Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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0125
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DE CENTRO GRAVIT. SOLID.
"/>
metrum habens e d. </
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<
s
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xml:space
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">Quoniam igitur circuli uel ellipſis
<
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a e c b grauitatis centrum eſt in diametro b e, & </
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<
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xml:space
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nis a e c centrum in linea e d: </
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<
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echoid-s3172
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xml:space
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">reliquæ portionis, uidelicet
<
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/>
a b c centrum grauitatis in ipſa b d conſiſtat neceſſe eſt, ex
<
lb
/>
octaua propoſitione eiuſdem.</
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<
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">THEOREMA V. PROPOSITIO V.</
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<
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">SI priſma ſecetur plano oppoſitis planis æqui
<
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diſtante, ſectio erit figura æqualis & </
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<
s
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echoid-s3175
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xml:space
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">ſimilis ei,
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quæ eſt oppoſitorum planorum, centrum graui
<
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tatis in axe habens.</
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<
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</
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<
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<
s
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xml:space
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">Sit priſma, in quo plana oppoſita ſint triangula a b c,
<
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d e f; </
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<
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">axis g h: </
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<
s
xml:id
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xml:space
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">& </
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>
<
s
xml:id
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xml:space
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">ſecetur plano iam dictis planis æquidiſtã
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te; </
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>
<
s
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xml:space
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">quod faciat ſectionem
<
emph
style
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>
l m; </
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<
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xml:space
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">& </
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<
s
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xml:space
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">axi in pũcto n occurrat.
<
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</
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<
s
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xml:space
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">Dico _k_ l m triangulum æquale eſſe, & </
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<
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="
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xml:space
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">ſimile triangulis a b c
<
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d e f; </
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>
<
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xml:space
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">atque eius grauitatis centrum eſſe punctum n. </
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<
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xml:space
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">Quo-
<
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/>
niam enim plana a b c
<
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/>
<
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xlink:label
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fig-0125-01
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xlink:href
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fig-0125-01a
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number
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82
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0125-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0125-01
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K l m æquidiſtantia ſecã
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cimi.</
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tur a plano a e; </
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<
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">rectæ li-
<
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neæ a b, K l, quæ ſunt ip
<
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ſorum cõmunes ſectio-
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nes inter ſe ſe æquidi-
<
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ſtant. </
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<
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xml:space
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">Sed æquidiſtant
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a d, b e; </
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<
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xml:space
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">cum a e ſit para
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lelogrammum, ex priſ-
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matis diffinitione. </
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<
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<
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& </
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<
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xml:space
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">al parallelogrammũ
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erit; </
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<
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xml:space
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">& </
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<
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">propterea linea
<
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<
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note-0125-02
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note-0125-02a
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">34. prim@</
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>
_k_l, ipſi a b æqualis. </
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<
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militer demonſtrabitur
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l m æquidiſtans, & </
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<
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">æqua
<
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lis b c; </
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<
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xml:space
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">& </
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<
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">m
<
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style
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ipſi c a.</
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<
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