Elements of Arithmetic

Augustus De Morgan was one of the nineteenth century's most original minds in mathematics and logic, and this 1830 textbook reveals why. Rather than presenting arithmetic as a collection of procedures to memorize, De Morgan insists that students understand the reasoning behind every operation. His approach feels almost modern in its emphasis on comprehension over computation, making this a surprisingly progressive text for its era. The book opens with a fascinating exploration of numeration, tracing how different civilizations counted and how those methods evolved into the number systems we use today. From there, De Morgan moves through the four basic operations, but always with an eye toward the principles that make them work. Appendices offer additional material for more advanced students, extending the book's reach beyond mere calculation. This is a book for anyone curious about how mathematics was taught before it became standardized, and for educators who want to understand the reasoning-first approach that many modern math educators advocate.