# Pascal's calculator

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Blaise Pascal invented the second mechanical calculator, called alternatively the * Pascalina* or the

*, in 1645, the first being that of Wilhelm Schickard in 1623.*

**Arithmetique**Pascal began work on his calculator in 1642, when he was only 19 years old. He had been assisting his father, who worked as a tax commissioner, and sought to produce a device which could reduce some of his workload. Pascal received a Royal Privilege in 1649 that granted him exclusive rights to make and sell calculating machines in France. By 1652 Pascal claimed to have produced some fifty prototypes and sold just over a dozen machines, but the cost and complexity of the Pascaline—combined with the fact that it could only add and subtract, and the latter with difficulty—was a barrier to further sales, and production ceased in that year. By that time Pascal had moved on to other pursuits, initially the study of atmospheric pressure, and later philosophy.

Pascalines came in both decimal
and non-decimal varieties, both of which exist in museums today. The
contemporary French currency system was similar to the Imperial pounds
("*livres*"), shillings ("*sols*") and pence ("*deniers*") in use in Britain until the 1970s.

In 1799 France changed to a metric system,
by which time Pascal's basic design had inspired other craftsmen,
although with a similar lack of commercial success. Child prodigy Gottfried Wilhelm Leibniz devised a competing design, the Stepped Reckoner,
in 1672 which could perform addition, subtraction, multiplication and
division; Leibniz struggled for forty years to perfect his design and
produce sufficiently reliable machines. Calculating machines did not
become commercially viable until the early 19th century, when Charles Xavier Thomas de Colmar's *Arithmometer*, itself using the key break through of Leibniz's design, was commercially successful [1].

The initial prototype of the Pascaline had only a few dials, whilst later production variants had eight dials, the latter being able to deal with numbers up to 9,999,999.

The calculator had spoked metal wheel dials, with the digit 0 through 9 displayed around the circumference of each wheel. To input a digit, the user placed a stylus in the corresponding space between the spokes, and turned the dial until a metal stop at the bottom was reached, similar to the way a rotary telephone dial is used. This would display the number in the boxes at the top of the calculator. Then, one would simply redial the second number to be added, causing the sum of both numbers to appear in boxes at the top. Since the gears of the calculator only rotated in one direction, negative numbers could not be directly summed. To subtract one number from another, the method of nines' complements was used. To help the user, when a number was entered its nines' complement appeared in a box above the box containing the original value entered.