member of the National Institute of Sciences and Arts, was born at Paris in the year 1735. He devoted his youth to self-instruction; and even at the age of thirty was far enough from suspecting that he was destined to instruct others in his turn. Chance brought him near to the celebrated Fontaine. That hexagenary geometrician easily divined the progress which Vandermonde would one day make in the mathematics; in him he anticipated, as it were, a successor to himself; he patronized and assisted him, let him into the secret of his researches, calculations, inventions, of that lively enjoyment which profound speculation gives to an elevated attentive mind; and which, blended with the sweets of tranquillity, the charms of retreat, and the consciousness of success, becomes often a sort of pallion, as felicitous as durable.

All that time Fontaine, whose attention was again directed to the researches which he had added to those of Jean Bernoulli, relative to the then famous question of the tautocones, had the glory to be vanquished only by D'Alembert and La Grange. Vandermonde, a witness to this combat, necessarily illustrious, animated by the honour which he saw annexed to that glorious defeat, enchanted with the sight of Fontaine, as happy, in spite of his age, from his love of geometry, as a youth of twenty could be with a sentiment less tranquil, thought he should infuse his happiness for ever, by yielding to a passion which the ice of age could not extinguish; in a word, he devoted himself to geometry.

His labours, however, were for some time secret; and perhaps the public would never have enjoyed the benefit of any of his works, if another geometrician (whose name, says Lapezede, cannot be pronounced, in this place, without a mixture of interest and regret) had not inspired him with a consciousness of his own strength, and courage to display it. Fontaine had already devoted him to geometry; Dufojour exhorted him to penetrate even into its sanctuary. In brief, he presented himself himself to the Academy of Sciences, into which he was admitted in 1771; and in that very year justified the suffrages of his associates, by a paper which he published relative to the resolution of equations.

From the 16th century the method of resolving equations of the four first degrees has been known, and since that time the general theory of equations has received great improvements. In spite, however, of the recent labours of many great geometers, the solutions of equations of the fifth degree had in vain been attempted. Vandermonde wished to consolidate his labours with those of other illustrious analysts; and he proposed a new theory of equations, in which he seems to have made it particularly his business to simplify the methods of calculation, and to contract the length of the formulae, which he considered as one of the greatest difficulties of the subject.

This work was quickly followed by another on the problems called by geometers' problems of situation. It seems to have been the destiny of Vandermonde, as well as of Fontaine, who first initiated him into the mysteries of mathematical science, to labour frequently upon subjects already handled by the greatest master. In his first memoir he had started, so to speak, in competition with La Grange and Euler; in his second, with Euler and Leibnitz. This last was of opinion that the analysis made use of in his time, by the geometers, was not applicable to all questions in the physical sciences; and that a new geometry should be invented, to calculate the relations of positions of different bodies, in space: this he called geometry of situation*. Excepting, however, one application, made by Leibnitz himself, to the game of solitaire, and which, under the appearance of an object of curiosity, scarcely worthy the subtlety and usefulness of geometry, is an example for solving the most elevated and important questions, Euler was almost the only one who had practised this geometry of situation. He had referred to it for the solution of a problem called the cavalier, which also appeared very familiar at first sight, and was also pregnant with useful and important applications. This problem, with the vulgar, consisted merely in running through all the cases of the chessboard, with the knights of the game of chess; to the profound geometer, however, it was a precedent for tracing the route which every body must follow, whose course is submitted to a known law, by conforming to certain required conditions, through all the points disposed over a space in a prescribed order. Vandermonde was chiefly anxious to find in this species of analysis a simple notation, likely to facilitate the making of calculations; and he gave an example of this, in a short and easy solution of the same problem of the cavalier, which Euler had rendered famous.

His taste for the high conceptions of the speculative sciences, as blended with that which the amor patriae naturally inspires for objects immediately useful to society, had led him to turn his thoughts towards perfecting the arts conversant in weaving, by indicating a manner of noting the points through which are to pass the threads intended to form the lines which terminate the surface of different regular bodies: accordingly a great part of the above memoir is taken up with this subject.

In the year following (1772) he printed a third memoir; in which he traced out a new path for geom-

ters, discovering, by learned analytical researches, irrational quantities of a new species, shewing the results of which these irrationals are the terms or the sum, and pointing out a direct and general method of making in them all the possible reductions.

In the same year appeared his work on the Elimination of unknown Quantities in Algebra. This elimination is the art of bringing back those equations which include many unknown quantities, to equations which only contain one. The perfection of researches in this art would consist in obtaining a general and particular formula of elimination in a form the most concise and convenient, in which the number of equations and their degrees should be denoted by indeterminate letters. Vandermonde, while he considered the geometers as very distant from this point, had some glimpse of the possibility of reaching it, and proposed some new methods of approaching nearer it.

In 1778, he presented, in one of the public fittings of the Academy, a new system of harmony, which he detailed more fully in another public fitting of 1780. In this system, Vandermonde reduces the modes of proceeding adopted until his time, to two principal rules, which thus become established on effects admitted by all musicians. These two general rules, one on the succession of according sounds, the other on the arrangement of the parts, depend themselves on a law more elevated, which, according to Vandermonde, ought to rule the whole science of harmony.

By the publication of this work, he satisfactorily attained the end he had proposed to himself, and obtained the suffrages of three great men, representatives, so to speak, of the three great schools of Germany, France, and Italy: Gluck, Philidor, and Piccini.

With these labours, intermingled with frequent researches on the mechanic arts, as well as on objects of political economy, the attention of Vandermonde was taken up; when, July 14, 1789, the voice of liberty resounded over the whole surface of France, and suddenly all the thoughts, as well as all the affections, of Vandermonde, were engaged on the side of what he called liberty.

He became so furious a democrat, so outrageous an enemy to every thing established, that he concurred in the abolition of the Royal Academy, of which he had been so ambitious of becoming a member, and associated himself closely with Robespierre, Marat, and the rest of that atrocious gang of villains, who covered France with ruins, with scaffolds, and with blood. This part of Vandermonde's history is suppressed by his eulogist Lacapeze, because, forsooth, discussions on political opinions ought not, in his opinion, to be admitted into the sanctuary of the sciences.

In that sanctuary he did not long remain. Soon after his atrocities, he was attacked by a disorder in his lungs, which almost taking away his breath, manifested itself by alarming symptoms, and conducted him by rapid steps to the tomb. He died in the end of the year 1795; a striking instance of the wayward violence of the human mind, which even the love of science could not keep at a distance from tumult and uproar.