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Deutsches Technikmuseum - November

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Exhibit of the Month November 2016

Leibniz Calculating Machine, 1695 (1992 reproduction)

November 14th is the 300th anniversary of the death of Gottfried Wilhelm Leibniz (1646-1716). Leibniz is mainly known as a philosopher but he had in fact many talents, including being an excellent mathematician.

Photo: The machine ist about 80 centimeters long and mainly made of copper. With two hand crank handles and eight rotary handles the numbers and types of arithmetic are set and transferred to the rollers at the rear.

Historic milestone: Leibniz’s "four-species calculator" (replica) © SDTB / Photo: C. Kirchner

Along with theoretical disquisitions he also applied himself to very practical mathematical questions: He sought to construct a calculating machine that would perform the basic arithmetical operations of addition, subtraction, multiplication and division. This automation was Leibniz’s attempt to free his contemporaries from the "menial work of calculation".

Oil painting: Gottfried Wilhelm Leibniz is depicted wearing a black long-hair wig which was typical for the period.

Portrait of Gottfried Wilhelm Leibniz by Johann Friedrich Wentzel, circa 1700. © Picture: Berlin-Brandenburgische Akademie der Wissenschaften, Wikimedia Commons, in the public domain.

A calculating machine, with which "numbers reckon themselves"

From 1670 on, Leibniz developed one such "four-species calculator", with which "numbers should reckon themselves".

This inferred that no manual transfer of intermediate results would be necessary. In 1673 he completed a wooden model of his machine and demonstrated it for the Royal Society in London. However, on this occasion it failed to function adequately - as it did most of the time. The main problem was that precision engineering in the 17th century had not yet advanced enough to build such a machine.

Leibniz, however, was not deterred and continued to build a number of improved versions during his lifetime. Starting in 1682, he consequently developed a new process for entering numbers by means of a so-called "Staffelwalze" - a stepped cylinder upon which nine teeth with differing lengths are attached. Calculators were still employing this principle in their construction as late as the 20th century.

The machine on display here is also based on a stepped cylinder. It is a reproduction of the only remaining Leibniz calculating machine that was built from 1695 on. The original is now housed in the Gottfried Wilhelm Leibniz Bibliothek Hannover.