Mathematical Treasure: Samuel Morland’s Two Arithmetick Instruments

The above portrait is of Englishman Sir Samuel Morland from his 1673 book The Description and Use of Two Arithmetick Instruments, about two hand calculators and a perpetual almanac that Morland invented. Below is the title page.

The first of the two instruments described in this work carries out addition and subtraction of English currency (pounds, shillings, pence, and farthings). The images below show the first page of the section of the book about this instrument, the beginning of the instructions on how to use it, a drawing of its gear wheels, and an example.

The book then has the description of a second handheld instrument which carries out multiplication.

Sir Morland commented that, using the two instruments together, one could add, subtract, multiply, divide, and extract roots. He also mentioned “Lord Napiers Bones.”

The next section of the book contains a short history of numeration as well as exposition on arithmetic, including operations with decimals and fractions.

The image above appears in a section on extracting square roots and is based on the identity \( (a + b )^2 = a^2+ 2ab + b^2 \).

A complete digital scan of Morland’s Two Arithmetick Instruments, call number QA75.M64 1673, can be found in the Linda Hall Library Digital Collections.

Images in this article are courtesy of the Linda Hall Library of Science, Engineering & Technology and used with permission. The images may be downloaded and used for the purposes of research, teaching, and private study, provided the Linda Hall Library of Science, Engineering & Technology is credited as the source. For other uses, check out the LHL Image Rights and Reproductions policy.

Reference

Turner, G. L’E. "Morland, Samuel." In Complete Dictionary of Scientific Biography. New York: Charles Scribner's Sons, 2007. Encyclopedia.com. https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/morland-samuel (accessed 26 February 2018).

Index to Mathematical Treasures