German mathematician and astronomer Johann Stoeffler (or Johannes Stöffler) wrote an influential book with the title *Elucidatio fabricae vsusque astrolabii*, on how to make and use an astrolabe*. *First published in 1513, the book went through 16 editions by the year 1620. According to the Oxford Museum of the History of Science, it was “one of the most influential books on a scientific instrument ever to be published. … Many authors of the many books on mathematical instruments to be published in the 16th century followed Stöffler’s example.”

The image below is the title page of a 1524 edition at the Linda Hall Library of Science, Engineering, and Technology in Kansas City, Missouri. The call number is CE73.S7 1518.

The first part of the book deals with the construction of astrolabes. The next image is the start of a section in the Second Part of the book about various types of geometry, both theoretical and practical. Near the center of the page is a listing of different units of measure including *digit* (finger), *palmus* (hand), *pes* (foot), *cubit*, *passus* (pace), *pertica* (perch or rod), *stadium* (furlong), *miliarium* (mile), and *leuca* (league). In the center of the page are line segments showing the length of a digit and hand, and on the side of the page is a line segment for a foot. The relations among the units are given: a hand is 4 digits, a foot is 4 hands (today a foot is considered 3 hands), a cubit is a foot and a half, a pace is 5 feet (today a pace is 2.5 feet), a rod is 10 feet (today a rod is 16.5 feet), a stadium/furlong is 125 paces (named after *stando*, the length Hercules could run in one breath or the length after which youth running would stop for a rest), a mile is 8 furlongs or 1000 paces (hence its name), and a league is a mile and a half or 1500 paces.

The second part of the book then gives instructions on taking measurements of objects such as towers and wells using an astrolabe, and includes many figures such as the one below which shows a man using an astrolabe to measure the height of a tower based on the length of its shadow.

An English translation of the 1553 edition of Stoeffler’s *Elucidatio* is available. A copy of the translation is also available at the Linda Hall Library, so one could compare the Latin 1524 edition side-by-side with an English translation of the 1553 edition.

*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

*Stoeffler's Elucidatio*. Paris, 1553. Translated and edited by Alessandro Gunella and John Lamprey. Cheyenne, Wyo.: Classical Science Press, 2007.

Index to Mathematical Treasures