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Mathematical Treasure: Cramer on His Rule and His Paradox

Frank J. Swetz (The Pennsylvania State University)

Gabriel Cramer (1704–1752) was a Swiss mathematician, academician, editor, and author of mathematical texts. Cramer associated with all the great European mathematicians of his day. His greatest work was Introduction a l’Analyse des Lignes Courbes Algebriques (1750), modeled after Newton’s work on the cubic equation.

This is the first page of Cramer’s book. In Chapter three, the author stated his famous rule, now known as “Cramer’s Rule,” and also pointed out “Cramer’s Paradox.”

In pages 657-659 of the “Appendix” Cramer considered the solution of four linear equations in four unknowns.

These images are used through the courtesy of the Lilly Library, Indiana University, Bloomington, Indiana.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Cramer on His Rule and His Paradox," Convergence (August 2019)