽ habet, quam utræ
<
lb
/>
que baſes, maior, & </
s
>
<
s
xml:id
="
echoid-s4365
"
xml:space
="
preserve
">minor ſimul ſumptæ vnà cũ
<
lb
/>
ea, quæ inter ipſas ſit proportionalis, ad baſim ma
<
lb
/>
iorem.</
s
>
<
s
xml:id
="
echoid-s4366
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>