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On the Equilibrium of Planes (Ancient Greek: Περὶ ἐπιπέδων ἱσορροπιῶν, romanized: perí epipédōn isorropiôn) is a treatise by Archimedes in two books. The first book contains a proof of the law of the lever and culminates with propositions on the centre of gravity of the triangle and the trapezium.
on the sphere and cylinder, book ii; measurement of a circle; on conoids and spheroids; on spirals; on the equilibrium of planes, book i; on the equilibrium of planes, book ii; the sand-reckoner; quadrature of the parabola; on floating bodies, book i; on floating bodies, book ii; book of lemmas
On the Equilibrium of Planes I, which contains seven postulates and fifteen propositions, uses the centre of gravity for both commensurable and incommensurable magnitudes to justify the law of the lever, though some argue not satisfactorily.
On the Equilibrium of Planes II shares the same subject matter as the first book but was most likely written at a later date. It contains ten propositions regarding the centre of gravity of parabolic segments exclusively, and examines these segments by substituting them with rectangles of equal area.
Sep 7, 2010 · Summary. “I postulate the following: Equal weights at equal distances are in equilibrium, and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance.
Here are two attempts at definitions, the first of which captures better what Archimedes does in Plane Equilibria and Quadrature of the Parabola, but keeping in mind the abstract nature of his works also fits the solid geometry of the Method and Floating Bodies.
On the Equilibrium of Planes (or Centres of Gravity of Planes; in two books) is mainly concerned with establishing the centres of gravity of various rectilinear plane figures and segments of the parabola and the paraboloid. The first book purports to establish the “law of… Read More.
