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Mathematical Treasure: Smith’s Edition of De Morgan’s Budget of Paradoxes

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

After his death, the wife of Augustus De Morgan (1806–1871) edited letters he had published in Athenaeum into the book Budget of Paradoxes (1872). In these letters, De Morgan classified and reviewed paradoxical books he had collected, including many standard types of faulty mathematical proofs—squarers of the circle, trisectors of the angle, duplicators of the cube, and constructors of perpetual motion—as well as “subverters of gravitation,” “stagnators of the earth,” and “builders of the universe.” In 1915, the American mathematics educator and book collector David Eugene Smith (1860–1944) published a second edition of the book’s two volumes.

The title page of volume 1 faced a portrait of De Morgan.

Title page for D. E. Smith's edition of De Morgan's Budget of Paradoxes (1915).

Smith provided Sophia De Morgan’s original preface as well as his own.

First page of Sophia's preface to De Morgan's Budget of Paradoxes (1915).

Second page of Sophia's preface to De Morgan's Budget of Paradoxes (1915).

Third page of Sophia's preface to De Morgan's Budget of Paradoxes (1915).

First page of D. E. Smith's preface to De Morgan's Budget of Paradoxes (1915).

Second page of D. E. Smith's preface to De Morgan's Budget of Paradoxes (1915).

Third page of D. E. Smith's preface to De Morgan's Budget of Paradoxes (1915).

A different portrait of De Morgan appeared as the frontispiece for volume 2.

Portrait of De Morgan in volume 2 of D. E. Smith's edition of De Morgan's Budget of Paradoxes (1915).

De Morgan’s comments on the possibilities of aviation.

Pages 8-9 from volume 2 of D. E. Smith's edition of De Morgan's Budget of Paradoxes (1915).

These images are from the copies of volume 1 and volume 2 owned by the University of California and digitized by the Internet Archive.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Smith’s Edition of De Morgan’s Budget of Paradoxes," Convergence (January 2023)