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      • Magnitudes are in equilibrium at distances reciprocally proportional to their weights. ΤΑ ΜΕΓΕΘΕΑ ΙΣΟΡΡΟΠΕΟΝΤΙ ΑΠΟ ΜΑΚΕΩΝ ΑΝΤΙΠΕΠΟΝΘΟΤΩΣ ΤΟΝ ΑΥΤΟΝ ΛΟΓΟΝ ΕΧΟΝΤΩΝ ΤΟΙΣ ΒΑΡΕΣΙΝ. This is the statement of the Law of the Lever that Archimedes gives in Propositions 6 and 7 of Book I of his work entitled On the Equilibrium of Planes.
      math.nyu.edu/Archimedes/Lever/LeverLaw.html
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  2. 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 .

  3. 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.

  4. 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.

  5. 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 .

  6. 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.

  7. But Archimedes in this work believes that the center of inclination of a plane figure is that hanging from which it remains parallel to the horizon, but the center of inclination or weight of two or more planes is that suspended from which the balance is parallel to the horizon.

  8. This is the statement of the Law of the Lever that Archimedes gives in Propositions 6 and 7 of Book I of his work entitled On the Equilibrium of Planes.

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