VARIGNON (Prrsa,) in biography, was born at Caen in 1654. He was the son of an architect, and intended at an early age for the church. Accident threw into his way a copy of Euclid's Elements, which gave him a strong bias towards mathematical learning. So intent was he in the pursuit of science, that he abridged himself of the necessaries of life, to pur chase books to aid him in the pursuit. From his relations he met with much op position, because they imagined that geo metry and algebra would ill accord with the course of theological studies. While he was at college he became acquainted with the Abbe St. Pierre ; and in their application to learning, they were mutu ally serviceable to one another. The abbe, to enjoy more of Varignon's com pany, determined to lodge with him ; and sensible of his merit, he resolved to give him a fortune, that he might fully pursue the bent of his genius, and improve his talents ; and out of only 1800 livres a year, which he had himself, he conferred 300 of them upon Varignon.
The abbe, persuaded that he could not do better than go to Paris to study philo sophy, settled there in 1686, with M. Va rignon, in the suburbs of St. Jacques. There each studied in his own way ; the abbe applying himself to the study of men, manners, and the principles of go vernment ; whilst Varignon was wholly occupied with the mathematics.
" I," says Fontenelle, "who was their countryman, often went to see them, sometimes spending two or three days with them. They had also room for a couple of visitors, who came from the same province. We joined together with the greatest pleasure. We were young, full of the first ardour for knowledge, strongly united, and, what we were not then perhaps disposed to think so great a happiness, little known. Varignon, who had a strong constitution, at least in his youth, spent whole days in study, without any amusement or recreation, except walking sometimes in fine weather. I have heard him say, that in studying after supper, as he usually did, he was often surprised to hear the clock strike two in the morning ; and was much pleased that four hours rest were sufficient to refresh him. He did not leave his studies with that heaviness which they usually create ; nor with that weariness which a long ap plication might occasion. He left off gay and lively, filled with pleasure, and impa tient to renew it. In speaking of mathe matics, he would laugh so freely, that it seemed as if he had studied for diversion.
No condition was so much to be envied as his ; his life was a continual enjoyment, delighting in quietness." In the solitary suburb of St. Jacques he formed, however, a connection with many other learned men ; as Du Hamel, Du Verney, De Is Hire, &c. Du Verney often asked his assistance in those parts of anatomy connected with mechanics : they examined. together the positions of the muscles, and their directions ; hence Varignon learned a good deal of anatomy from Du Verney, which he repaid by the application of mathematical reasoning to that subject.
At length, in 1687, Varignon made him self known to the public by a treatise on new mechanics, dedicated to the Acade my of Sciences. His thoughts on the sub ject were, in effect, quite new. He dis covered truths, and laid open their sour ces. In this work he demonstrated the necessity of an equilibrium, in such cases as it happens in, though the cause of it is not exacly known. This discovery Varignon made by the theory of com pound motions, and is what this essay turns upon. This new treatise on mecha nics was greatly admired by the mathe maticians, and procured the author two considerable places, the one of geometri cian in the Academy of Sciences, the other of professor of mathematics in the college of Mazarine ; to this honout he was the first person raised.
Varignon catched eagerly at the sci ence of infinitesimals as soon as it appear ed in the world, and became one of its mostearly cultivators. Severe and unre mitted study injured his health very much, and in 1705 he had a dangerous illness, which confined him to his bed many months, and the effects of which he did not recover for three years. Indeed it can scarcely be said that he ever per fectly regained the vigour which he had formerly enjoyed. Ile could not lay aside his studies, and these were deemed in compatible with his health. Ile died in 1722: by Fontenelle he is described as an excellent man, not apt to be jealous of the fame of others ; he was as simple in Iris manners as his understanding was su perior. He was at the head of the French mathematicians, and one of the best in Europe. He was apt to be over hasty when a new object presented itself; and too impetuous towards those who oppos ed him. His works, which were published separately, were " Projet d'une ,nouvelle lvlechanique," 4to. " Des nouvelles Con jecture sur la Pesanteur." " Nouvelle Mechanique ou Statique." Besides a vast number of separate memoirs.