Pierre-Simon Laplace

The knowledge which we at present possess of the mechanics of the heavens, gives us the means of judging with certainty of the stability of the solar system.

The perturbations produced by the mutual action of the planets are periodic, and confined within narrow limits; so that the system can never be destroyed by their action.

The theory of probabilities holds to considerations so delicate, that it is not surprising that with the same data two persons should arrive at different results.

The small inequalities which we observe in the movements of the planets, have enabled us to ascertain their masses.

The application of analysis to the theory of probabilities, is one of the most remarkable facts of the present age.

The more we know, the more we feel our ignorance; the more we feel how much remains unknown.

The simplicity of the law by which the celestial bodies move, and the relations of their masses and distances, permit analysis to follow their motions up to a certain point; and in order to determine the state of the system of these great bodies in past or future centuries, it suffices for the mathematician that their position and their velocity be given by observation for any moment in time.

The analytical equations, unknown to the ancients, which Descartes was the first to introduce into the study of curves and surfaces, are not limited to the properties of figures, and to those properties which are the object of rational mechanics; they extend to all general phenomena.

The phenomena of nature are most often enveloped by so many strange circumstances, and so many disturbing causes mix their influence, that it is very difficult to recognize them.

The stability of the equilibrium of the seas, the conservation of the atmosphere, the return of the seasons, and the perpetuation of the species are founded upon principles which are immutable like the laws of gravitation.

The happiness of a people consists in the union of liberty with obedience to the laws.

The discovery of the law of universal gravitation is the most beautiful achievement of the human mind.

The method of least squares, by its simplicity, its generality, and its rigorous accuracy, is one of the most beautiful discoveries of analysis applied to the observation of phenomena.

The regularity which astronomy shows us in the movements of the comets doubtless occurs also in all phenomena.

The arrangement of the universe is the most perfect possible, because it is the work of an all-wise Creator.

Let us run over the chain of human knowledge; we shall see that the most certain and the most numerous branches are those which have been subjected to calculation.

The theory of probabilities holds to considerations so delicate, that it is not surprising that with the same data two persons arrive at different results.

The greater the number of repetitions, the more the results tend to a fixed limit.

The most important questions of life are indeed, for the most part, only problems in the doctrine of chances.

The analytical method, which I have followed, has the advantage of leading with certainty to the general equations of the problem, and of reducing its solution to the integration of these equations.