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
|<
<
(44)
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-s4986
"
xml:space
="
preserve
">
<
pb
o
="
44
"
file
="
0199
"
n
="
199
"
rhead
="
DE CENTRO GRAVIT. SOLID.
"/>
relinquetur p e ipſi n χ æqualis. </
s
>
<
s
xml:id
="
echoid-s4987
"
xml:space
="
preserve
">cum autem b e ſit dupla
<
lb
/>
e d, & </
s
>
<
s
xml:id
="
echoid-s4988
"
xml:space
="
preserve
">o p dupla p n, hoc eſt ipſius e χ, & </
s
>
<
s
xml:id
="
echoid-s4989
"
xml:space
="
preserve
">reliquum, uideli-
<
lb
/>
cet b o unà cum p e ipſius reliqui χ d duplnm erit. </
s
>
<
s
xml:id
="
echoid-s4990
"
xml:space
="
preserve
">eſtque
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0199-01
"
xlink:href
="
note-0199-01a
"
xml:space
="
preserve
">19. quinti</
note
>
b o dupla ζ d. </
s
>
<
s
xml:id
="
echoid-s4991
"
xml:space
="
preserve
">ergo p e, hoc eſt n χ ipſius χ ρ dupla. </
s
>
<
s
xml:id
="
echoid-s4992
"
xml:space
="
preserve
">ſed d n
<
lb
/>
dupla eſt n ζ. </
s
>
<
s
xml:id
="
echoid-s4993
"
xml:space
="
preserve
">reliqua igitur d χ dupla reliquæ χ n. </
s
>
<
s
xml:id
="
echoid-s4994
"
xml:space
="
preserve
">ſunt au-
<
lb
/>
tem d χ, p n inter ſe æquales: </
s
>
<
s
xml:id
="
echoid-s4995
"
xml:space
="
preserve
">itemq; </
s
>
<
s
xml:id
="
echoid-s4996
"
xml:space
="
preserve
">æquales χ n, p e. </
s
>
<
s
xml:id
="
echoid-s4997
"
xml:space
="
preserve
">qua-
<
lb
/>
re conſtat n p ipſius p e duplam eſſe. </
s
>
<
s
xml:id
="
echoid-s4998
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4999
"
xml:space
="
preserve
">idcirco p e ipſi e n
<
lb
/>
æqualem. </
s
>
<
s
xml:id
="
echoid-s5000
"
xml:space
="
preserve
">Rurſus cum ſit μ ν dupla o ν, & </
s
>
<
s
xml:id
="
echoid-s5001
"
xml:space
="
preserve
">μ σ dupla σ ν; </
s
>
<
s
xml:id
="
echoid-s5002
"
xml:space
="
preserve
">erit
<
lb
/>
etiam reliqua ν σ o dupla. </
s
>
<
s
xml:id
="
echoid-s5003
"
xml:space
="
preserve
">Eadem quoque ratione
<
lb
/>
cõcludetur π υ dupla υ m. </
s
>
<
s
xml:id
="
echoid-s5004
"
xml:space
="
preserve
">ergo ut ν σ ad σ O, ita π υ ad υ m:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s5005
"
xml:space
="
preserve
">componendoq;</
s
>
<
s
xml:id
="
echoid-s5006
"
xml:space
="
preserve
">, & </
s
>
<
s
xml:id
="
echoid-s5007
"
xml:space
="
preserve
">permutando, ut υ o ad π m, ita o σ ad
<
lb
/>
m υ & </
s
>
<
s
xml:id
="
echoid-s5008
"
xml:space
="
preserve
">ſunt æquales ν o, π m. </
s
>
<
s
xml:id
="
echoid-s5009
"
xml:space
="
preserve
">quare & </
s
>
<
s
xml:id
="
echoid-s5010
"
xml:space
="
preserve
">o σ, m υ æquales. </
s
>
<
s
xml:id
="
echoid-s5011
"
xml:space
="
preserve
">præ
<
lb
/>
terea σ π dupla eſt π τ, & </
s
>
<
s
xml:id
="
echoid-s5012
"
xml:space
="
preserve
">ν π ipſius π m. </
s
>
<
s
xml:id
="
echoid-s5013
"
xml:space
="
preserve
">reliqua igitur σ ν re
<
lb
/>
liquæ m τ dupla. </
s
>
<
s
xml:id
="
echoid-s5014
"
xml:space
="
preserve
">atque erat ν σ dupla σ o. </
s
>
<
s
xml:id
="
