About the same time a problem of quite a different kind attracted the attention of M. la Grange. Fermat, one of the greatest mathematicians of his time, had left very remarkable theorems respecting the properties of numbers, which he probably discovered by induction. He had promised the demonstrations of them ; but at his death no trace of them could be found. Whether he had sup pressed them as insufficient, or from some other cause, cannot now be ascertained. These theorems perhaps may appear more curious than useful. But it is well known that difficulty constitutes a strong attraction for all men, especially for mathematicians. Without such a motive would they have attached so much importance to the pro blems of the brachystrochonon, of the isoperimeters, and of the orthogonal trajectories ? Certainly not. They wish ed to create the science of calculation, and to perfect me thods which could not fail some clay of finding useful ap plications. With this view, they attached themselves to the first question which required new resources. The system of the world discovered by Newton was a most fortunate event for them. Never could the transcend ant calculus find a subject more worthy or more rich. Whatever progress is made in it, the first discoverer will always retain his rank. Accordingly, M. la Grange, who cites him often as the greatest genius that ever existed, adds also, " and the most fortunate. We do not find every day a system of the world to establish." It has required 100 years of labours and discoveries to raise the edifice of which Newton laid the foundation. But every thing is ascribed to him, and we suppose him to have traversed the whole country upon which he merely entered.
Many mathematicians doubtless employed themselves on the theorems of Fermat; but none had been success ful. Euler alone had penetrated into that difficult road in which M. Legendre and M. Gauss afterwards signalized themselves. M. la Grange, in demonstrating or rectify ing sonic opinions of Euler, resolved a problem which appears to be the key of all the others ; and from which he deduced a useful result ; namely, the complete resolu tion of equations of the second degree, with two indeter initiates, which must be whole numbers.
This memoir, printed like the preceding, among those of the Turin Academy, is notwithstanding dated B rlin, the 20th September 1768. This date points out to us one of the few events which render the life of La Grange not entirely a detail of his writings.
His stay at Turin was not agreeable to him. He saw no person there who cultivated the mathematics with suc cess. He was impatient to see the philosophers of Pal is, with whom' he corresponded. M. de Caraccioli, with whom he lived in the greatest intimacy, was appointed ambassador to London, and was to pass through Paris on his way, where he intended to spend some time. He pro posed this journey to M. la Grange, who consented to it with joy, and who was received as he had a right to expect by D'Alembert, Clairaut, Condorcet, Fontaine, Nollet, Marie, and the other philosophers. Falling dangerously ill after a dinner in the Italian style given him by Nollet, he was not able to accompany his friend to London, who had received sudden orders to repair to his post, and who was obliged to leave hint in a furnished lodging, under the care of a confidential person charged to provide every thing.
This incident changed his projects. He thought only
of returning to Turin. He devoted himself to the mathe matics with new ardour, when he understood that the Academy of Berlin was threatened with the loss of Euler, who thought of returning to Petersburgh. D'Alembert speaks of this project of Euler, in a letter to Voltaire, dated the 3d March 1766: " I shall be sorry for it," says he ; " he is a man by no means amusing, but a very great mathematician." It was of little consequence to D'Alem bert, whether this man, by no means amusing, went seven degrees nearer the pole. He could read the works of the great mathematician as well in the Petersburgh Memoirs as in those of Berlin. What troubled D'Alembert was the fear of seeing himself called upon to tilt his place, and the difficmty of giving an answer to offers which he was determined riot to accept. Frederick in fact offered him again the place of president of his Academy, which he had kept in reserve for him ever since the death of Maupertuis. D'Alembert suggested the idea of patting La Grange in the place of Euler; and, if we believe the author of the Secret History of the Court of Berlin, (vol. ii. p. 414,) Euler had already pointed out La Grange as the only man capable of filling his place. In fact, it was na tural that Euler, who wished to obtain permission to leave Berlin, and D'Alembert, who wanted a pretext not to go there, should both of them, without any communication, have cast their eyes on the man who was best fitted to maintain the eclat, which the labours of Euler had thrown round the Berlin Academy.
La Grange was pitched upon. He received a pension of 1500 Prussian crowns, about 250/., with the title of Di rector of the Academy for the Physico-mathematical Sci ences. We may be surprised that Euler and La Grange, put successively in the place of Maupertuis, received only the half of his salary, which the king offered entire to D'Alembert. The reason is, that this prince, who at his leisure hours cultivated poetry and the arts, had 110 idea of the sciences, though he considered himself obliged to protect them as a king. He had very little respect for the mathematics, against which he wrote three pages in verse, and sent them to D'Alembert himself, who deferred wri ting an answer till the termination of the siege of Schweid nitz; because he thought it would be too much to have both Austria and the mathematics on his hands at once. Notwithstanding the prodigious reputation of Euler, we see, from the king's correspondence with Voltaire, that he gave him no other appellation than his narrow-minded geometer, whose ears were not capable of feeling the deli cacy of poetry. To which Voltaire replies : We are a small number of adepts who know one another : the rest are profane. .We see that Voltaire, who had written so well in praise of Newton, endeavours in this place to flatter Frederick. He enters out of complaisance into the ideas of this prince, who wished to put at the head of his aca demy, a man who had at least some pretensions to litera ture. Fearing that a mathematician would not take suffi cient interest in the direction of literary labours, and that a man of literature would have been still worse placed at the head of a society composed in part of philosophers, of whose language he was ignorant; on that account he divided the situation, and put two persons in it, that it might be completely filled.