(Lewis), was, in 1663, born in the province of Brie in France; and refusing to enter into the service of the church, for which his education was intended to fit him, he incurred the displeasure of his father. His resources being thus cut off, he was obliged to quit the university, and go out into the world without employment or the means of subsistence. In this exigency he was somehow introduced to the celebrated Malebranche, and retained by him as an amanuensis. Under this great master he studied mathematics and metaphysics, and could hardly fail to become strongly attached to the latter science. After residing seven years with Malebranche, he resolved to enter upon some employment, which might procure him a less precarious establishment than what could be enjoyed by the favour of any individual: and with that view he began at Paris a course of lectures in mathematics, metaphysics, and moral philosophy, to such young ladies and gentlemen as chose to put themselves under his tuition. When we think of the master under whom he himself studied those sciences, we cannot wonder that he made geometry serve merely as an introduction to his beloved metaphysics; and indeed the order of his course deserves to be universally adopted. It is surely much better to accustom the youthful mind to steady apprehension and patient thinking in the study of the ancient geometry, before it proceed to sciences more abstract, than to hurry it at once, as is the practice in some universities, into all the maze and intricacies of what is called the first philosophy.

But although M. Carré gave the preference to metaphysics, he did not neglect mathematics; and while he taught both, he took care to make himself acquainted with all the new discoveries in the latter. This was all that his constant attendance on his pupils would allow him to do till the year 1697, when M. Varignon, so remarkable for his extreme scrupulousness in the choice of his elevés, took M. Carré to him in that station. Soon after, viz. in the year 1700, our author, thinking himself bound to do something that might render him worthy of that title, published the first complete work on the integral calculus, under the title of "A Method of Measuring Surfaces and Solids, and finding their Centres of Gravity, Percussion, and Oscillation." He afterwards discovered some errors in the work, and was candid enough to own and correct them in a subsequent edition.

In a little time M. Carré became associate, and at length one of the pensioners of the Academy. And as this was a sufficient establishment for one who knew so well how to keep his desires within just bounds, he gave himself up entirely to study; and as he enjoyed the appointment of mechanician, he applied himself more particularly to mechanics. He took also a survey of every branch relating to music; such as the doctrine of sounds, and the description of musical instruments; though he despised the practice of music as a mere sensual pleasure. Some sketches of his ingenuity and industry in this way may be seen in the Memoirs of the French Academy of Sciences. M. Carré also composed some treatises on other branches of natural philosophy, and some on mathematical subjects; all which he bequeathed. ed to that illustrious body, though it does not appear that any of them have yet been published. It is not unlikely that he was hindered from putting the last hand to them by a train of disorders proceeding from a bad digestion, which, after harassing him during the space of five or six years, at length brought him to the grave in 1711, at 45 years of age.

Though he possessed a considerable degree of science and much ingenuity, like many other eminent men he had neglected in his youth to study the language of his native country. In consequence of this, one of the earliest of his female pupils, perceiving that his language was the reverse of elegant, told him pleasantly, that as an acknowledgment for the trouble which he had taken to teach her philosophy, she would in return teach him French; and he ever afterwards said, that from her lessons he had reaped great advantage. To this circumstance probably it was owing that he thought more highly of the genius of women than that of men.

The following is a chronological list of his memoirs printed in the volumes of the Academy.

1. The rectification of curve lines by tangents, 1701. 2. Solution of a problem proposed to geometers, &c., 1701. 3. Reflections on the table of equations, 1701. 4. On the cause of the refraction of light, 1702. 5. Why the tides are always augmenting from Bretagne to St Malo, and diminishing along the coasts of Normandy, 1702. 6. The number and the names of musical instruments, 1702. 7. On the vinegar which causes small stones to roll upon an inclined plane, 1703. 8. On the rectification, &c., of the caustics by reflection, 1703. 9. Method for the rectification of curves, 1704. 10. Observations on the production of sound, 1704. 11. On a curve formed from a circle, 1705. 12. On the refraction of musket-balls in water, and on the refraction of that fluid, 1705. 13. Experiments on capillary tubes, 1705. 14. On the proportion of pipes to have a determinate quantity of water, 1705. 15. On the laws of motion, 1706. 16. On the properties of pendulums, with some new properties of the parabola, 1707. 17. On the proportion of cylinders, that their sounds may form the musical cords, 1709. 18. On the elasticity of the air, 1710. 19. On catoptries, 1710. 20. On the Monochord: in the Machinerie, tom. 1, with some other pieces, not mathematical.