Lalouvère, Antoine De

(b. Rieux, Haute-Garonne, France, 24 August 1600; d. Toulouse, France, 2 September 1664)

mathematics.

Lalouvére is often referred to by the Latin form of his name, Antonius Lalovera. Such a use avoids the problem of known variants; for example, Fermat wrote to CArcavi, on 16 February 1659, that the mathematician had a nephew who called himself Simon de La Loubé. Whatever the spelling, the family was presumably noble, since a chāteau near Rieux bears their name.

Lalouvére himself became a Jesuit, entering the order on 9 July 1620, at Toulouse, where he was later to be professor of humanities, rhetoric, Hebrew, theology, and mathematics. The general of the order was at that time Guldin, a mathematician who may be considered, along with Cavalieri, Fermat, Vincertio, Kepler, Torricelli, Valerio—and indeed, Lalouvére—one of the precursors of modern integral calculus. That lalouvére was on friendly terms with Fermat is evident in a series of letters; he further maintained a close relationship with Pardies in France and Wallis in England. His mathematics was essentially conservative; while modern analysis was alien to him he was expert in the work of the Greeks, the Aristotelian-Scholastic tradition, and the commentators of antiquity. He depended strongly upon Archimedes.

Lalouvére’s chief book is the Quadratura circuli, published in 1651, in which he drew upon the work of Charles de La Faille, Guldin, and Vincetio. His method of attack was an Archimedean summation of areas; he found the volumes and centers of gravity of bodies of rotation, cylindrical ungulae, and curvilinearly defined wedges by indirect proofs. He was then able to proceed by inverting Guldin’s rule whereby the volume of a body of rotation is equal to the product of the generating figure and the path of its center of gravity. Thus, Lalouvére established the volume of the body of rotation and the center of gravity of its cross section; then by simple division he found hte volume of the cross section.

By the time he published this work, lalouvére was teaching Scholastic theology rather than mathematics, and believed that he had reached his goals as a mathematician. Indeed, he stated that he preferred to go on to easier tasks, more suited “to my advanced age.” Nonetheless, he was drawn into the dispute with Pascal for which his name is best known.

In June 1658, Pascal made his conclusions on cycloids the subject of an open competition. The prize was able to be sixty Spanish gold doubloons, and solutions to the problems he set were to be submitted by the following 1 October. Lalouvére’s interest was attracted by the nature of the problems, rather than by the prize, and Fermat transmitted them to him on 11 July. Lalouvére returned his solutions to Pascal’s first two problems only ten days later, having reached them by simple proportions rather than by calculation. The calculation of the volumes and centers of gravity of certain parts of cycloids and of the masses formed by their rotation around an axis was central to Pascal’s problems, however; he did not accept Lalouvére’s solutions, and Lalouvére himself later discovered and corrected an error in computation (although another remained undetected). The matter might have ended there had not Pascal, in his Histoire de la roulette, accused Lalouvére (without naming him) of plagiarizing his solutions from Roberval. Pascal’s allegations were without foundation; Lalouvére asserted that he had reached all his conclusions independently, and became embittered, while Fermat, who might have helped to resolve the quarrel, chose instead to remain neutral. A second, incomplete solution to Pascal’s problems was submitted by Wallis, and on 25 November 1658 the prize committee decided not to give award to anyone.

Having returned to mathematics, Lalouvére went on to deal with bodies in free fall and the inaccuracies of Gassendi’s observations in Propositiones geometricae sex (1658). He returned to problems concerning cyclodis—including those posed by Pascal—in 1660, in Veterum geometria promota in septem de cycloide libris. In addition to these publications, Lalouvére maintained an active correspondence on mathematical subjects, several of his letter to Pascal being extant. Two of his letters to D. Petau may be found in the latter’s Petavii orationes; the same work contains Petau’s refutation of Lalouvére’s views on the astronomical question of the horizon and calculation of the calendar.

Lalouvére’s work, rooted firmly in that of the ancients, was not innovative; nevertheless, he showed himself to be a man of substantial knowledge and clear judgement. He was a tenacious worker with a great command of detail. Montucla thought his style sufficient to keep “the most intrepid reader from straying.”

BIBLIOGRAPHY

I. Original Works. Lalouvére’s writings are Quadratura circuli et hyperbolae segmentorum ex dato eorum centro gravitatis … (Toulouse, 1651); Propostitiones geometricae sex quibus ostenditur ex carraeciana hypothesi circa proportionem, qua gravia decidentia accelerantur … (Toulouse, 1658); Propositio 36^α excerpta ex quarto libro de cycloide nondum edito (Toulouse, 1659); Veterum geometria promota in septem de cycloide libris (Toulouse, 1660), which has an appendix Fermat’s “De limarum curvarum cum lineis rectis comapartione dissertation geometrica “and De cycloide Galilei et Torricelli propositiones viginti (n.p., n.d.).

Works apparently lost are “Tractatus de principiis librae” and “De communi sectione plani et turbinatate superficiei ex puncto quiescente a linea recta per ellipsim …,” both mentioned by Lalouvére in his works; and “Opusculum de materia probablie” and “Explicatio vocum geometricarum …,” mentioned by Collins in a letter to Gregory of 24 Mar. 1671 (or 1672).

A reference to several letters to D. Petau (1631–1644) at Tournon and Toulouse may be found in Poggendorff, II, col. 412.

Two letters from Petau to Lalouvé are in Dionysii Petavii, Aurelian Society of Jesus Orations (Paris, 1563).

II. Secondary Literature. On Lalouvére or his work, see A. de Backer and C. Sommervogel, eds., Bibliothéque de la Compagnie de Jesus, V (Brussels—Paris, 1894), cols. 32–33; Henry Bosmans, in Archives internationales d’histoire des sciences, 3 (1950), 619–656; Pierre Costabel, in Revue d’histoire des sciences et de leurs applications, 15 (1962), 321–350, 367–369; James Gregory, Tercentenary Memorial Volume, Herbert Turnball, ed. (London, 1839), p. 225; Gerhard Kropp. De quadratura circuli et hyperholae segmentroum des Antonii de Lalouvére, thesis (Berlin, 1944), contains a long list of secondary literature; J. E. Montucla, Histoire des mathématiques, II (Paris, 1758), 56–57; and P. Tannery, “PAscal et Lalouvére,” in Memoires de la Société des sciences physiques et naturelles de Bordeaux 3rd ser., 5 (1890), 55–84.

Herbert Oettel