Peletier, Jacques

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(b. Le Mans, France, 25 July 1517; d. Paris, France, July 1582)

mathematics, medicine.

Peletier was the ninth of fifteen children born to Pierre Peletier, a barrister in Le Mans, and Jeanne le Royer. His family, educated in theology, philosophy, and law, wanted him to pursue these diciplines. He therefore studied philosophy at the College de Navarre (Paris) and read law for five years in Le Mans. But when he became secretary in the late 1530’s to Rene du Bellay, bishop of Le Mans, he decided that his interests were not in philosophy or law.

In 1541 Peletier published L’art poëtique d’Horace, traduit en vers Françios, the preface of which pleaded for a national language, thus anticipating the ideas of the later Pleiade. He also studied Greek, mathematics, and later medicine, always as an autodidact. In 1543 he became rector of the Collège de Bayeux in Paris, a post that soon bored him. He therefore left Paris in 1547 and lived as a vagabond. Among the cities he visited were Bordeaux, Poitiers, Lyons, Paris, and Basel. Working alternately as a teacher in mathematics and as a surgeon, he devoted his life to poetry and science. Peletier shared with the Pleiade, a group of seven poets whose leader was Pierre de Ronsard, a desire to create a French literature. He also stated that French was the perfect instrument for the sciences and planned to publish mathematical books in the vernacular. Temporarily, however, he published only in Latin (1557–1572) because no one would accept his somewhat peculiar French orthography. Peletier’s poetry had scientific aspects, especially the second part of L’amour des amours (1555), in which he published descriptive-lyric verses on nature, natural phenomena, and astronomy which revealed the influence of Lucretius. He also published two minor works on medicine.

In 1545 Peletier published a short comment on Gemma Frisius’ Artihemticae practicae methodus facilis. In 1549 the Arithmetique appeared. In this work Peletier tried to satisfy both the theoretical requirements and the practical needs of the businessman. This topic had been previously discussed in Latin by C. Tunstall and Gemma Frisius, but Peletier was the first to combine both in a textbook in the vernacular. Peletier wrote L’algebre (1554) in French in his own orthographic style. In this work he adopted several orignial and ingenious ideas from stifel’s Arithmetica integra (1544) and showed himself to have been strongly influenced by Cardano. Peletier’s work presented the achievements already reached in Germany and Italy, and he was the first mathematician to see relations between coefficients and roots of equations.

In the In Euclidis elementa demonstrationum (1557) Peletier rejected the method of superposition as nongeometric. His arguments for this opinion, however, were used for the contrary view by Petrus Ramus. A long note on the angle of contact—in Peletier’s view not a finite quantity and not an angle at all—was the starting point for various disputes, especially with C. Clavius. This work was vehemently criticized by J. Buteo.

Translations into French or Latin and several reprints, especially of the French editions, indicate that Peletier’s works were quite successful. His other mathematical publications were devoted to such topics as the measurement of the circle, contact of straight lines and curves with curves, and duplication of the cube. The basic ideas in these publications often origniated in Peletier’s discussions with Buteo and Clavius.


I. Original Works. An incomplete bibliography of Peletier’s works is given by C. Jugé in Jacques Peletier du Mans (Paris, 1907). His major works include Arithmeticae practicae methodus facilis per Gemmam Frisium, huc accesserunt Peletarii annotationes (Paris, 1545), subsequent eds. between 1549 and 1557; L’arithmétique departie en quatre livres (Poitiers, 1549), with later eds. between 1552 and 1969; L’algebre departie en deus livres (Lyons, 1545; 3rd ed., 1620), with a Latin trans. as De occulta parte numerorum (Paris, 1560); In Euclidis elementa geometrica demonstrationum libri sex (Lyons, 1557; 2nd ed., Geneva, 1610), with a French trans. (Geneva, 1611); Commentarii tres, primus de dimensione circuli, secundus de contactu linearum, tertius de constitutione horoscopi (Basel, 1563), an ed. of the second part also appeared (Paris, 1581); Disquisitiones geometricae (Lyons, 1567); and In C. Clavium de contactu linearum apologia (Paris, 1579).

Peletier’s letter ad Razallium against Buteo was published at the end of De occulta parte numerorum. The In Euclidis elementa of 1573, mentioned by Juge, is not Peletier’s work but one of the many eds. “cum praefatione St. Gracilis.”

II. Secondary Literature. C. Juge (see above) provides a biography of Peletier. For works on his poetry, see A. Boulanger, L’art poetique de Jacques Peletier (Paris, 1830); Dictionnaire des lettres francaises, le seizieme siecle (Paris, 1951), 561–563; F. Letessier, “Un humaniste Manceau: Jacques Peletier (1517–1582),” in Letters d’humanité. Bulletin de l’Association Guillaume Bude, supp. 9 (1950), 206–263; H. Staub, Le curieux désir. Sceve et Peletier du Mans poetes de la connaissance (Geneva, 1967); and D. B. Wilson, “The Discovery of Nature in the Work of Jacques Peletier du Mans,” in Bibliotheque d’humanisme et renaissance, 16 (1954), 298–311. His contacts with the Pleiade are discussed by H. Chamard in Histoire de la Pleiade (Paris, 1961–1963), passim, and in L. C. Porter’s intro. to the repr. of Peletier’s Dialogue de l’ortografe e prononciation francoese (Poitiers, 1550; repr. Geneva, 1966).

Peletier’s mathematics is discussed by H. Bosmans, “L’algebre de J. Peletier du Mans,” in Revue des questions scientifiques, 61 (1907), 117–173, which uses the 1556 ed. of L’algebre; N. Z. Davis, “Sixteenth-century French Arithmetics on the Business Life,” in Journal of the History of Ideas, 21 (1960), 18–48; V. Thebault, “A French Mathematician of the Sixteenth Century: Jacques Peletier (1517–1582),” in Mathematics Magazine, 21 (1948), 147–150; M. Thureau, “J. Peletier, mathématicien manceau au XVIe siecle,” in La province du Maine, 2nd, sec., 15 (1935), 149–160 187–199; and J.J Verdonk, Petrus Ramus ed de wiskunde (Assen 1966) 264–268; on his contacts with P. Nunez, see Matos, Les Portugais en France au XVIe siecle (Coimbra, 1952), 123–125.

J.J Verdonk