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Early devices used to aid in calculation include the abacus (still common in E Asia) and the counting rods, or "bones," of the Scottish mathematician John Napier. The slide rule, invented in 1622 by William Oughtred, an English mathematician, was widely used to make approximate calculations, but it has been replaced by the electronic calculator. In 1642, Blaise Pascal devised what was probably the first simple adding machine using geared wheels.

In 1671 an improved mechanism for performing multiplication by the process of repeated addition was designed by Gottfried W. von Leibniz. A machine using the Leibniz mechanism was the first to be produced successfully on a commercial scale; devised in 1820 by the Frenchman Charles X. Thomas, it could be used for adding, subtracting, multiplying, or dividing. A mechanism permitting the construction of a more compact machine than the Leibniz mechanism was incorporated into a machine devised late in the 19th cent. by the American inventor Frank S. Baldwin. Later the machine was redesigned by Baldwin and another American inventor, Jay R. Monroe. At about the same time, W. T. Odhner of Russia constructed a machine using the same device as Baldwin's. Charles Babbage, an English mathematician, and William S. Burroughs, an American inventor, also made important contributions to the development of the calculating machine.

Early mechanical adding machines were equipped with a keyboard on which numbers to be added were entered, a lever to actuate the addition process, and an accumulator to display the results. A full keyboard consisted of 10 columns of keys with 9 keys in each column, numbered 1 through 9. Each column could be used to enter a figure in a particular decimal place so that a number up to 10 digits long could be entered; if no key was pressed in a given column, a zero was entered in that decimal place. The lever was pulled in one direction when a number was to be added and in the opposite direction when it was to be subtracted. The accumulator was a set of geared wheels, each corresponding to a decimal place and having the digits 0 through 9 printed on its circumference. When a given wheel made a complete rotation, the next wheel was advanced by one digit. The mechanical adding machine remained essentially the same until the mid-1960s, with improvements consisting of motors to actuate additions and subtractions and mechanisms to print out results on a paper tape.

- Introduction
- Mechanical and Electromechanical Calculators
- Electronic Calculators
- Bibliography

*The Columbia Electronic Encyclopedia,* 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.