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Mathematical Treasure: De Morgan’s Elements of Algebra

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. In De Morgan’s Elements of Algebra (1835), a reader begins to realize the conceptual problems of algebra. Just what is algebra? Is it merely arithmetic using symbols rather than numbers? These were controversial questions at the time.

Title page of Augustus De Morgan's 1835 Elements of Algebra.

On pages 44 and 45, the issue of “negative numbers” is confronted: Do they exist? If so, how does one work with them?

Page 44 of Augustus De Morgan's 1835 Elements of Algebra.Page 45 of Augustus De Morgan's 1835 Elements of Algebra.

On page 151 of his Algebra, De Morgan considered the hazards of treating “0” as an independent quantity within operations.

Page 151 of Augustus De Morgan's 1835 Budget of Paradoxes.

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 Elements of Algebra ," Convergence (October 2016)

Dummy View - NOT TO BE DELETED