Five geometers--Clairaut, Euler, D'Alembert, Lagrange, and Laplace--shared between them the world whose existence Newton had disclosed. They explored it in all directions, penetrated into regions hitherto inaccessible, and pointed out phenomena hitherto undetected. Finally--and it is this which constitutes their imperishable glory--they brought under the domain of a single principle, a single law, everything that seemed most occult and mysterious in the celestial movements. Geometry had thus the hardihood to dispose of the future, while the centuries as they unroll scrupulously ratify the decisions of science. If Newton gave a complete solution of celestial movements where but two bodies attract each other, he did not even attempt the infinitely more difficult problem of three. The "problem of three bodies" (this is the name by which it has become celebrated)--the problem of determining the movement of a body subjected to the attractive influence of two others--was solved for the first time by our countryman, Clairaut. Though he enumerated the various forces which must result from the mutual action of the planets and satellites of our system, even the great Newton did not venture to investigate the general nature of their effects. In the midst of the labyrinth formed by increments and diminutions of velocity, variations in the forms of orbits, changes in distances and inclinations, which these forces must evidently produce, the most learned geometer would fail to discover a trustworthy guide. Forces so numerous, so variable in direction, so different in intensity, seemed to be incapable of maintaining a condition of equilibrium except by a sort of miracle. Newton even suggested that the planetary system did not contain within itself the elements of indefinite stability. He was of opinion that a powerful hand must intervene from time to time to repair the derangements occasioned by the mutual action of the various bodies. Euler, better instructed than Newton in a knowledge of these perturbations, also refused to admit that the solar system was constituted so as to endure forever.