La Roche, Estienne De

(fl. Lyons, France, ca. 1520),

arithmetic.

La Roche, known as Villefranche, was born in Lyons. A pupil of Nicolas Chuquet, he taught arithmetic for twenty-five years in the commercial center of his native town and was called “master of ciphers.”

La Roche’s Larismetique, published at Lyons in 1520, was long considered the work of an excellent writer who, early in the sixteenth century, introduced into France the Italian knowledge of arithmetic and useful notations for powers and roots. His fame decreased remarkably in 1880, when Aristide Marre published Chuquet’s “Triparty,” written in 1484 but preserved only in manuscript. The first part of Larismetique was then seen to be mostly a copy of the earlier work, with the omission of those striking features that established Chuquet as an algebraist of the first rank. Chuquet, for example, employed a more advanced notation for powers and he introduced zero as an exponent. It is not clear why La Roche failed to publish the “Triparty.” He may have suppressed it in order to claim the credit for himself, or perhaps he thought it too far beyond the comprehension of prospective readers. Nevertheless, through Larismetique some of Chuquet’s innovations influenced such French arithmeticians as Jean Buteo and Guillaume Gosselin.

The second, and greater, part of La Roche’s work has, apart from some geometrical calculations at the end, a commercial character. The author states that as a basis he used “the flower of several masters, experts in the art” of arithmetic, such as Luca Pacioli, supplemented by his own knowledge of business practice. The result was a good but traditional arithmetic that presented an outstanding view of contemporary methods of computation and their applications in trade.

BIBLIOGRAPHY

Larismetique nouellement composee par maistre Estienne de la Roche dict Villefranche natif de Lyon sur le Rosne divisée en deux parties … (Lyons, 1520) was republished as Larismetique et geometrie de maistre Estienne de la Roche dict Ville Franche, nouvellement imprimee et des faultes corrigee … (Lyons, 1538).

See M. Cantor, Vorlesungen über Geschichte der Mathematik, II (Leipzig, 1913), 371-374; and N. Z. Davis, “Sixteenth-Century French Arithmetics on the Business Life,” in Journal of the History of Ideas, 21 (1960), 18-48. On Chuquet and La Roche, see Aristide Marre, “Notice sur Nicolas Chuquet,” in Bullettino di bibligrafia e di storia delle scienze matematiche e fisiche, 13 (1880), esp. 569-580.

J. J. Verdonk