On the Equilibrium of PlanesArchimedes

Archimedes' On the Equilibrium of Planes is a treatise in two books on statics. Book I proves the law of the lever and locates the centers of gravity of the parallelogram, the triangle, and the trapezium. Magnitudes in equilibrium at certain lengths remain in equilibrium when equal magnitudes replace them. Unequal weights balance at distances inversely proportional to their weights.

Book II, written later and drawing on the Quadrature of the Parabola, finds the centers of gravity of parabolic segments. Center of gravity becomes the key concept. Renaissance mathematicians from Guidobaldo del Monte to Galileo took its axiomatic style as a model for mathematical physics.