Archimedes - Triangle Quotes

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First then I will set out the very first theorem which became known to me by means of mechanics, namely that
Any segment of a section of a right angled cone (i. e., a parabola) is four-thirds of the triangle which has the same base and equal height,
and after this I will give each of the other theorems investigated by the same method. Then at the end of the book I will give the geometrical [proofs of the propositions]...

Archimedes

It follows at once from the last proposition that the centre of gravity of any triangle is at the intersection of the lines drawn from any two angles to the middle points of the opposite sides respectively.

Archimedes

In any triangle the centre of gravity lies on the straight line joining any angle to the middle point of the opposite side.

Archimedes