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Mathematical Treasure: Three Books by Simon L'Huilier

Author(s): 
Frank J. Swetz (The Pennsylvania State University)

Simon L’Huilier (1750-1840) was a Swiss mathematician remembered for his contributions to the fields of mathematical analysis and topology. He was the first mathematician to use the abbreviation “lim” for “limit” in the mathematical sense. In 1786, he won the gold prize offered by the Berlin Academy of Sciences for his work on the foundations of calculus. This work was published as a book, Exposition élémentaire des principes des calculs supérieurs (Elementary exposition of the principles of the higher calculus), in 1786.

Title page of Exposition élémentaire des principes des calculs supérieurs by Simon L'Huilier, 1786

In his “Introduction,” L’Huilier discussed his research.

First page of introduction to Exposition élémentaire des principes des calculs supérieurs by Simon L'Huilier, 1786

Second page of introduction to Exposition élémentaire des principes des calculs supérieurs by Simon L'Huilier, 1786

The text begins with appropriate definitions.

First page of first chapter in Exposition élémentaire des principes des calculs supérieurs by Simon L'Huilier, 1786

 

In 1804, L’Huilier published Élemens raisonnés d’algèbre (Reasoned elements of algebra) for the use of his students. The professor’s pedigree of honors covers much of the title page.

Title page of Élemens raisonnés d’algèbre by Simon L'Huilier, 1804

L'Huilier's opening comments supply a rationale for the study of algebra.

Page 1 of Élemens raisonnés d’algèbre by Simon L'Huilier, 1804

Page 2 of Élemens raisonnés d’algèbre by Simon L'Huilier, 1804

The examples and explanations are clear and concise.

Page 12 of Élemens raisonnés d’algèbre by Simon L'Huilier, 1804

Page 13 of Élemens raisonnés d’algèbre by Simon L'Huilier, 1804

 

In 1809, Simon L’Huilier published his Élémens d’analyse géométrique et d’analyse algébrique (Elements of geometric and algebraic analysis) in which he discussed the applications of mathematics to geometric spaces.

Title page of Élémens d’analyse géométrique et d’analyse algébrique by Simon L'Huilier, 1809

The first three pages of the author’s preliminary comments are examined here.

Page 1 of Élémens d’analyse géométrique et d’analyse algébrique by Simon L'Huilier, 1809

Page 2 of Élémens d’analyse géométrique et d’analyse algébrique by Simon L'Huilier, 1809

Page 3 of Élémens d’analyse géométrique et d’analyse algébrique by Simon L'Huilier, 1809

 

The images above were obtained through the courtesy of e-rara, where each of the three works may be viewed in their entirety.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Three Books by Simon L'Huilier," Convergence (August 2018)

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