PHILIP DE LA, one of the most laborious and most useful of the French geometricians, was born at Paris in the year 1640. His father, who was painter to the king, designed to bring up his son to the same profession, and with this view taught him drawing and such parts of the mathematics as are intimately connected with it. At the age of twenty he visited Italy to enlarge his knowledge of his favourite art, and resided in that country about four years. But the study of the mathematics, which he continued to prosecute on his return to his native city, afterwards engaged his whole attention; and the publication of some works having procured him a high reputation, he was chosen a member of the Academy of Sciences in the year 1678. When the minister Colbert conceived the design of constructing a better map of France than any at that time to be met with, Lahire was nominated, in conjunction with Picard, to make the necessary observations; and this engaged his attention for some years in the different provinces. In the year 1683 he was employed in continuing the meridian line which had been commenced by Picard in 1669. He continued it from Paris towards the north, whilst Cassini carried it on towards the south; but on the death of Colbert, which happened the same year, the work was discontinued. He was afterwards employed, in conjunction with other eminent philosophers, in taking the necessary levels for the grand aqueducts about to be constructed by Louis XIV. The works published by Lahire are very numerous; and as he was professor of the Royal College and Academy of Architecture, he must have been constantly employed. He had the circumspection and prudence of an Italian, which made him appear reserved in the estimation of his versatile countrymen, yet he was regarded by all as an honest and disinterested man. Lahire died in the year 1718, at the advanced age of seventy-eight. His principal works are, 1. Nouvelle Méthode de Géométrie pour les Sections des Superficies Coniques et Cylindriques, Paris, 1673, in 4to; 2. De Cycloide Opusculum, ibid. 1676, in 4to; 3. Nouveaux Éléments des Sections Coniques, les Lieux Géométriques, la construction ou affection des Equations, ibid. 1679, in 12mo; 4. La Gnomonique, ou l'art de tracer des cadran, ibid. 1682, in 12mo; 5. Sections Coniques, in ix. libros distributa, ibid. 1685, in folio; 6. Tabula Astronomica, Ludovici Magni jussu et munificentia exarata, ibid. 1702, in 4to; 7. L'École des Arpenteurs, avec un Abrégé du Nivelllement, Paris, 1689, in 8vo, reprinted in 1692 and in 1728; 8. Traité de Mécanique, où Pon explique tout ce qui est nécessaire dans la pratique des Arts, ibid. 1675, in 12mo; 9. A great number of Mémoires, in different journals, and in the Collection of the Academy. Lahire was besides the editor of the Traité du Nivelllement by Picard; of the Traité du Mouvement des Eaux by Mariotte, and joint editor with Boivin and Thévenot of the Vetores Mathematici Graec. et Latin. 1693, in folio.