Proportiones. Gaspar LAX.

A Spanish Mathematician in Paris


Title within ornate woodcut architectural border. Woodcut printer’s device on title. 26 unnumbered leaves. Small folio, cont. pigskin-backed wooden boards, spine & boards stamped in blind, orig. brass catches on upper cover, one (of two) orig. clasps. Paris: N. de La Barre for E. Le Fevre, 6 October 1515.

[bound with]:

—. Arithmetica Speculativa…duodecim libris demonstrata. Title within ornate woodcut architectural border which is printed in red & black. Woodcut printer’s device on title. Several woodcuts in the text. 100 unnumbered leaves. Small folio (some foxing). Paris: N. de La Barre for E. Le Fevre, 18 December 1515.

First edition of two very uncommon mathematical works, printed in Paris. “After studying the arts and theology in Zaragoza, Lax (1487-1560), taught in Paris…Lax had an agile mind and an excellent memory, but he became so engrossed with the logical subtleties of the nominalist school that he was soon known as ‘the Prince of the Parisian sophistae’…Lax taught at Paris until 1523…In 1525 he taught mathematics and philosophy at the studium generale of Zaragoza. He remained there until his death, at which time he was vice-chancellor and rector…

“Lax achieved greater fame as a mathematician than as a logician or as a philosopher. He published his Arithmetica speculativa and Proportiones at Paris in 1515…The first is described by D.E. Smith as a ‘very prolix treatment of theoretical arithmetic, based on Boethius and his medieval successors’ (p. 121). The Proportiones is a more compact and formalistic treatment of ratios, with citations of Euclid, Jordanus, and Campanus; unlike most sixteenth-century treatises on ratios, however, it does not deal with the velocities of motion in the Mertonian and Parisian traditions.”–D.S.B., VIII, p. 100.

These two works of Lax are bound with three other unrelated (apart from size and date) but interesting and scarce books:

1. Agricola, Rudolphus. Dialectica. Louvain: T. Martens, January 1515. Second edition of his masterwork, in which he describes how he taught a deaf child to communicate orally and in writing. It is a pioneering work in education.

2. Alciati, Andrea. In tres posteriores Codicis Iustiniani annotationes. Strasbourg: J. Schott, 1515. First edition of an uncommon legal work.

3. Hilarius Pictaviensis, Saint. Opera complura. Paris: Jodocus Badius, 1510. The first collected edition of the writings of Saint Hilary (ca. 315-ca. 368), bishop of Poitiers, and an outspoken champion of orthodoxy against the Arians.

Fine and complete copies.

❧ Lax: Moreau, II, 1153 & 1154. Smith, History of Mathematics, I, p. 345. Smith, Rara Arithmetica, pp. 121-22.

Price: $22,500.00

Item ID: 5253

See all items by