A: Innenstadt I, Frankfurt am Main, Hessen, Germany

1784

In 1784 Johann Helfrich von Müller issued from Frankfurt a 50-page instruction manual for a beautiful calculating machine that he designed and built: *Beschreibung seiner neu erfundenen Rechenmaschine, nach ihrer Gesalt, ihrem Gebrauch und Nutzen*. *Herausgegeben und mit einer Vorrede begleitet von Ph. E. Klipstein. *Müller's calculating machine was based on the principles of Leibniz's stepped reckoner, and could do addition, subtraction, multiplication and division. To this work Müller added a two-page appendix which can be translated as "Further Inventions of Superior Calculating Machines and an Arithmetical Printing Machine." In this he stated that he intended to build a difference engine that could calculate and print mathematical tables by the method of differences. Müller estimated that his device would be capable of one addition per second, and that a table of the cubes of the integers from 1 to 100,000 could be produced by 'a common laborer' in about 10.5 days.

Charles Babbage, who collected extensively on mathematical tables and calculating machines, owned a copy of Müllers book that John Herschel found on a trip to the Continent.

Muller's original calculator is preserved in the Grossherz Hessichen Museum at Darmstadt.