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 Academy of Sciences. He was induced to remain in Paris from that time until 1681, when he returned to his native city, partly for consideration of his health and partly on account of the revocation of the Edict of Nantes.

The majority of his profound discoveries were made with aid of the ancient geometry, though at times he used the geometry of Descartes or of Cavalieri and Fermat. Thus, like his illustrious friend, Sir Isaac Newton, he always showed partiality for the Greek geometry. Newton and Huygens were kindred minds, and had the greatest admiration for each other. Newton always speaks of him as the "Summus Hugenius."

To the two curves (cubical parabola and cycloid) previously rectified he added a third,—the cissoid. He solved the problem of the catenary, determined the surface of the parabolic and hyperbolic conoid, and discovered the properties of the logarithmic curve and the solids generated by it. Huygens' De horologio oscillatorio (Paris, 1673) is a work that ranks second only to the Principia of Newton and constitutes historically a necessary introduction to it.[13] The book opens with a description of pendulum clocks, of which Huygens is the inventor. Then follows a treatment of accelerated motion of bodies falling free, or sliding on inclined planes, or on given curves,—culminating in the brilliant discovery that the cycloid is the tautochronous curve. To the theory of curves he added the important theory of "evolutes." After explaining that the tangent of the evolute is normal to the involute, he applied the theory to the cycloid, and showed by simple reasoning that the evolute of this curve is an equal cycloid. Then comes the complete general discussion of the centre of oscillation. This subject had been proposed for investigation by Mersenne and discussed by Descartes and Roberval. In Huygens' assumption that the common centre