mentioned which, as the theory has since verified, were real onward steps. The perusal of this chapter will shew to what extent we are indebted to our great philosopher; at the same time we cannot fail being impressed with reverence for the genius and perseverance of the men who preceded him, and whose elaborate and multiplied hypotheses were in some measure necessary to the discovery of his simple and single law. I take this opportunity of acknowledging my obligations to several friends, whose valuable suggestions have added to the utility of the work. St. John's College, Cambridge, HUGH GODFRAY. IN the present edition, besides the change of form and the incorporation of the figures with the text, which it is hoped will render the work more commodious, very few alterations have been thought necessary; and, except in one or two instances, where additional paragraphs have been introduced, nothing but the wording of some of the sentences has been altered. October, 1859. Page. Values deduced by the Solution of a large number of simultaneous Equations . ib. ་་ 91 The Moon is retained in her orbit by gravity 92 The Moon's orbit is everywhere concave to the Sun. 93 Effects of Central and Tangential Forces separately considered 109 Description of the Eccentric and the Epicycle 112 Hipparchus's mode of representing the Motion of the Apse 113 Substitution of the Elliptic for the Circular Orbit 120 Boulliaud, D'Arzachel, Horrocks consider it in a different manner 110 121 Tycho Brahe's discovery and representation of the Variation 112 123 Tycho Brahe's discovery and representation of the Annual 124 Tycho's Table for the Reduction 125 Inclination of the Moon's orbit and motion of the Node cal- 126 Tycho Brahe's discovery of the change of inclination and of the |