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By William Elwood Byerly

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Example text

The vertical plane passing through αβ “will cut the body into two parts that are in equilibrium with each other and which will be hung in such a way, on one side of the plane and on the other, as to be equal with respect to their weight. ” Fig. 7 Now suspend the body from a point γ and draw the vertical γδ through the point of suspension when equilibrium is established. Take a second point of suspension γ′ and, in the same way, draw the vertical γ′δ′. The two lines γδ, γ′δ′ necessarily intersect.

And in the Fourteenth Century, the Oxford School, which in other respects indulged in such artificial quibbling, was to clarify the laws of the kinematics of uniformly accelerated motion. The mechanics of the Middle Ages received something of a check during the Renaissance, which caused a return to classical traditions. The Schools were attacked by the humanists. Yet, before Galileo, Dominico Soto successfully formulated the exact laws of heavy bodies even if he did not verify them experimentally.

9 For the rest, the treatise On the Equilibrium of Planes is concerned with the determination of the centres of gravity of particular geometrical figures. After having obtained the centres of gravity of a triangle, a parallelogram and a trapezium, Archimedes determined the centre of gravity of a segment of a parabola by means of an analysis which is a milestone in the history of mathematics (Book II, Proposition VIII). We shall now concern ourselves with Archimedes’ treatise on Floating Bodies.

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