Mathematical Treasure: Leupold's Practical Arithmetic and Geometry

Jacob Leupold (1674-1727) was a German mathematician, engineer, physicist and instrument maker. His magnum opus was a ten-volume encyclopedia of the technology and machine design of his time, titled Theatrum machinarum (1724-1739). The seventh volume in this series, Theatrum arithmetico-geometricum ... (The Theater of the Arithmetic of Geometry, Showplace of Reckoning and Measurement), is considered the best illustrated reference concerning calculation in the 18th century. The book contains discussions of the digital calculating machines of Schott (1668), Grillet (1673), Leibniz (1674), and Poleni (1709), as well as one constructed by Leupold himself. The following images are from the 1774 edition of the work.

The text on page 2 discusses the art of “Finger Reckoning.”

Table II demonstrates the postures of finger reckoning.

On page 8 is a discussion of “A Roman Reckoning Table,” or abacus.

Table III attempts to show the relationship of finger postures to their corresponding Hindu-Arabic numerals.

Table V illustrates a calculator that incorporates Napier’s Bones or Rods in its functioning.

Table VII shows the workings of the Poleni calculator.       

Table IX reveals the functioning of a gear driven calculator of the time.

Table XXI illustrates some measuring and drawing tools of the period.

The images above are supplied through the courtesy of the University of California Libraries. The work may be viewed in its entirety in the Internet Archive.

Index to Mathematical Treasures