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Mathematical Treasure: Arithmetic for Farmers and Mechanics

Frank J. Swetz (The Pennsylvania State University)

The Farmers’ and Mechanics’ Assistant or Companion, or A New System of Decimal Arithmetic (1824), is a noteworthy book in two respects. First, the title shows a shift in emphasis of the teaching of arithmetic from the needs of commerce to those of more common workmen, farmers, and mechanics. Secondly, as a pedagogical learning innovation, some of the text is given in verse. The shift in teaching reflects the changes in American society: the movement to an industrial as well as an agricultural country. Unfortunately, little is known of the author, John Graham, as there are several John Grahams known for this period of American history with none denoted as involved in textbook writing.

The “Table of Contents” still carries a concern for measurement and exchange. The topic of circular motion reflects on the popularity of machines and the era of industrialization. The author’s comments in his “Preface” are worth recalling:

In fact, no bounds can be set to its utility or extent. Arithmetic must therefore flourish and be cultivated as long as time shall remain; or till mankind sink back into such a state of ignorance that the bare supposition of the degeneracy would dishonor human nature.

I have endeavored, for the encouragement of the learner, to do all that I possibly could; the rules are all very plain and easy to be understood; to which I would advise every scholar particularly to attend; for I, myself, have observed,

Study the rule, your question pry,
You'll gain the answer by and by.

This little book, peruse it well; I hope in it you'll find Some entertaining, useful work, to cultivate the mind; From it you may, if well applied, some information gain; Arithmetical rules you'll find, both easy, short and plain. My best advice to youth I give, improve your golden span; Seek for knowledge while you're young—education makes the man.

Graham’s use of verse also extended to his statement of problems; for example, here is a problem from page 110 concerning a lion:

Dear friend, I request you with caution and care,
To measure this Hon, exact to a hair.
His head is twelve inches, from his ears to his nose:
This measure I give you the rest to disclose.
His tail is as long as his head and a half
Of his body, when found, do secure it safe.
His body is the length of his head and his tail;
He's a surly old rogue, yet you cannot well fail
To tell his whole length, when his substance you see;
You've the length of his head, as was given to me.
The question required, is separately to tell,
His whole length, his body's length, and the length of his tail.

These images are used through the courtesy of the Lilly Library, Indiana University, Bloomington, Indiana.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Arithmetic for Farmers and Mechanics," Convergence (August 2019)