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Mathematical Treasure: Leupold's Practical Arithmetic and Geometry

Author(s): 
Frank J. Swetz (The Pennsylvania State University)

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.

Title page of Theatrum arithmetico-geometricum by Jacob Leupold, 1774

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

Page 2 from Theatrum arithmetico-geometricum by Jacob Leupold, 1774

Table II demonstrates the postures of finger reckoning.

Table II from Theatrum arithmetico-geometricum by Jacob Leupold, 1774

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

Page 8 from Theatrum arithmetico-geometricum by Jacob Leupold, 1774

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

Table III from Theatrum arithmetico-geometricum by Jacob Leupold, 1774

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

Table V from Theatrum arithmetico-geometricum by Jacob Leupold, 1774

Table VII shows the workings of the Poleni calculator.       

Table VII from Theatrum arithmetico-geometricum by Jacob Leupold, 1774

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

Table IX from Theatrum arithmetico-geometricum by Jacob Leupold, 1774

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

Table XXI from Theatrum arithmetico-geometricum by Jacob Leupold, 1774

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

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Leupold's Practical Arithmetic and Geometry," Convergence (August 2018)

Dummy View - NOT TO BE DELETED