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
1
2
3
4
5
6
7
8
9
10
11
12
13
1
14
15
2
16
17
3
18
19
4
20
21
5
22
23
6
24
25
7
26
27
8
28
29
9
30
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 213
>
page
|<
<
(45)
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div281
"
type
="
section
"
level
="
1
"
n
="
94
">
<
p
>
<
s
xml:id
="
echoid-s5041
"
xml:space
="
preserve
">
<
pb
o
="
45
"
file
="
0201
"
n
="
201
"
rhead
="
DE CENTRO GRAVIT. SOLID.
"/>
ad punctum ω. </
s
>
<
s
xml:id
="
echoid-s5042
"
xml:space
="
preserve
">Sed quoniam π circum ſcripta itidem alia
<
lb
/>
figura æquali interuallo ad portionis centrum accedit, ubi
<
lb
/>
primum φ applieuerit ſe ad ω, & </
s
>
<
s
xml:id
="
echoid-s5043
"
xml:space
="
preserve
">π ad punctũ ψ, hoc eſt ad
<
lb
/>
portionis centrum ſe applicabit. </
s
>
<
s
xml:id
="
echoid-s5044
"
xml:space
="
preserve
">quod fieri nullo modo
<
lb
/>
poſſe perſpicuum eſt. </
s
>
<
s
xml:id
="
echoid-s5045
"
xml:space
="
preserve
">non aliter idem abſurdum ſequetur,
<
lb
/>
ſi ponamus centrum portionis recedere à medio ad par-
<
lb
/>
tes ω; </
s
>
<
s
xml:id
="
echoid-s5046
"
xml:space
="
preserve
">eſſet enim aliquando centrum figuræ inſcriptæ idem
<
lb
/>
quod portionis centrũ. </
s
>
<
s
xml:id
="
echoid-s5047
"
xml:space
="
preserve
">ergo punctum e centrum erit gra
<
lb
/>
uitatis portionis a b c. </
s
>
<
s
xml:id
="
echoid-s5048
"
xml:space
="
preserve
">quod demonſtrare oportebat.</
s
>
<
s
xml:id
="
echoid-s5049
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s5050
"
xml:space
="
preserve
">Quod autem ſupra demõſtratum eſt in portione conoi-
<
lb
/>
dis recta per figuras, quæ ex cylindris æqualem altitudi-
<
lb
/>
dinem habentibus conſtant, idem ſimiliter demonſtrabi-
<
lb
/>
mus per figuras ex cylindri portionibus conſtantes in ea
<
lb
/>
portione, quæ plano non ad axem recto abſcinditur. </
s
>
<
s
xml:id
="
echoid-s5051
"
xml:space
="
preserve
">ut
<
lb
/>
enim tradidimus in commentariis in undecimam propoſi
<
lb
/>
tionem libri Archimedis de conoidibus & </
s
>
<
s
xml:id
="
echoid-s5052
"
xml:space
="
preserve
">ſphæroidibus.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s5053
"
xml:space
="
preserve
">portiones cylindri, quæ æquali ſunt altitudine eam inter ſe
<
lb
/>
ſe proportionem habent, quam ipſarum baſes; </
s
>
<
s
xml:id
="
echoid-s5054
"
xml:space
="
preserve
">baſes autẽ
<
lb
/>
quæ ſunt ellipſes ſimiles eandem proportionem habere,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0201-01
"
xlink:href
="
note-0201-01a
"
xml:space
="
preserve
">corol. 15
<
lb
/>
deconoi-
<
lb
/>
dibus &
<
lb
/>
ſphæroi-
<
lb
/>
dibus.</
note
>
quam quadrata diametrorum eiuſdem rationis, ex corol-
<
lb
/>
lario ſeptimæ propoſitionis libri de conoidibus, & </
s
>
<
s
xml:id
="
echoid-s5055
"
xml:space
="
preserve
">ſphæ-
<
lb
/>
roidibus, manifeſte apparet.</
s
>
<
s
xml:id
="
echoid-s5056
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div284
"
type
="
section
"
level
="
1
"
n
="
95
">
<
head
xml:id
="
echoid-head102
"
xml:space
="
preserve
">THEOREMA XXIIII. PROPOSITIO XXX.</
head
>
<
p
>
<
s
xml:id
="
echoid-s5057
"
xml:space
="
preserve
">SI à portione conoidis rectanguli alia portio
<
lb
/>
abſcindatur, plano baſi æquidiſtante; </
s
>
<
s
xml:id
="
echoid-s5058
"
xml:space
="
preserve
">habebit
<
lb
/>
portio tota ad eam, quæ abſciſſa eſt, duplam pro
<
lb
/>
portio nem eius, quæ eſt baſis maioris portionis
<
lb
/>
ad baſi m minoris, uel quæ axis maioris ad axem
<
lb
/>
minoris.</
s
>
<
s
xml:id
="
echoid-s5059
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>