Traité de mécanique céleste (transl. "Treatise of celestial mechanics") is a five-volume treatise on celestial mechanics written by Pierre-Simon Laplace and published from 1798 to 1825 with a second edition in 1829. In 1842, the government of Louis Philippe gave a grant of 40,000 francs for a 7-volume national edition of the Oeuvres de Laplace (1843–1847); the Traité de mécanique céleste with its four supplements occupies the first 5 volumes.
Newton laid the foundations of Celestial Mechanics, at the close of the seventeenth century, by the discovery of the principle of universal gravitation. Even in his own hands, this discovery led to important consequences, but it has required a century and a half, and a regular succession of intellects the most powerful, to fill up the outline sketched by him. Of these, Laplace himself was the last, and, perhaps after Newton, the greatest; and the task commenced in the Principia of the former, is completed in the Mécanique Céleste of the latter. In this last named work, the illustrious author has proposed to himself his object, to unite all the theories scattered throughout the various channels of publication, employed by his predecessors, to reduce them to one common method, and present them all in the same point of view. If one were asked to name the two most important works in the progress of mathematics and physics, the answer would undoubtedly be, the Principia of Newton and the Mécanique Céleste of Laplace. In their historical and philosophical aspects these works easily outrank all others, and furnish thus the standard by which all others must be measured. The distinguishing feature of the Principia is its clear and exhaustive enunciation of fundamental principles. The Mécanique Céleste, on the other hand, is conspicuous for the development of principles and for the profound generality of its methods. The Principia gives the plans and specifications of the foundations; the Mécanique Céleste affords the key to the vast and complex superstructure.
Tome I. (1798)
Livre I. Des lois générales de l'équilibre et du mouvement Chap. I. De l'équilibre et de la composition des forces qui agissent sur un point matériel Chap. II. Du mouvement d'un point matériel Chap. III. De l'équilibre d'un système de corps Chap. IV. De l'équilibre des fluides Chap. V. Principes généraux du mouvement d'un système de corps Chap. VI. Des lois du mouvement d'un système de corps, dans toutes les relations mathématiquement possibles entre la force et la vitesse Chat. VII. Des mouvemens d'un corps solide de figure quelconque Chap. VIII. Du mouvement des fluides
Livre II. De la loi pesanteur universelle, et du mouvement des centres de gravité des corps célestes
Tome II. (1798)
Livre III. De la figure des corps céleste
Livre IV. Des oscillations de la mer et de l'atmosphère
Livre V. Des mouvemens des corps célestes, autour de leurs propre centres de gravité
Tome III. (1802)
Livre VI. Théorie particulières des mouvemens célestes
Livre VII. Théorie de la lune
Tome IV. (1805)
Livre VIII. Théorie des satellites de Jupiter, de Saturne et d'Uranus
Livre IX. Théorie des comètes
Livre X. Sur différens points relatifs au système du monde This book contains a discussion of continued fractions and a computation of the complementary error function in terms that came to be called the Laplace continued fraction, 1/(1+q/(1+2q/(1+3q/(...))).
Tome V. (1825)
Livre XI. De la figure et de la rotation de la terre
Livre XII. De l'attraction et de la répulsion des sphères, et des lois de l'equilibre et du mouvement des fluides élastiques
Livre XIII. Des oscillations des fluides qui recouvrent les planètes
Livre XIV. Des mouvemens des corps célestes autour de leurs centres de gravité
Livre XV. Du mouvement des planètes et des comètes
Livre XVI. Du mouvement des satellites
English translations During the early nineteenth century at least five English translations of Mécanique Céleste were published. In 1814 the Reverend John Toplis prepared a translation of Book 1 entitled The Mechanics of Laplace. Translated with Notes and Additions. In 1821 Thomas Young anonymously published a further translation into English of the first book; beyond just translating from French to English he claimed in the preface to have translated the style of mathematics: The translator flatters himself, however, that he has not expressed the author's meaning in English words alone, but that he has rendered it perfectly intelligible to any person, who is conversant with the English mathematicians of the old school only, and that his book will serve as a connecting link between the geometrical and algebraical modes of representation.The Reverend Henry Harte, a fellow at Trinity College, Dublin translated the entire first volume of Mécanique Céleste, with Book 1 published in 1822 and Book 2 published separately in 1827. Similarly to Bowditch (see below), Harte felt that Laplace's exposition was too brief, making his work difficult to understand:... it may be safely asserted, that the chief obstacle to a more general knowledge of the work, arises from the summary manner in which the Author passes over the intermediate steps in several of his most interesting investigations.
Bowditch's translation The famous American mathematician Nathaniel Bowditch translated the first four volumes of the Traité de mécanique céleste but not the fifth volume; however, Bowditch did make use of relevant portions of the fifth volume in his extensive commentaries for the first four volumes.
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