Ciruelo, Pedro

also known asPedro Sánchez Ciruelo (b. Daroca, Spain, 1470; d. Salamanca [?], Spain, 1554), mathematics, logic, natural philosophy.

Ciruelo learned logic and arts at Salamanca during the latter part of the fifteenth century, then proceeded to the University of Paris to complete his education. He studied theology there from 1492 to 1502, supporting himself by “the profession of the mathematical arts.” In 1495 he published at Paris a treatise on practical arithmetic, Tractatus arithmeticae practicae, that went through many subsequent printings; in the same year he also published revised and corrected editions of Bradwardine’s Arithmetica speculativa and Geometria speculativa that enjoyed a similar success. Dating from this same period are Ciruelo’s editions of the Sphere of Sacrobosco, including the questions of Pierre d’Ailly (Élie cites editions of 1494, 1498, and 1515; Villoslada mentions others of 1499, 1505, and 1508 under a modified title). By 1502 Ciruelo was teaching mathematics at Paris; presumably he continued this career until about 1515, when he returned to Spain, attracted to the newly founded University of Alcalá.

At Alcalá, Ciruelo taught the theology of Aquinas; among his students was the young Domingo de Soto. Ciruelo maintained an interest in mathematics and philosophy, however, and in 1516 published his Cursus quatuor mathematicarum artium liberalium; this included a paraphrase of Boethius’ Arithmetica, “more clearly and carefully edited than that of Thomas Bradwardine”; a brief compendium of Bradwardine’s geometry, “with some additions”; another short compendium of John Peckham’s Perspectiva communis, “to which also have been added a few glosses”; a treatise on music; and two short pieces on squaring the circle, both of which he recognized as defective. The Cursus appeared at both Paris and Alcalá, being reprinted at Alcalá in 1518 and in both places in 1523, 1526, and 1528. At Alcalá, Ciruelo also published his edition of the Apotelesmata astrologiae christianae in 1521 and a new edition of the Sphere in 1526. He transferred to the University of Salamanca some time after this; his first work to be published there was a Summulae (1537) that is a more mature treatment of logic than his Prima pars logices (Alcalá, 1519). Also published at Salamanca was his Paradoxae quaestiones (1538), two questions on logic, three on physics, and five on metaphysics and theology; these contain his somewhat singular views on gravity and impetus and his criticisms of the Jewish cabala, particularly as evaluated by Giovanni Pico della Mirandola.

BIBLIOGRAPHY

Ciruelo’s works are listed and appraised in fragmentary fashion in the following: Vicente Muñoz Delgado, O. M., “La lógica en Salamanca durante la primera mitad del siglo XVI,” in Salmanticensis, 14 (1967), 171–207, esp. 196–198 (logic); 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. 236–237 (general); J. Rey Pastor, Los matemáticos españoles delsiglo XVI (Toledo, 1926), pp. 54–61 (mathematics): David E. Smith, Rara arithmetica (Boston-London, 1908), see index; Lynn Thorndike, The Sphere of Sacrohosco and Its Commentators (Chicago, 1949), see index: and R. G. Villoslada, S. J., La universidad de Paris durante los estudios de Francisco de Vitoria (1507–1522), Analecta Gregoriana, no. 14 (Rome, 1938), pp. 402–404, passim (general).

William A. Wallace, O. P.