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Mathematical Treasure: Lazare Carnot’s Geometry

Frank J. Swetz (The Pennsylvania State University)

Lazare Carnot (1753–1823) is perhaps best remembered for being the father of Sadi Carnot, the pioneer of steam power and thermodynamics; however, he was quite an influential man in his time. Besides being a military engineer, a general in the army, and a politician in Napoleon Bonaparte’s government, Lazare Carnot was also a well respected mathematician. Of the four books he wrote on mathematics, Géométrie de Position, published in 1803, is considered a pioneering work in projective geometry. Among the innovations Carnot introduced in projective geometry were a systematic use of directed magnitudes and the concept of cross ratios for four collinear points.

On this page, Carnot considered the problem of constructing a sphere in space tangent to four given spheres.

In Plate XI of the supporting illustrations, Figure 148 pertains to Carnot’s sphere problem.

The Special Collections staff at the Linderman Library of Lehigh University in Bethlehem, Pennsylvania, is pleased to cooperate with the Mathematical Association of America to exhibit this and other items from the Library’s holdings in Mathematical Treasures. In particular, Convergence would like to thank Lois Fischer Black, Curator, Special Collections, and Ilhan Citak, Archives and Special Collections Librarian, for their kind assistance in helping to make this display possible. You may use these images in your classroom; all other uses require permission from the Special Collections staff, Linderman Library, Lehigh University.

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Lazare Carnot’s Geometry," Loci (June 2014)