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Mathematical Treasure: De Morgan’s Calculus Textbooks

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

Augustus De Morgan (1806-1871) was a British mathematician, perhaps best remembered today for his work in logic. De Morgan’s Differential and Integral Calculus was published in 1842. It was sponsored by the Society for the Diffusion of Useful Knowledge, an organization devoted to bringing knowledge to the “common man,” i.e. the British working class. De Morgan also wrote 712 articles for the Society’s Penny Cyclopedia, a cheap periodical intended for the same purpose. In his mathematical writing, he took great care to tailor the material to the learning needs of his audience.

Title page of Augustus De Morgan's 1842 calculus textbook.

The “Advertisement” found in the front of De Morgan’s Calculus serves as a preface to the work, clarifying the author’s intentions in writing the work.

Page 2 of Augustus De Morgan's 1842 calculus textbook.Page 4 of Augustus De Morgan's 1842 calculus textbook.

Instruction in differentiation begins on page 117. Note De Morgan’s use of a table to promote recognition of an operational pattern.

Page 117 of Augustus De Morgan's 1842 calculus textbook.

Often included with his Calculus was De Morgan's Elementary Illustrations for the Differential and Integral Calculus (1832), a sort of study-guide that clarified important points and supplied further advice on learning calculus. In 1899, Open Court published a revised and updated edition of this work.

Title page of Augustus De Morgan's 1832 guide to calculus.

A bibliography provided in this book indicates the popular English language calculus texts available at the close of the 19th century.

Page 135 of De Morgan's Elementary Illustrations.Page 136 of De Morgan's Elementary Illustrations.

Page 137 of De Morgan's Elementary Illustrations.

The images above are presented courtesy of the University of Pennsylvania Libraries.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: De Morgan’s Calculus Textbooks," Convergence (October 2016)

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