page_title: Stepped reckoner
section_title: History
hierarchical_section_title: Stepped reckoner / History
caption_attribution_description: English: Photo of the mechanism of the 'Stepped Reckoner' a prototype mechanical calculator invented by German mathematician Gottfried Wilhelm Leibniz in 1671 and completed in 1694. About 67 cm (26 in.) long. This was the first calculator able to perform all the elementary operations: addition, subtraction, multiplication, and division. The housing is removed to show the mechanism. It consists of two parallel parts: the 16 digit accumulator section to the rear, and the 8 digit input section to the front. The input section is mounted on rails, and can be moved parallel to the accumulator with a crank and worm gear on the left end (the crank is removed and lying in the foreground), to align the digits of the operand with different digits of the accumulator. The 16 vertical wheels on the front of accumulator section are the output dials, with numbers 0-9 around their circumference that appear in windows in the top plate. The 8 shiny horizontal disks on the input section in front are the operand dials, with knobs for setting the operand into the machine. The crank on the front performs the calculation. For more information see James Redin (2007) World of Calculators, A Brief History of Calculators Part 1: The Age of the Polymaths.
context_page_description: The step reckoner was a digital mechanical calculator invented by the German mathematician Gottfried Wilhelm Leibniz around 1673 and completed in 1694. The name comes from the translation of the German term for its operating mechanism, Staffelwalze, meaning "stepped drum". It was the first calculator that could perform all four arithmetic operations.
  Its intricate precision gearwork, however, was somewhat beyond the fabrication technology of the time; mechanical problems, in addition to a design flaw in the carry mechanism, prevented the machines from working reliably.
  Two prototypes were built; today only one survives in the National Library of Lower Saxony in Hanover, Germany. Several later replicas are on display, such as the one at the Deutsches Museum, Munich. Despite the mechanical flaws of the stepped reckoner, it suggested possibilities to future calculator builders. The operating mechanism, invented by Leibniz, called the stepped cylinder or Leibniz wheel, was used in many calculating machines for 200 years, and into the 1970s with the Curta hand calculator.
context_section_description: Leibniz got the idea for a calculating machine in 1672 in Paris, from a pedometer. Later he learned about Blaise Pascal's machine when he read Pascal's Pensees. He concentrated on expanding Pascal's mechanism so it could multiply and divide. He presented a wooden model to the Royal Society of London on 1 February 1673 and received much encouragement. In a letter of 26 March 1673 to Johann Friedrich, where he mentioned the presentation in London, Leibniz described the purpose of the "arithmetic machine" as making calculations "leicht, geschwind, gewiß" [sic], i.e. easy, fast, and reliable. Leibniz also added that theoretically the numbers calculated might be as large as desired, if the size of the machine was adjusted; quote: "eine zahl von einer ganzen Reihe Ziphern, sie sey so lang sie wolle (nach proportion der größe der Machine)"  [sic]. In English: "a number consisting of a series of figures, as long as it may be (in proportion to the size of the machine)". His first preliminary brass machine was built between 1674 and 1685. His so-called older machine was built between 1686 and 1694. The 'younger machine', the surviving machine, was built from 1690 to 1720.
  In 1775 the 'younger machine' was sent to the University of Göttingen for repair, and was forgotten. In 1876 a crew of workmen found it in an attic room of a university building in Göttingen. It was returned to Hanover in 1880. From 1894 to 1896 Artur Burkhardt, founder of a major German calculator company restored it, and it has been kept at the Niedersächsische Landesbibliothek ever since.
caption: Stepped reckoner mechanism with the housing removed
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