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Funding for this project generously provided by Overdeck Family Foundation


Lincoln's Cyphering Book

President Lincoln's multiplication practice

Cyphering books (where "cyphering" is an archaic term for arithmetic) are practice books written by students. Their use dates back centuries and may have originated in the Middle East and India. A cyphering book was typically prepared by an instructor, used by a male student and written in ink. The subjects in the cyphering book began with basic arithmetic and progressed to higher levels of mathematics as the student advanced. Cyphering books were often shared among family members or passed down from parent to child; the two most valued books a family owned were often the Bible and a cyphering book.

Lincoln's Cyphering Book

Like many children, Abraham Lincoln, the 16th president of the United States, learned to read, write and do his 'rithmetic. This page (the fourth in the numbering of Ellerton and Clements) from Lincoln's cyphering book, shows how he learned to multiply numbers and "cast out nines" to check his work. In all, 22 pages of Lincoln's cyphering book survive but are spread across multiple locations in the United States.

Artifact dimensions

1.5 cm × 12.9 cm × 20.4 cm

Artifact origin

Indiana, United States

Current artifact location

Rare Book & Manuscript Library, Butler Library, Columbia University in the City of New York

Catalog number



MathematicsEducation timeline babylonian-scribe-school-multiplication-tablet Rhind Papyrus Slate with Numeral Frame Derby Museum Hornbook North American Hornbook Wood Hornbook with Abacus Maria Agnesi's Analytical Institutions Midshipman's Cyphering Book Samuel Fay's Cyphering Book Lincoln's Cyphering Book Orville Wright's Arithmetic Textbook New York State Regents Exams in Mathematics

Interactive Content

Computational Explanation

Additional Reading

  • Ellerton, N. and Clements, M. "He Would Be Good: Abraham Lincoln's Early Mathematics, 1819–1826." Ch. 6 in Abraham Lincoln's Cyphering Book, and Ten Other Extraordinary Cyphering Books. New York: Springer, pp. 123–186, 2014.
  • Ellerton, N. and Clements, M. Rewriting the History of School Mathematics in North America 1607–1861. New York: Springer, 2012.