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Mathematical Treasure: De Morgan's Arithmetical Books

Sidney J. Kolpas (Delaware County Community College)

Augustus De Morgan (1806–1871) was a British mathematician and bibliographer whose main field was the study of logic. A founder of the London Mathematical Society and its first president, his pupils included Isaac Todhunter (1820–1884) and James Joseph Sylvester (1814–1897). In 1828, he became professor of mathematics at the University of London (now University College London). There, through his works and pupils, he exercised a wide influence on mathematicians and mathematics education. Together with George Boole (1815–1864), De Morgan can be credited with stimulating the interest in logic that took place in the mid-nineteenth century.

Title page for De Morgan's 1847 bibliography of Arithmetical Books.

Title page of Arithmetical Books, from the collection of Dr. Sid Kolpas.

Also a book collector—much of his library is preserved in London and available for consultation either in person or digitally—De Morgan discussed the volumes chiefly focused on arithmetic in his 1847 Arithmetical Books from the Invention of Printing to the Present Time. The rare bookseller, Rootenberg Rare Books, describes this book as “one of the earliest, if not the first significant scientific bibliography.” De Morgan provides chronologically-ordered complete descriptions of almost five hundred works, each of which is annotated with specific details of the work’s publication as well as the author and the book’s importance in the history of mathematics. He also includes a list of over 1,500 authors of books on mathematics as a partial index to the bibliography. According to Erwin Tomash, the book “contains digressions into other subjects (use of the decimal point, length of the font, use of the words addition, subtraction, multiplication, and division by various authors, etc.)” (D chapter, p. 374).

Two sample pages follow, from the copy provided to GoogleBooks by Harvard University:

Page 11 from De Morgan's 1847 Arithmetical Books.

Page 105 from De Morgan's 1847 Arithmetical Books.


Arithmetical books from the invention of printing to the present time being brief notices of a large number of works drawn up from actual inspection.” Rootenberg Rare Books & Manuscripts.

Tomash, Erwin, and Michael R. Williams. The Erwin Tomash Library On The History of Computing: An Annotated and Illustrated Catalog. 2008.

Index to Mathematical Treasures

Sidney J. Kolpas (Delaware County Community College), "Mathematical Treasure: De Morgan's Arithmetical Books," Convergence (May 2021)