The merit of our actual system of numeration consists in including the expression of all numbers in a single idea, making the value of each figure ten times that to the right, and filling all intervals with zeros. The expression of infinite numbers is reduced to the simplicity of a single rule based upon a single idea; the relation of position with a tenfold value. Logarithms have enabled arithmetic to make a great advance by diminishing the number of its fundamental operations, since, with them it reduces multiplication and division to addition and subtraction. Algebra is only the generalization of arithmetical expressions and operations, their simplification. The application of algebra to geometry is the generalization of geometrical expressions; formulas of lines, figures, bodies, only the expression of their universal idea. In this idea as in a type, geometry preserves its first and generative idea, and it requires only the simplest applications in order to form an exact calculation of all lines belonging to the same class, which can possibly be met with in practice. In the simple expression dz/dx = A, called the differential coefficient, is contained the whole idea of infinitesimal calculus. It originated in geometrical considerations, but so soon as its universality was conceived, it poured a flood of light upon every branch of mathematical and natural science, and led to the discovery of a new world, whose confines are still unknown. The prodigious fecundity of this calculus emanates from its simplicity, its prompt generalization of both algebra and geometry, and its uniting them in a single point which is the relation of the limits of the differentials of any function. 49. It is to this unity of idea that the human intellect in its ambition aspires, and once obtained, it proves the cause of great progress. The glory of the greatest geniuses is that they discovered it: the advance of science has consisted in profiting by it. Vieta explained and applied the principle of the general expression of arithmetical quantities; Descartes extended this to geometrical quantities. Newton established the principle of universal gravitation; and he, at the same time with Leibnitz, invented the infinitesimal calculus; and the exact and natural sciences march, by the light of a vast flambeau, with gigantic strides along paths never before trodden. And all this because intelligence has approached unity, and become possessed of a generative idea, involving infinite other ideas.