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Mathematical Treasure: Samuel Morland’s Two Arithmetick Instruments

Author(s): 
Cynthia J. Huffman (Pittsburg State University)

Portrait of Samuel Morland from his 1673 The Description and Use of 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.

Title page from Samuel Morland's 1673 The Description and Use of Two Arithmetick Instruments.

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.

Section title page from Samuel Morland's 1673 The Description and Use of Two Arithmetick Instruments.First page of instructions from Samuel Morland's 1673 The Description and Use of Two Arithmetick Instruments.

Depiction of instrument from Samuel Morland's 1673 The Description and Use of Two Arithmetick Instruments.

Example of use from Samuel Morland's 1673 The Description and Use of Two Arithmetick Instruments.

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

Section title page for second instrument from Samuel Morland's 1673 The Description and Use of Two Arithmetick Instruments.

Second instrument from Samuel Morland's 1673 The Description and Use of Two Arithmetick Instruments.

Example of use from Samuel Morland's 1673 The Description and Use of Two Arithmetick Instruments.

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.

Page 13 from Samuel Morland's 1673 The Description and Use of Two Arithmetick Instruments.

Page 38 from Samuel Morland's 1673 The Description and Use of Two Arithmetick Instruments.

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

Cynthia J. Huffman (Pittsburg State University), "Mathematical Treasure: Samuel Morland’s Two Arithmetick Instruments," Convergence (June 2018)

Dummy View - NOT TO BE DELETED

Mathematical Treasures: The Linda Hall Library