Lax, Gaspar

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Lax, Gaspar

(b. Sariñena, Aragon, Spain, 1487; d. Zaragoza, Spain, 23 February 1560)

mathematics, logic, natural philosophy.

After studying the arts and theology in Zaragoza, Lax taught in Paris in 1507 and 1508 at the Collége de Calvi, also known as the “Little Sorbonne.”He transferred to the Collège de Montaigu, where he continued to teach and to study under the Scottish master John Maior; in 1517 he returned to the Collège de Calvi. 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.” A prolific writer, he turned out a series of ponderous tomes on exponibilia, insolubilia, and other topics of terminist logic. His student, the humanist Juan Luis Vives, later reported that he heard Lax and his colleague, John Dullaert of Ghent, moan over the years they had spent on such trivialities. Lax taught at Paris until 1523; possibly he returned to Spain in 1524, along with his countryman Juan de Celaya, when foreigners were asked to leave the university. 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 (Villoslada adds to these a De propositionibus arithmeticis, same place and date). 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. Possibly Lax treated this interesting topic in his Quaestiones phisicales, printed at Zaragoza, 1527, according to early lists. (I have searched extensively for this, with no success.)


None of Lax’s works is translated from the Latin, and copies of the originals are rare; positive microfilms of the Arithmetica speculativa and various logical works are obtainable from the Vatican Library.

A brief general treatment of Lax is in R. G. Villoslada, S. J., La universidad de Paris durante los estudios de Francisco de Vitoria (1507-1522), Analecta Gregoriana XIV (Rome, 1938), pp. 404-407 and passim. See also Hubert Élie, “Quelques maîtres de l’université de Paris vers l’an 1500,”in Archives d’histoire doctrinale et littéraire du moyen âge,18 (1950-1951), 193-243, esp. 214-216.

Lax’s logical and philosophical thought is treated by Marcial Solana, Historia de la filosofia española, Época del Renacimiento (siglo XVI) (Madrid, 1941), III, 19-33. His arithmetic is described in D. E. Smith, Rara arithmetica (Boston-London, 1908), p. 121.

William A. Wallace, O.P.