Antoine de Lalouvère

Background

Antoine de Lalouvère was born on August 24, 1600, in Rieux, Haute-Garonne, France, in an aristocratic family. A chateau near Rieux bears their name.

Education

On July 9, 1620, at the age of 20, Lalouvère entered the Society of Jesus in Toulouse. After completing his religious training, he was ordained a priest in 1631 or 1632.

Career

Lalouvère served as a 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, Vincentio, Kepler, Torricelli, Valerio - and indeed, Lalouvère - one of the precursors of modern integral calculus. That Lalouvère 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.

Lalouvère’s chief book is the Quadratura circuli, published in 1651, in which he drew upon the work of Charles de La Faille, Guldin, and Vincentio. 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, Lalouvère established the volume of the body of rotation and the center of gravity of its cross-section; then by simple division, he found the volume of the cross-section.

By the time he published this work, Lalouvère 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 open competition. The prize was to be sixty Spanish gold doubloons, and solutions to the problems he set were to be submitted by the following October 1. Lalouvère’s interest was attracted by the nature of the problems, rather than by the prize, and Fermat transmitted them to him on July 11. Lalouvère 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 Lalouvère’s solutions, and Lalouvère himself later discovered and corrected an error in computation. The matter might have ended there had not Pascal, in his Histoire de la roulette, accused Lalouvère of plagiarizing his solutions from Roberval. Pascal’s allegations were without foundation; Lalouvère 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 November 25, 1658, the prize committee decided not to give the award to anyone.

Having returned to mathematics, Lalouvère 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 cycloids - including those posed by Pascal - in 1660, in Veterum geometría promota in septem de cycloide libris. In addition to these publications, Lalouvère maintained an active correspondence on mathematical subjects, several of his letters 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 Lalouvère’s views on the astronomical questions of the horizon and calculation of the calendar.

Achievements

• Although Antoine de Lalouvère didn't become an innovator in the field of mathematics, he is still remembered for his prolific work as a professor of humanities, rhetoric, Hebrew, theology, and mathematics, and also for his works on mathematics, including Quadratura Circuli Et Hyperbolae Segmentorum, De Cycloide Galilaei et Torricelli propositions viginli and Responsio ad duplicem quaestionem moralem. He is also remembered for his study of the properties of the helix, and for his dispute with Pascal on the cycloids.

Works

More photos

• book

  • Quadratura Circuli Et Hyperbolæ Segmentorum 1651
  • Veterum geometrica 1660

Religion

Laloubère was a member of the Society of Jesus.

Views

Lalouvère's 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.

Personality

Lalouvère showed himself to be a man of substantial knowledge and clear judgment. He was a tenacious worker with a great command of detail. Montucla thought his style sufficient to keep “the most intrepid reader from straying.”

Connections

Nothing is known about Lalouvère's family.

opponent:

Blaise Pascal

Friend:

Pierre de Fermat

Friend:

Ignace-Gaston Pardies

Friend:

John Wallis

References

• Dictionary of Scientific Biography, Volume 7
  1973