Fig. 59.—An ellipse.
Thus if, in the figure, S and H are the foci, and P, Q are any two points on the curve, then the distances S P, H P added together are equal to the distances S Q, Q H added together, and each sum is equal to the length A A′ of the ellipse. The ratio of the distance S H to the length A A′ is known as the eccentricity, and is a convenient measure of the extent to which the ellipse differs from a circle.
[88] The ellipse is more elongated than the actual path of Mars, an accurate drawing of which would be undistinguishable to the eye from a circle. The eccentricity is 1∕3 in the figure, that of Mars being 1∕10.
[89] Astronomia Nova αἰτιολογητος seu Physica Coelestis, tradita Commentariis de Motibus Stellae Martis. Ex Observationibus G. V. Tychonis Brahe.
[90] It contains the germs of the method of infinitesimals.
[91] Harmonices Mundi Libri V.
[92] There may be some interest in Kepler’s own statement of the law: “Res est certissima exactissimaque, quod proportionis quae est inter binorum quorumque planetarum tempora periodica, sit praecise sesquialtera proportionis mediarum distantiarum, id est orbium ipsorum.”—Harmony of the World, Book V., chapter III.
[93] Epitome, Book IV., Part 2.