The Zebulon Southard Cyphering Book

By Jacquelyn Harbison

Mathematics lessons during the 18th and early 19th centuries were slightly different than today. In modern schools we utilize textbooks and notebooks to learn simple and complex mathematical concepts. During this earlier period, students (often under the supervision of private tutors) used notebooks called ciphering books. Filled with rules, definitions, examples, and exercises, these books offered students a guide to simple addition and subtraction, algebra, geometry, and specific arithmetic needed for various professions. Word problems were common in higher level ciphering books, usually focusing on the math needed for store management, surveying, or the calculation of interest. Ciphering books offer an invaluable window into the history of education and student learning patterns.[1]

Among the Dutchess County Historical Society’s collections is a ciphering book from 1760 belonging to Zebulon Southard of Fishkill.[2] Southard’s ciphering book follows the traditional forms for the period, suggesting that he used it during his preteen or teenage years to prepare for entry into the world of commerce and farming. Through a careful analysis of the book, a historian can arrive at a better understanding of exactly what role Southard’s instructors were preparing him to play in adult life.

Southard’s ciphering book begins with “the rule of three” in direct proportions and inverse. The purpose for these lessons was for students to comprehend the basics of mathematics; mainly the ability to gain the skills to understand proportions and ratios. To fully comprehend the rule of three in direct proportions and inverse, teachers and students would apply the rules to realistic scenarios. For example, Southard wrote, “If a mans (sic) spend (sic) 7d per Day how much is That in A Year.” Beneath the word problem, Southard proceeded to write, “If 1 Day---7d---365 Days”, and beneath the previous “if statement” is a division problem, where the answer is labeled copying the “if statement” with the answer to the word problem. Historians understand the Rule of Three to be the equivalent of elementary education today.

Subsequent portions of the book reveal that Southard studied the topic of interest in great detail, including different time spans of principle interest rates. He also studied the topics of tare and trett, land areas, commission of brokerage, rebate or discount, and equation of payment. Like the Rule of Three, each higherlevel topic developed through word problems between the heading and work. Toward the very end of the book, there are mock scenarios for common business dealings regarding interest, and discounts, along with samples of apprentice indentures and bonds. These legal documents would be regular features of a storekeeper’s life. The word “indebted” is written on several pages of the word problems. On one of the final pages of the ciphering book, Zebulon wrote the same quote repetitively from the top of the page to the bottom. He wrote, “In all concerns on Virtue fix your Eyes and vice.” On the bottom of the page, he wrote, “Zebulon Southard his book 1760.”

How does studying and analyzing ciphering books help us in the modern era? Education has changed dramatically since the introduction of public schools in Dutchess County during the early nineteenth century. During the 1760s, students would learn from private tutors or as an apprentice before starting their own business or going into the trades or farming. In the case of Zebulon Southard, other items within his family papers preserved at the Dutchess County Historical Society reveal that he operated a store and tavern in addition to other commercial activities. When paired with his ciphering book, it is clear that Southard’s parents and instructors prepared him for his adult occupation early in life, offering an example of how education in the eighteenth century was closely linked to applied real-world scenarios that students could expect to encounter later in life.

1 Nerida Ellerton and M.A. Clements, “The Mathematical Content in Cyphering Books,” in Rewriting the History of School Mathematics in North America 1607-1861: The Central Role of Cyphering Books, (New York: Springer, 2012), 3-4, 93, 104–116; Ashley K. Doar, “Cipher Books in the Southern Historical Collection” (master’s thesis, University of North Carolina at Chapel Hill, 2006), 9,21,30,58. accessed March 21, 2022, https://ils.unc. edu/MSpapers/3160.pdf; Rauner Library, “Ciphering Books,” Library Muse - Inspiring Ideas from the Dartmouth Library, November 14, 2014, accessed March 1, 2022, https://sites.dartmouth.edu/library/2014/11/14/cipheringbooks-2/.

2 Zebulon Southard Book 1029.1, Dutchess County Historical Society, Poughkeepsie, NY.