by Corry Shores
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[“On the Equilibrium of Planes”, Entry Directory]
Archimedes
On the Equilibrium of Planes
or
The Centres of Gravity of Planes,
Book I
Proposition 8
[The following is quotation]
Proposition 8.
P8. If AB he a magnitude whose centre of gravity is C, and AD a part of it whose centre of gravity is F, then the centre of gravity of the remaining part will he a point G on FC produced such that
GC : GF = (AD) :(DE).
For, if the centre of gravity of the remainder (DE) be not G, let it be a point H. Then an absurdity follows at once from Props. 6,7.
From:
Archimedes. “On the Equilibrium of Planes or The Centres of Gravity of Planes, Book I”. In The Works of Archimedes. Ed. T.L. Heath. Cambridge UP, 1897. Obtained at
https://archive.org/details/worksofarchimede00arch
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