Towards the end of the seventeenth century, Newton published his discovery of universal gravitation. Mathematicians have, since that epoch, succeeded in reducing to this great law of nature all the known phenomena of the system of the world, and have thus given to the theories of the heavenly bodies, and to astronomical tables, an unexpected degree of precision. My object is to present a connected view of these theories, which are now scattered in a great number of works. The whole of the results of gravitation, upon the equilibrium and motions of the fluid and solid bodies, which compose the solar system, and the similar systems, existing in the immensity of space, constitute the object of Celestial Mechanics, or the application of the principles of mechanics to the motions and figures of the heavenly bodies. Astronomy, considered in the most general manner, is a great problem of mechanics, in which the elements of the motions are the arbitrary constant quantities. The solution of this problem depends, at the same time, upon the accuracy of the observations, and upon the perfection of the analysis. It is very important to reject every empirical process, and to complete the analysis, so that it shall not be necessary to derive from observations any but indispensable data. The intention of this work is to obtain, as much as may be in my power, this interesting result. I hope, in consideration of the difficulty and importance of the subject, that mathematicians and astronomers will receive it with indulgence, and that they will find the results sufficiently simple to be used in their researches. It will be divided into two parts. In the first part, I shall give the methods and formulas, to determine the motions of the centres of gravity of the heavenly bodies, the figures of those bodies, the oscillations of the fluids which cover them, and the motions about their centres of gravity. In the second part, I shall apply the formulas found in the first, to the planets, satellites, and comets; and I shall conclude the work, with an examination of several questions relative to the system of the world, and with an historical account of the labours of mathematicians upon this subject. I shall adopt the decimal division of the right angle, and of the day, and shall refer the linear measures to the length of the metre, determined by the are of the terrestrial meridian comprised between Dunkirk and Barcelona.
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