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Mathematical Treasures - Jacob Kobel's Geometry

Frank J. Swetz and Victor J. Katz



This is the title page of the geometry book of Jacob Köbel (1460 - 1533). Köbel was not only a Rechenmeister (reckoning master, or arithmetic teacher) but was also the town clerk in Oppenheim, a German town near Mainz. Köbel wrote the geometry book toward the end of his life, but it was reprinted many times after his death, including this 1608 edition. (Images from an edition published two years after Köbel's death can also be found on Convergence.) The book dealt primarily with measurement, showing its readers how to use various instruments to measure fields, determine heights of buildings, and perform various other necessary tasks.

Three other pages from this book follow:


In this image, Köbel demonstrates how to determine a "rood": one takes sixteen men leaving church on a Sunday and lines up their feet. The total length of the sixteen feet is a "rood". For more information, see the article by Peter Ransom, entitled "The Right and Lawful Rood."


Measuring the height of a tower, when one can measure the distance to the tower. To determine the angle, the surveyor is employing reflection on a smooth surface or mirror (here a polished plate is being used). This technique is based on the principle of "angle of incidence equals angle of reflection."


Measuring the height of a tower using quadrants, when one cannot measure the distance to the tower.

Index to Mathematical Treasures

Frank J. Swetz and Victor J. Katz, "Mathematical Treasures - Jacob Kobel's Geometry," Convergence (January 2011)

Mathematical Treasures from the Smith and Plimpton Collections at Columbia University