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Mathematical Treasure: Hill's Arithmetick

Frank J. Swetz (Pennsylvania State University)

Arithmetick, Both in the Theory and Practice (1772) is a comprehensive 18th century arithmetic text intended for commercial training. In 416 pages, it covers topics such as percentage, commissions, monetary exchange, arithmetic and geometric progressions, and the use of logarithms. Although Humphrey Ditton, a respected mathematician of the time, provided a Preface for the work, little is known about the author, John Hill, other than that he described himself as a ‘Gentleman’. Other existing mathematics texts of this same period bear the authorship of a John Hill, Accountant. Such an occupation would seem likely for the author of this Arithmetick, for which the title page is shown above.

Page 125, above, includes a discussion of arithmetic progressions.

Page 176, above, contains some examples of monetary conversion.

Pages 378 and 381, the adjoining misnumbered pages shown above, present some student exercises a reader may wish to attempt.

The images above are provided courtesy of Archives and Special Collections, Dickinson College, Carlisle, Pennsylvania.

Mathematical Treasures Index

Frank J. Swetz (Pennsylvania State University), "Mathematical Treasure: Hill's Arithmetick," Convergence (August 2015)