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Mathematical Treasure: Robert Tanner's A Mirror for Mathematiques

Frank J. Swetz (The Pennsylvania State University)

Tanner's Mirror

On the cover of his 1587 book, Robert Tanner describes himself as a “Gentleman practitioner of Astrologie & Phisick.” His book bears the title, A Mirror for Mathematiques and, alternately, as a running head inside, The Travailers [Traveller’s] Joy and Felicitie (see the images below). It promises to be a "golden gem" for geometricians, surveyors and astrologers. The book is about the use of the astrolabe. It attests to the scientific importance of this instrument in its day, which might be equated to the impact of the laptop computer today. The astrolabe allowed for the reckoning of physically unattainable distances and was applied in land surveying, navigation, astronomy, and astrology. These instruments were revered for their potential usefulness, were elaborately constructed and embellished, and were possessed as a symbol of scientific acuity, both by owners who used them and some who did not. Queen Elizabeth I had her own astrolabe as well as an accompanying court astrologer.

For more images of astrolabes, join the author for a virtual visit to the Museum of the History of Science in Oxford, England.

from Tanner's mirror

On the pages shown above and below, woodcut prints demonstrate the use of the astrolabe and its “cousin”, the quadrant, in determining the height of a tower. The image below is for the more complicated situation in which the tower sits on a hill, its base elevated from the observer.

from Tanner's mirror

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 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.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Robert Tanner's A Mirror for Mathematiques," Convergence (August 2012)