You are here

Mathematical Treasure: Algorithmus Demonstratus

Frank J. Swetz (The Pennsylvania State University)

While we know that the comprehensive arithmetic and algebra book Algorithmus Demonstratus, first published in 1534, was edited by Johann Schöner, the mathematical work compiled in the volume is sometimes attributed instead to Regiomontanus (1436–1476) or Jordanus Nemorarius (1225–1260). The title page of this work is shown below, where the reader was assured that the instructions had been clearly written for them. The last sentence of this introductory information extolled the reader, “Buy, read, and save [this book].”

Title page of Algorithmus Demonstratus, Regiomontanus, 1534

The first page of the text outlined the scope of the book and provided some basic definitions and concepts: “A digit is a whole number less than ten,” “An article is ten times a digit,” “A square [number] is the product of a number with itself,” “A cube is multiplied by itself twice and a cube root is a number in itself twice multiplied.”

First page of Algorithmus Demonstratus, Regiomontanus, 1534

On page 10 of the Algorithmus, we find crude attempts to employ symbolic notation. For example, the third paragraph down notes that digit a multiplied by digit b will result in articulum c. An example is given in the margin: 5 x 4 = 20; also articulum a times articulum b gives [the product n, 50 x 40 = 2000].

Page 10 of Algorithmus Demonstratus, Regiomontanus, 1534

See images from another copy in Mathematical Treasures.

The images above are supplied through the courtesy of the United States Library of Congress and may be viewed at its website.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Algorithmus Demonstratus," Convergence (January 2020)