VARIGNON (Peter)

, a celebrated French mathematician and priest, was born at Caen in 1654, and died suddenly in 1722, at 68 years of age. He was the son of an architect in middling circumstances, but had a college education, being intended for the church. An accident threw a copy of Euclid's Elements in his way, which gave him a strong turn to that kind of learning. The study of geometry led him to the works of Des Cartes on the same science, and there he was struck with that new light which has, from thence, spread over the world.

He abridged himself of the necessaries of life to purchase books of this kind, or rather considered them of that number, as indeed they ought to be. What contributed to heighten this passion in him was, that he studied in private: for his relations observing that the books he studied were not such as were commonly used by others, strongly opposed his application to them. As there was a necessity for his being an ecclesiastic, he continued his theological studies, yet not entirely sacrificing his favourite subject to them.

At this time the Abbé St. Pierre, who studied philosophy in the same college, became acquainted with him. A taste in common for rational subjects, whether physics or metaphysics, and continual disputations, formed the bonds of their friendship. They were mutually serviceable to each other in their studies. The Abbé, to enjoy Varignon's company with greater ease, lodged him with himself; thus, growing still more sensible of his merit, he resolved to give him a fortune, that he might fully pursue his genius, and improve his talents; and, out of only 18 hundred livres a year, which he had himself, he conferred 300 of them upon Varignon.

The Abbé, persuaded that he could not do better than go to Paris to study philosophy, settled there in 1686, with M. Varignon, in the suburbs of St. Jacques. There each studied in his own way; the Abbé applying himself to the study of men, manners, and the principles of government; 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 that a long application might occasion. He left off gay <*>d lively, filled with pleasure, and impatient to renew it. In speaking of mathematics, 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 la 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 himself known to the public by a Treatise on New Mechanics, dedicated to the Academy of Sciences. His thoughts on this subject were, in effect; quite new. He discovered truths, and laid open their sources. In this work, he demonstrated the necessity of an equilibrium, in such cases as it happens in, though the cause of it is not exactly known. This discovery Varignon made by the theory of compound motions, and is what this essay turns upon.

This new Treatise on Mechanics was greatly admired by the mathematicians, and procured the author two considerable places, the one of Geometrician in the Academy of Sciences, the other of Professor of Mathematics in the College of Mazarine, to which he was the first person raised.

Varignon catched eagerly at the Science of Infinitesimals as soon as it appeared in the world, and became one of its most early cultivators. When that sublime and beautiful method was attacked in the Academy it- | self (for it could not escape the fate of all innovations) he became one of its most zealous defenders, and in its favour he put a violence upon his natural character, which abhorred all contention. He sometimes lamented, that this dispute had interrupted him in his enquiries into the Integral Calculation so far, that it would be difficult for him to resume his disquisition where he had left it off. He sacrificed Infinitesimals to the interest of Infinitesimals, and gave up the pleasure and glory of making a farther progress in them when called upon by duty to undertake their defence.

All the printed volumes of the Academy bear witness to his application and industry. His works are never detached pieces, but complete theories of the laws of motion, central forces, and the resistance of mediums to motion. In these he mak<*> such use of his rules, that nothing escapes him that has any connection with the subject he treats.

Geometrical certainty is by no means incompatible with obscurity and confusion, and those are sometimes so great, that it is surprising a mathematician should not miss his way in so dark and perplexing a labyrinth. The works of M. Varignon never occasion this disagreeable surprise, he makes it his chief care to place every thing in the clearest light; he does not, as some great men do, consult his ease by declining to take the trouble of being methodical, a trouble much greater than that of composition itself; he does not endeavour to acquire a reputation for profoundness, by leaving a great deal to be guessed by the reader.

He was perfectly acquainted with the history of mathematics. He learned it not merely out of curiosity, but because he was desirous of acquiring knowledge from every quarter. This historical knowledge is doubtless an ornament in a mathematician, but it is an ornament which is by no means without its utility. Indeed it may be laid down as a maxim, the more different ways the mind is occupied in, upon a subject, the more it improves.

