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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.[1] 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.[2]
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.[3][4]
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.[5] 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.
Description
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Further information: Leibniz wheel
Drawing of a stepped reckoner from 1897 Meyers Konversations-Lexikon, showing a 12-digit version
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.[4] This section describes the surviving 16 digit prototype in Hanover.
Leibniz wheel
In the position shown, the counting wheel meshes with 3 of the 9 teeth on the Leibniz wheel
The machine is about 67 cm (26 inches) long, made of polished brass and steel, mounted in an oak case.[1] 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:
add or subtract an 8-digit number to / from a 16-digit number
multiply two 8-digit numbers to get a 16-digit result
divide a 16-digit number by an 8-digit divisor
Addition or subtraction is performed in a single step, with a turn of the crank. Multiplication and division are performed digit by digit on the multiplier or divisor digits, in a procedure equivalent to the familiar long multiplication and long division procedures taught in school. Sequences of these operations can be performed on the number in the accumulator; for example it can calculate roots by a series of divisions and additions.
History
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Stepped reckoner mechanism with the housing removed
Further information: Precursors to the mechanical calculator
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.
Answer:
Leibniz calculator was a mechanical device developed by the famous German mathematician Leibniz in 1671. It was a improvement.