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Mathematical Treasure: Buot’s Introduction to Mathematics

Frank J. Swetz (The Pennsylvania State University)

Jacques Buot (ca. 1623-1678) was a French mathematician, astronomer, cartographer, and royal engineer. He collaborated with several other mathematicians who, as a group, encouraged the formation of France’s Royal Academy of Sciences. Buot’s handwritten manuscript, Introduction aux Mathematiques, was compiled sometime after 1675. It is a rather theoretical work consisting of definitions, demonstrations, and remarks concerning algebra, the mathematics of quantity, and geometry. Diagrams accompany most of the geometrical discussions.

Buot’s discussion of multiplication reveals a pedagogical approach to the subject. Multiplication is introduced algebraically: first the product of a monomial with a binomial is considered, then the product of two binomials. To further facilitate understanding, the operation of multiplication is demonstrated using arrays of dots or, perhaps, jetons.

The following is a typical page of text where definitions are introduced.

Introduction aux Mathematiques is a large work consisting of four books that, in total, comprise 232 folio pages. Three of the books are devoted to geometry. A sample of the geometric presentation is shown below.

The images above were obtained through the courtesy of the University of Pennsylvania Libraries. The complete manuscript can be viewed via the reference MS 808.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Buot’s Introduction to Mathematics," Convergence (May 2017)