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Mathematical Treasure: Gunter's Measuring Instruments

Frank J. Swetz (The Pennsylvania State University)

Edmund Gunter (1581-1626) was a British mathematician and Professor of Astronomy at Gresham College, London. He is noted for his invention of mathematical measuring instruments and the popularization of their use. In 1606, he devised his sector used for determining angles to distant bodies. It went by many names including “proportional compass” and “military compass,” the latter name denoting its usefulness in gunnery exercises. Seventeen years later, in 1623, he invented the bow quadrant or mariner’s bow, its name emphasizing the instrument’s maritime importance. His manual on the use of such instruments, entitled The Description and Use of the Sector, Cross-staff and other Instruments, was published in 1624. The title page of the second edition, released in 1636, is shown above. Written in English rather than Latin, this book was intended for common surveyors and sailors. The title page illustrates the use of four instruments in use during this period: moving in a clockwise direction starting at the upper left corner, we see the sector, the cross-staff, the quadrant, and finally the bow quadrant.

Shown above is the first page of Chapter One of the First Book, in which Gunter described the construction and functioning of the sector.

As shown above, the Second Book on the sector discusses the computation of the standard trigonometric ratios. Note that the measures of the angles at point A are indicated as arc lengths along the circumference of the circle.

These three images are provided courtesy of the Beinecke Rare Book and Manuscript Library, Yale University. You may use them in your classroom; all other uses require permission from the Beinecke Rare Book and Manuscript Library. The Mathematical Association of America is pleased to cooperate with the Beinecke Library and Yale University to make these images available to a larger audience.

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Gunter's Measuring Instruments," Convergence (April 2014)