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Mathematical Treasure: Darjes's Ground of All Mathematics

Frank J. Swetz (The Pennsylvania State University)

Joachim Georg Darjes (or Daries, 1714-1791) was a Prussian logician, lawyer, and Lutheran cleric. In his Erste Grunde der gesamten Mathematik (The Ground, or Basis, of all Mathematics, Theoretical and Practical, 1757), he applied a logical ordering to the then known branches of mathematics.


The “Table of Contents,” above, supplies Darjes’ division for mathematics: Mathesis pura, pure or theoretical mathematics, contains four branches; whereas Mathesis adplicata, applied or practical mathematics, has thirteen categories ranging from the needs of merchants to geography.

In section 2 of page 77, Darjes introduced his readers to the binary number system. Then he attempted to document the official “discovery” of binary numbers by Leibniz, citing his announcement of their existence in the Memoires de l’Académie Royale des Science “1703 page 76.” Actually, Leibniz did have his article “Explication de l’arithmetique binaire ...” published in the 1703 issue of the journal but on pages 85-89.

On page 95, the author provided subtraction examples for base 2, base 4, and decimal expressions.

On page 107, we find a division example for two binary numbers.

The images above were obtained from the Rare Book Collection at Franklin and Marshall College, Lancaster, Pennsylvania.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Darjes's Ground of All Mathematics," Convergence (January 2016)