Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
"/>
trianguli g h K, & </
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<
s
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xml:space
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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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<
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<
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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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<
lb
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uiſiones planum ducatur; </
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<
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xml:space
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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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">Deinde iuncta a c per lineas a c, a e ducatur
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lb
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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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<
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triangulorum a b c, e f g gra-
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0137-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0137-01
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figure
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uitatis centra o p: </
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<
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<
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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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<
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<
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no _k_ l m n occurrant in pun-
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ctis s t. </
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<
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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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<
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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:space
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<
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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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tis a d c, e h g. </
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<
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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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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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<
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xml:id
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xml:space
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u x, quæ ſecet lineam ſ t in y. </
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<
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<
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cabit enim cum ſint in eodem
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<
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note
>
plano: </
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<
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<
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">erit y grauitatis centrum quadril ateri _K_ lm n.
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</
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<
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tius priſmatis. </
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<
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tatis centrum eſt y: </
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<
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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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<
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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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