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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.
7 de sept. de 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.
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.
Using further postulates of Archimedes, the two weights w,won either side of a fulcrum and of distances d,d(respectively) to the fulcrum are in equilibrium if and only if (*) holds. This is his Law-of-the-lever. Now this is ‘proved’ by Archimedes, subject to his postulates.
IX. On the Equilibrium of Planes or Centres of Gravity of Planes. Book I; pp. 286-313
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.
27 de jun. de 2024 · ON THE EQUILIBRIUM OF PLANES, BOOK II. Published online by Cambridge University Press: 07 September 2010. Archimedes. Edited by. Thomas L. Heath. Chapter. Get access. Cite.
