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The Artistry of Learning Math: The Ellerton-Clements Cyphering Book Collection

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A selection of interesting bindings were shown off during processing of the Ellerton-Clements Cyphering Book Collection in November 2021.

This guest post is by Manuscript Division archivist Katherine Madison.

Modern schoolchildren may think that the textbooks they know (and love to hate) have been around forever, but that’s not the case. In the history of school mathematics, for instance, widespread student access to commercially distributed textbooks didn’t become the norm until the twentieth century. Before then – and for several centuries – Western school-age children learned mathematical concepts through what was called the “cyphering tradition” and created textbooks of their very own. The Manuscript Division recently acquired the largest single collection of cyphering books prepared by students in colonial America and the United States from 1666 to 1907. Originally assembled by mathematics professors Nerida F. Ellerton and M. A. “Ken” Clements, the collection is now processed and open for research use in the Manuscript Reading Room.

Cyphering (or “ciphering”) books were handwritten reference books created by students as they learned mathematical principles. “During the period 1200-1850,” Ellerton and Clements write, “almost all Western European and North American students aged 10 years, or more, who learned mathematics at school or with a private tutor were expected to prepare cyphering books.”[1] Pages usually included “introductory notes on topics, rules, cases, model examples, and completed exercises” either copied from another text or dictated by a teacher.[2] Cyphering books were a fixture in the households of students with access to formal mathematics education, including George Washington and Abraham Lincoln. Pages from both of their books are already held by the Manuscript Division.

The volumes in the Ellerton-Clements Cyphering Book Collection represent a variety of students from different backgrounds and states, including a large number of female students. While learning mathematical principles, students often filled their books with everyday problems like bookkeeping or land surveying or, for students in port towns, navigation. Their books are certainly of interest to those who study math and early modern education, but many also possess a unique kind of artistry. The books and bindings were generally handmade rather than mass-produced, meaning that each volume shows a great deal of individuality. As physical objects – both inside and out – there’s a lot to analyze and appreciate.

One of the interesting things about these cyphering books is the variety of their bindings. Many books have lost their coverings over the years, but others are bound in scraps of leather, newsprint or colored paper, linen and other types of cloth, and even with pieces of vibrant, patterned wallpaper. Lined, commercially available notebooks begin appearing in the collection in the early nineteenth century – many with marbleized covers, and others with printed images showing off local sites or historical events to advertise the stationery store from which the book was procured.

The insides of the volumes are even more interesting. The cyphering tradition required that “headings and sub-headings… be done in calligraphic style” and that the entries be formatted by “introducing a topic in sentence form and then setting out rules, cases, model examples and exercises associated with that topic,” giving the books a standard and stylized structure.[3] However, students still injected their own personalities. Many of the details they left behind will be familiar to modern students and teachers. Doodles abound, such as faces, animals, and the occasional ship. In some cases, students even used the margins of their books for handwriting practice! The identity of a manuscript’s creator was sometimes discoverable because of these marginalia. The cyphering book of Barbara Ann Newman, for instance, was housed with that of Anderson Newman – but only Anderson’s 1824 volume was described in the inventory that arrived with the collection at the Manuscript Division. Barbara Ann’s signature clearly marked the book as hers!

Some of the cyphering books also contain beautiful illustrations. In 1820, Mary Waters created a watercolor rose with the words “The Rule of Three Direct” (a foundational mathematical principle) written across its petals. In 1811, Oliver Parry, from New Hope, Pennsylvania, created a compass rose on the inside cover of his third and last cyphering book. These personal touches accompanied the more traditional line drawings that illustrated geometrical, and occasionally algebraic, principles – a talent also held by Oliver Parry.

Child's drawing of black and yellow cat
On the inside cover of his cyphering book, Nathan Clifton of Ohio drew a picture of a cat-like creature that would be as recognizable as any modern child’s drawing, circa 1830. Box 36, Ellerton-Clements Collection, Manuscript Division, Library of Congress.

According to Ellerton and Clements, a student’s cyphering book was often treated like a family heirloom. Some volumes in the collection were passed on from sibling to sibling and even across generations, and different handwriting and signatures can be seen on various pages. Some of the late eighteenth- and early nineteenth-century books were repurposed as scrapbooks by later generations, with newspaper clippings pasted over mathematical equations and drawings. Some books with blank leaves were reworked into ledgers or spelling books, often by the same student or by a sibling.

Despite the strict structures of the cyphering tradition, each book in this collection has a distinct personality. Some volumes have been painstakingly rebound or even restored by later owners, but most arrived at the Manuscript Division in a condition their original creators would recognize (plus some light water damage or foxing and, in a few cases, absent a few corners that were nibbled on by mice or bookworms). While the cyphering tradition is no longer a part of math class for American schoolchildren, this collection of surviving cyphering books remains a testament to the work of these young students from centuries ago – and to the all-too-familiar feelings of pride, joy, and frustration that can still accompany schoolwork.

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[1] Nerida F. Ellerton and M. A. Clements, Abraham Lincoln’s Cyphering Book and Ten Other Extraordinary Cyphering Books (New York: Springer, 2014), 2.

[2] Ellerton and Clements, Lincoln’s Cyphering Book, 7.

[3] Nerida F. Ellerton and M. A. Clements, Cyphering Books Prepared in the North American Colonies (But Not Canada) or in the United States of America, 1667-1907 (Perth: Meridian Press, 2021), 2.


  1. Thanks for this interesting article. We have a small collection of cipher books, and it is interesting to learn more about their origins and purpose. The most recent one we bought has really elaborate headings, and was obviously drawn by a truly talented student.

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