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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.
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 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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Pleasant it is, when over a great sea the winds trouble the waters, to gaze from shore upon another's tribulation: not because any man's troubles are a delectable joy, but because to perceive from what ills you are free yourself is pleasant.
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