Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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0137
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DE CENTRO GRAVIT. SOLID.
"/>
trianguli g h K, & </
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<
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">ipſius ρ τ axis medium.</
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<
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<
s
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">Sit priſma a g, cuius oppoſita plana ſint quadrilatera
<
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a b c d, e f g h: </
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<
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echoid-s3473
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">ſecenturq; </
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<
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echoid-s3474
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">a e, b f, c g, d h bifariam: </
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<
s
xml:id
="
echoid-s3475
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xml:space
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">& </
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>
<
s
xml:id
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echoid-s3476
"
xml:space
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">per di-
<
lb
/>
uiſiones planum ducatur; </
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>
<
s
xml:id
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echoid-s3477
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">quod ſectionem faciat quadrila-
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terum _K_ l m n. </
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<
s
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echoid-s3478
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">Deinde iuncta a c per lineas a c, a e ducatur
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lb
/>
planum ſecãs priſma, quod ipſum diuidet in duo priſmata
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/>
triangulares baſes habentia a b c e f g, a d c e h g. </
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<
s
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echoid-s3479
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">Sint autẽ
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/>
triangulorum a b c, e f g gra-
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/>
<
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xlink:label
="
fig-0137-01
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xlink:href
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fig-0137-01a
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number
="
92
">
<
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file
="
0137-01
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0137-01
"/>
</
figure
>
uitatis centra o p: </
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<
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">& </
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<
s
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">triangu-
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lorum a d c, e h g centra q r:
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</
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<
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">iunganturq; </
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<
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">o p, q r; </
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<
s
xml:id
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echoid-s3484
"
xml:space
="
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">quæ pla-
<
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no _k_ l m n occurrant in pun-
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/>
ctis s t. </
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<
s
xml:id
="
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"
xml:space
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">erit ex iis, quæ demon
<
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/>
ſtrauimus, punctum s grauita
<
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/>
tis centrum trianguli k l m; </
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<
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xml:space
="
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">& </
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<
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<
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ipſius priſmatis a b c e f g: </
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<
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xml:id
="
echoid-s3488
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xml:space
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">pun
<
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/>
ctum uero t centrum grauita
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/>
tis trianguli _K_ n m, & </
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<
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xml:id
="
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">priſma-
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tis a d c, e h g. </
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<
s
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">iunctis igitur
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o q, p r, s t, erit in linea o q cẽ
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trum grauitatis quadrilateri
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a b c d, quod ſit u: </
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<
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xml:id
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xml:space
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">& </
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<
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xml:id
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echoid-s3492
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xml:space
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">in linea
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/>
p r cẽtrum quadrilateri e f g h
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/>
ſit autem x. </
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<
s
xml:id
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xml:space
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">deniqueiungatur
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u x, quæ ſecet lineam ſ t in y. </
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>
<
s
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">ſe
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cabit enim cum ſint in eodem
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<
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xlink:label
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xlink:href
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note-0137-01a
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">5. huius.</
note
>
plano: </
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<
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">atq; </
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<
s
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">erit y grauitatis centrum quadril ateri _K_ lm n.
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</
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>
<
s
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xml:space
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">Dico idem punctum y centrum quoque gra uitatis eſſe to-
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tius priſmatis. </
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>
<
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xml:id
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xml:space
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">Quoniam enim quadri lateri k lm n graui-
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tatis centrum eſt y: </
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<
s
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">linea s y ad y t eandem proportionem
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/>
habebit, quam triangulum k n m ad triangulum k lm, ex 8
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/>
Archimedis de centro grauitatis planorum. </
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>
<
s
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">Vtautem triã
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gulum k n m ad ipſum k l m, hoc eſt ut triangulum a d c ad
<
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/>
triangulum a b c, æqualia enim ſunt, ita priſina a d c e h </
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