Stepped reckoner

... it is beneath the dignity of excellent men to waste their time in calculation when any peasant could do the work just as accurately with the aid of a machine.

The step reckoner (or stepped reckoner) was a digital mechanical calculator invented by the German mathematician Gottfried Wilhelm Leibniz around 1672 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 (Niedersächsische Landesbibliothek) 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.

The stepped reckoner was based on a gear mechanism that Leibniz invented and that is now called a Leibniz wheel. It is unclear how many different variants of the calculator were made. Some sources, such as the drawing to the right, show a 12 digit version. This section describes the surviving 16 digit prototype in Hanover.

The machine is about 67 cm (26 inches) long, made of polished brass and steel, mounted in an oak case. It consists of two attached parallel parts; an accumulator section to the rear, which can hold 16 decimal digits, and an 8 digit input section to the front. The input section has 8 dials with knobs to set the operand number, a telephone-like dial to the right to set the multiplier digit, and a crank on the front to perform the calculation. The result appears in the 16 windows on the rear accumulator section. The input section is mounted on rails and can be moved along the accumulator section with a crank on the left end that turns a worm gear, to change the alignment of operand digits with accumulator digits. There is also a tens-carry indicator and a control to set the machine to zero. The machine can:

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