[2] Upon his return to Paris, he became a disciple of Girard Desargues from whom he learned geometrical perspective[2] and was received as a master painter on 4 August 1670.

He was taught by the French Jesuit theologian, mathematician, physicist and controversialist Honoré Fabri and became part of a circle formed by Fabri which included Giovanni Domenico Cassini, Claude François Milliet Dechales, Christiaan Huygens and his brother Constantijn, Gottfried Leibniz, René Descartes and Marin Mersenne.

[4] He became a member of French Academy of Sciences in 1678, upon the death of Jacques Buot, and subsequently became active as an astronomer, calculating tables of the movements of the Sun, Moon, and planets and designing contrivances for aiming aerial telescopes.

[5] From 1679–1682 he made several observations and measurements of the French coastline,[6] and in 1683 aided in mapping France by extending the Paris meridian to the north.

La Hire wrote on graphical methods, 1673; on conic sections, 1685; a treatise on epicycloids, 1694; one on roulettes, 1702; and, lastly, another on conchoids, 1708.