echoid-s5015
"
xml:space
="
preserve
">ergo m τ, σ o æ-
<
lb
/>
quales ſunt: </
s
>
<
s
xml:id
="
echoid-s5016
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s5017
"
xml:space
="
preserve
">ita æquales m υ, n φ. </
s
>
<
s
xml:id
="
echoid-s5018
"
xml:space
="
preserve
">at o σ, eſt æqualis
<
lb
/>
m υ. </
s
>
<
s
xml:id
="
echoid-s5019
"
xml:space
="
preserve
">Sequitur igitur, ut omnes o σ, m τ, m υ, n φ in-
<
lb
/>
ter ſe ſint æquales. </
s
>
<
s
xml:id
="
echoid-s5020
"
xml:space
="
preserve
">Sed ut ρ π ad π τ, hoc eſt ut 3 ad 2, ita n d
<
lb
/>
ad d χ: </
s
>
<
s
xml:id
="
echoid-s5021
"
xml:space
="
preserve
">permutãdoq; </
s
>
<
s
xml:id
="
echoid-s5022
"
xml:space
="
preserve
">ut ρ π ad n d, ita π τ ad d χ. </
s
>
<
s
xml:id
="
echoid-s5023
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s5024
"
xml:space
="
preserve
">ſũt æqua
<
lb
/>
les ζ π, n d. </
s
>
<
s
xml:id
="
echoid-s5025
"
xml:space
="
preserve
">ergo d χ, hoc eſt n p, & </
s
>
<
s
xml:id
="
echoid-s5026
"
xml:space
="
preserve
">π τ æquales. </
s
>
<
s
xml:id
="
echoid-s5027
"
xml:space
="
preserve
">Sed etiam æ-
<
lb
/>
quales n π, π m. </
s
>
<
s
xml:id
="
echoid-s5028
"
xml:space
="
preserve
">reliqua igitur π p reliquæ m τ, hoc eſt ipſi
<
lb
/>
n φ æqualis erit. </
s
>
<
s
xml:id
="
echoid-s5029
"
xml:space
="
preserve
">quare dempta p π ex p e, & </
s
>
<
s
xml:id
="
echoid-s5030
"
xml:space
="
preserve
">φ n dempta ex
<
lb
/>
n e, relinquitur p e æqualis e φ. </
s
>
<
s
xml:id
="
echoid-s5031
"
xml:space
="
preserve
">Itaque π, ρ centra figurarũ
<
lb
/>
ſecundo loco deſcriptarum a primis centris p n æquali in-
<
lb
/>
teruallo recedunt. </
s
>
<
s
xml:id
="
echoid-s5032
"
xml:space
="
preserve
">quòd ſi rurſus aliæ figuræ deſcribantur,
<
lb
/>
eodem modo demonſtrabimus earum centra æqualiter ab
<
lb
/>
his recedere, & </
s
>
<
s
xml:id
="
echoid-s5033
"
xml:space
="
preserve
">ad portionis conoidis centrum propius ad
<
lb
/>
moueri. </
s
>
<
s
xml:id
="
echoid-s5034
"
xml:space
="
preserve
">Ex quibus conſtat lineam π φ à centro grauitatis
<
lb
/>
portionis diuidi in partes æquales. </
s
>
<
s
xml:id
="
echoid-s5035
"
xml:space
="
preserve
">Si enim fieri poteſt, non
<
lb
/>
ſit centrum in puncto e, quod eſt lineæ π φ medium: </
s
>
<
s
xml:id
="
echoid-s5036
"
xml:space
="
preserve
">ſed in
<
lb
/>
ψ: </
s
>
<
s
xml:id
="
echoid-s5037
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s5038
"
xml:space
="
preserve
">ipſi π ψ æqualis fiat φ ω. </
s
>
<
s
xml:id
="
echoid-s5039
"
xml:space
="
preserve
">Cum igitur in portione ſolida
<
lb
/>
quædam figura inſcribi posſit, ita ut linea, quæ inter cen-
<
lb
/>
trum grauitatis portionis, & </
s
>
<
s
xml:id
="
echoid-s5040
"
xml:space
="
preserve
">inſcriptæ figuræ interiicitur,
<
lb
/>
qualibet linea propoſita ſit minor, quod proxime demon-
<
lb
/>
ſtrauimus: </
s
>
<
s
xml:id
="
echoid-s5041
"
xml:space
="
preserve
">perueniet tandem φ centrum inſcriptæ </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>