Give me a lever long enough and a fulcrum on which to place it and I'll move the world - Archimedes

The centre of gravity of a parallelogram is the point of intersection of its diagonals.

I thought fit to... explain in detail in the same book the peculiarity of a certain method, by which it will be possible... to investigate some of the problems in mathematics by means of mechanics. This procedure is... no less useful even for the proof of the theorems themselves; for certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards... But it is of course easier, when we have previously acquired, by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.

Any segment of a right-angled conoid (i.e., a paraboloid of revolution) cut off by a plane at right angles to the axis is 1½ times the cone which has the same base and the same axis as the segment