On the Equilibrium of Planes

Archimedes' work, On the Equilibrium of Planes, primarily focuses on establishing the centers of gravity for various plane figures, including segments of parabolas. It also aims to prove the law of the lever, which states that magnitudes balance at distances from a fulcrum inversely proportional to their weights. While this treatise is considered foundational for theoretical mechanics, some parts are believed to be later additions or reworkings, suggesting that the basic principles of the law of the lever and the concept of the center of gravity may have been established by scholars before Archimedes. His contribution was in extending these concepts to conic sections.12