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History of Mathematics

Guide to materials about the history and teaching of mathematics held by The Bancroft Library.


From the late seventeenth through the early nineteenth centuries, arithmetic was taught through a set of rules that could be used in solving problems. Commercial topics and vocational applications were predominant. Instructors taught by dictation. They presented the rules along with examples and practice problems. Students would work individually on finding solutions to set exercises, often on a slate or on scraps of paper. These would be shown to the teacher and if approved, the student would then create entries in their copybook for that topic. The copybooks would feature fine calligraphy for the headings and neat penmanship. Advanced copybooks covered geometry, navigation, and surveying and often contained hand drawn illustrations.


The Bancroft Library holds over twenty of these books dating from the 1790s through the 1850s. The majority were created before 1820.  Most feature arithmetic problems but there are several with geometry and trigonometry problems. There are two with navigation problems with hand-colored illustrations. Half are from Massachusetts with the next largest group from Pennsylvania. Three of the copybooks were created by female students.


Most of the problems are practical but the student’s personality also shines through in problems like this one from Ingoldsby Work Cranford’s copybook (page 59):

“An ignorant fop wanting to purchase an elegant house, a facetious gentleman told him that he had one which he would sell on these moderate terms, that he would have only one penny for the first door, 2 pence for the second,4 for the third, and so doubling at every door. The number of which is 36; it is a bargain said the simpleton; pray what would the house cost him?”


Several of the copybooks include annotations that help to explain how the books were created such as this statement by Daniel Heard:

“The figure is not put in, on account of the Book not being large enough to admit it so large as it ought to be drawn. The question has been wrought and comes out agreeable to the answer above likewise the figure was drawn on a slate.”


Here are sample pages from two of the copy books:


Image of reduction of coin rules from Mary Mead's cipherbookReduction of coin - Variations of this problem are in most early copybooks.

Mary Elizabeth Mead notebook : [United States?] : copybook, 1821.
BANC MSS 2002/373"



This geometry problem illustrates the artistry and fine detail that students employed when creating their copybooks.

Image of illustrated page from Rufus Brackett cypherbook





Rufus Brackett notebook : Shapleigh [Me.] : copybook, 1816 Feb. 16-1818 May 4.
BANC MSS 2002/375