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If two equal weights have not the same centre of gravity, the centre of gravity of both taken together is at the middle point of the line joining their centres of gravity.
The centre of gravity of any cylinder is the point of bisection of the axis.
The centre of gravity of a parallelogram is the point of intersection of its diagonals.
The centre of gravity of any cone is [the point which divides its axis so that] the portion [adjacent to the vertex is] triple [of the portion adjacent to the base].
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.
The centre of gravity of any hemisphere [is on the straight line which] is its axis, and divides the said straight line in such a way that the portion of it adjacent to the surface of the hemisphere has to the remaining portion the ratio which 5 has to 3.
The centre of gravity of any parallelogram lies on the straight line joining the middle points of opposite sides.
In any triangle the centre of gravity lies on the straight line joining any angle to the middle point of the opposite side.
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