Lancret, Michel Ange

(b. Paris, France, 15 December 1774; d. Paris, 17 December 1807)

differential geometry, topography, architecture.

Son of the architect François Nicolas Lancret—who was the son of an engraver and nephew of the painter Nicholas Lancret—and Germaine MArguerite Vinache de Mountblain, the daughter of a sculptor, Michel Ange Lancret was initiated into the plastic arts and architecture at a very early age. He entered the école des Ponts et Chaussées in 1793 and was sent as a student to the port of Dunkerque. Admitted on 21 November 1794 to the first graduating class of the École Polytechnique (at that time the école Centrale des Travaux Publics), he studied there for three years and, along with twenty-four of his fellow students—including J. B. Biot and E.-L. Malus—he served as monitor. After several months of specialization Lancret was named engineer of bridges and highways in April 1798, and in this capacity he was made a member of the Commission of Arts and Sciences attached to the Egyptian expedition. He reached Egypt on 1 July 1798 and was entrusted with important topographical operations, irrigation projects, and canal maintenance, as well as with archaeological studies, the description of the ancient monuments of the Upper Kingdom, and entomological studies.

On 4 July 1799 Lancret was named a member of the mathematics section of the Institut d’éypte, where he presented several memoirs on his topographical work and communications from others, including one on the discovery of the Rosetta stone (19 July 1799) and Malus’s first memoir on light (November 1800). Sent home at the end of 1801, he was soon appointed secretary of the commission responsible for the Description de l’Egypte, eventually succeeding Nicolas Conté as the official representative of the government in December 1805. The author of several memoirs on topography, architecture, and political economy, and of numerous drawings of monuments, he devoted himself passionately to this editorial assignment while continuing to do research in infinitesimal geometry.

In his first memoir on the theory of space curves, presented in April 1802, Lancret cites and unpublished theorem of Fourier’s on the relationships between the curvature and torsion of a curve and the corresponding elements of the cuspidal edge of its polar curve. In addition he studied the properties of the rectifying surface of a curve and integrated the differential equations of its evolutes. In a second memoir (December 1806) he developed the theory of “développoÏdes,” cuspidal edges of developable surfaces with pas through a given curve and whose generating lines make a constant angle with this curve.

Although limited in extent, this work places Lancret among the most direct disciples of Monge in infinitesimal geometry.

BIBLIOGRAPHY

I. Original Works. Lancret’s writings on Egypt appeared in the collection Description de l’égypte: “Description de l’Ile de Philae,” in no. 1, Antiquityé. Descriptions, I (Paris, 1809), 1–60; “Mémoire sur le systéme d’imposition territoriale et sur l’administration des provinces de l’égypte dans les derniéres années du gouvernement des Mamlouks,” in no. 71, état moderne, I (Paris, 1809), 233–260; “Notice sur la branche Canoptique,” in no. 46, Antiquité. Mémoires, I (Paris, 1809), 251–254; “Mémoire sur le canal d’Alexandrie,” in no. 90, Eétat moderne, II (Paris, 1812), 185–194, written with F.-J. C. de Chabrol, previously pub. in La décade égyptienne, II (Cairo, 1799–1800), pp. 233–251; “Notice topographique sur la partie de l’égypte comprise entre Rahmánich et Alexandrie et sur les environs du lac Maréotis,” in no. 100, état moderne, II (Paris, 1812), 483–490, written with Chabrol; and “Description d’Héliopolis,” in no, 28, Antiquité. Descriptions, II (Paris, 1818), 1–18, written with J. M. J. Dubois-Aymé. Architectural illustrations are in Antiquité. Descriptions, I, II, III, and V.

His mathematical writings include “Mémoire sur les courbes à double courbure,” in Mémoires présentés par divers savants …, 2nd ser., 1 (1806), 416–454, an extract of which had appeared in Correspondance sur l’école polytechnique, 1 , no. 3 (Jan.-Feb. 1805), 51–52; and “Mémoire sur les développoÏdes des courbes à double courbure et des surface développables,” ibid., 2 (1811), 1–79, extracts in Nouveau Bulletin des Sciences par la Société philomatique de Paris, 2nd series, 1 (1807), issues 56 and 57, and in Correspondance sur l’école polytechnique, 3 , no. 2 (May 1815), 146–149.

II. Secondary Literature. These are only a few brief and incomplete accounts of LAncret’s life: G. Guémard, in Bulletin de l’Institut d’égypte, 7 (1925), 89–90; J. P. N. Hachette, in Correspondance sur l’Eécole polytechnique, 1 , no. 9 (Jan. 1808), 374; A. Jal, in Dictionnaire critique de biographie et d’histoire (Paris, 1872), pp. 734–735; A. de Lapparent, in école polytechnique, livre du centenaire, I (Paris, 1895), 91–92; A. Maury, in Michaud’s Biographie universelle, new ed., XXIII (Paris, n.d.), 137–138; and F. P. H. Rarbé de Saint-Hardouin, in Notices biographiques sur les ingénieurs des Ponts et Chaussées … (Pairs, 1884), pp. 123–124.

His mathematical work, on the other hand, has been analyzed quite thoroughly by M. Chasles, Rapport sur les progrés de la géométrie (Paris, 1870), pp. 10–13; J. L. Coolidge, A History of Geometrical Methods (Oxford, 1940), p. 323; N. Nielsen, Géométres français sous la Révolution (Copenhagen, 1929), pp. 155–157; M. d’Ocagne, Historie abrégée des sciences mathématiques (Paris, 1955), 199; and R. Taton, L’oeuvre scientifique de Gaspard Monge (Paris, 1951), see index.

RenÉ Taton