page_title: On the Equilibrium of Planes
section_title: Introduction
hierarchical_section_title: On the Equilibrium of Planes / Main Theorem / Introduction
context_page_description: On the Equilibrium of Planes is a treatise by Archimedes in two volumes. The first book establishes the law of the lever, and locates the centre of gravity of the triangle and the trapezoid. According to Pappus of Alexandria, Archimedes' work on levers caused him to remark: "Give me a place to stand on, and I will move the Earth.". The second book, which contains ten propositions, examines the centres of gravity of parabolic segments.
context_section_description: In postulate one Archimedes states that "Equal weights at equal distances are in equilibrium" (meaning one equal weight on either side of the lever arm). At propositions four, and five, he expands this observation to include the concept of the centre of gravity; wherein it is proven that the centre of gravity of any system consisting of an even number of equal weights, equally distributed, will be located at the midpoint between the two centre weights (hence introducing multiple weights on either side of the lever arm).
caption: Equal weights at equal distances.