Though Varignon's constitution did not seem easy to be impaired, assiduity and constant application brought upon him a severe disease in 1705. Great abilities are generally dangerous to the possessors. He was six months in danger, and three years in a languid state, which proceeded from his spirits being almost entirely exhausted. He said that sometimes when delirious with a fever, he thought himself in the midst of a forest, where all the leaves of the trees were covered with algebraical calculations. Condemned by his physicians, his friends, and himself, to lay aside all study, he could not, when alone in his chamber, avoid taking up a book of mathematics, which he hid as soon as he heard any person coming. He again resumed the attitude and behaviour of a sick man, and seldom had occasion to counterfeit.

In regard to his character, Fontenelle observes, that it was at this time that a writing of his appeared, in which he censured Dr. Wallis for having advanced that there are certain spaces more than infinite, which that great geometrician ascribes to hyperbolas. He maintained, on the contrary, that they were finite. The criticism was softened with all the politeness and respect imaginable; but a criticism it was, though he had written it only for himself. He let M. Carré see it, when he was in a state that rendered him indifferent about things of that kind; and that gentleman, influenced only by the interest of the sciences, caused it to be printed in the memoirs of the Academy of Sciences, unknown to the author, who thus made an attack against his inclination.

He recovered from his disease; but the remembrance of what he had suffered did not make him more prudent for the future. The whole impression of his Project for a New System of Mechanics, having been sold off, he formed a design to publish a second edition of it, or rather a work entirely new, though upon the same plan, but more extended. It must be easy to perceive how much learning he must have acquired in the interval; but he often complained, that he wanted time, though he was by no means disposed to lose any. Frequent visits, either of French or of foreigners, some of whom went to see him that they might have it to say that they had seen him; and others to consult him and improve by his conversation: works of mathematics, which the authority of some, or the friendship he had for others, engaged him to examine, and which he thought himself obliged to give the most exact account of; a literary correspondence with all the chief mathematicians of Europe; all these obstructed the book he had undertaken to write. Thus a man acquires reputation by having a great deal of leisure time, and he loses this precious leisure as soon as he has acquired reputation. Add to this, that his best scholars, whether in the College of Mazarine or the Royal College (for he had a professor's chair in both), sometimes requested private lectures of him, which he could not refuse. He sighed for his two or three months of vacation, for that was all the leisure time he had in the year; no sooner were they come but he retired into the country, where his time was entirely his own, and the days seemed always quickly ended.

Notwithstanding his great desire of peace, in the latter part of his life he was involved in a dispute. An Italian monk, well versed in mathematics, attacked him upon the subject of tangents and the angle of contact in curves, such as they are conceived in the arithmetic of infinites; he answered by the last memoir he ever gave to the Academy, and the only one which turned upon a dispute.

In the last two years of his life he was attacked with an asthmatic complaint. This disorder increased every day, and all remedies were ineffectual. He did not however cease from any of his customary business; so that, after having finished his lecture at the College of Mazarine, on the 22d of December 1722, he died suddenly the following night.

His character, says Fontenelle, was as simple as his superior understanding could require. He was not apt to be jealous of the fame of others: indeed he was at the head of the French mathematicians, and one of the best in Europe. It must be owned however, that when a new idea was offered to him, he was too hasty to object. The sire of his genius, the various insights into every subject, made too impetuous an opposition to those that were offered; so that it was not easy to obtain from him a favourable attention.

His works that were published separately, were,

1. Projet d'une Nouvelle Mechanique; 4to, Paris 1687. |

2. Des Nouvelles Conjectures sur la Pesanteur.

3. Nouvelle Mechanique ou Statique, 2 tom. 4to, 1725.

As to his memoirs in the volumes of the Academy of Sciences, they are far too numerous to be here particularized; they extend through almost all the volumes, down to his death in 1722.

VASA Concordiæ, in Hydraulics, are two vessels, so constructed, as that one of them, though full of wine, will not run a drop, unless the other, being full of water, do run also. Their structure and apparatus may be seen in Wolsius, Element. Mathes. tom. 3, Hydraul.