Page:Mécanique céleste Vol 1.djvu/19

 CONTENTS OF THE FIRST VOLUME.

Preface, plan of the work. xxiii

FIRST BOOK.

ON THE GENERAL LAWS OF EQUILIBRIUM AND MOTION.

CHAPTER I. ON THE EaUILIBRIUM AND COMPOSITION OF FORCES WHICH ACT ON A MATERIAL POINT 1

On motion and force, also on the composition and resolution of forces, [1 — 17]. . . . § 1, 2

Equation of the equilibrium of a point acted upon by any number of forces, in any directions whatever, [18]. Method of determining, when the point is not free, the pressure it exerts upon the surface, or upon the curve to which it is subjected, [19 — ^26]. Theory of the momentum of any force about an axis, [29] § 3

CHAPTER II. ON THE MOTION OF A MATERIAL POINT 23

On the laws of inertia, uniform motion, and velocity, [29"] § 4

Investigation of the relation which exists between force and velocity. In the law of nature they are proportional to each other. Results of this law, [30 — 34'"] § 5j 6

Equations of the motions of a point acted upon by any forces, [37] § 7

General expression of the square of the velocity, [40]. The point describes the curve in which the integral of the product of the velocity, by the element of the curve, is a minimum, [49^]. § 8

Method of computing the pressure which a point, moving upon a surface, or upon a curve, exerts on it, [54]. On the centrifugal force, [54'] § 9

Application of the preceding principles to the motion of a material point, acted upon freely by gravity, in a resisting medium. Investigation of the law of resistance necessary to make the moving body describe a given curve. Particular examination of the case in which the resistance is nothing, [54^—67" ] §10