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 11
[The following is quotation]
Proposition 11
P11. If abc, ABC he two similar triangles, and g, G two points in them similarly situated with respect to them respectively, then, if g be the centre of gravity of the triangle abc, G must be the centre of gravity of the triangle ABC.
Suppose ab : bc : ca = AB : BC : CA.
The proposition is proved by an obvious reductio ad absurdum. For, if G be not the centre of gravity of the triangle ABC, suppose H to be its centre of gravity.
Post. 5 requires that g, H shall be similarly situated with respect to the triangles respectively; and this leads at once to the absurdity that the angles HAB, GAB are equal.
(Heath 196)
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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