The Aritmometer was the first device capable of performing mathematical calculations automatically. It was invented in 1623 by the German mathematician and philosopher Wilhelm Schickard. However, Schickard’s original machine was lost, and no specimen survived. The oldest Aritmometer for which documentation exists dates back to 1642 and was created by the French scientist, engineer, astronomer, and mathematician Blaise Pascal.

Pascal’s Aritmometer (which he called Pascaline) operated using a set of toothed wheels that could rotate individually and were marked with digits from 0 to 9. Each wheel represented a different decimal place, allowing calculations with any number. To perform addition, subtraction, multiplication, or division, the operator manually turned the wheels to align the correct digits based on calculation tables.

Although a rather rudimentary machine compared to today’s calculators, Pascal’s Aritmometer was a significant technological advancement for its time. It allowed automatic calculations without the need for an abacus or tedious manual calculations. Pascal built approximately 20 models of his Aritmometer, which were relatively large and heavy as they were entirely made of metal.

Pascalines by Blaise Pascal at the Musée des Arts de Métiers, Paris | photo Edal Anton Lefterov on Wikimedia Commons

In 1673, the German mathematician Gottfried Leibniz refined Pascal’s design by introducing a gear system that automatically aligned the wheels during calculations. With Leibniz’s improvements, the Aritmometer could add, subtract, multiply, and divide much more easily than the original model, as the wheels spun automatically to display the final result.

The main improvements Gottfried Leibniz introduced to the Aritmometer’s design were a gear system that automatically aligned the wheels during calculations. In Pascal’s original model, the operator had to manually turn each wheel to align the numbers. With Leibniz’s gear system, the wheels rotated on their own during the calculation process.

This made calculations much simpler and faster, as the user did not have to worry about turning each wheel in the correct order and position. They only needed to input the initial numbers, and the Aritmometer displayed the result automatically.

Leibniz also improved the overall design of the Aritmometer to make it more robust and reliable. The gears allowed a more precise movement of the wheels.

He introduced mechanisms to prevent the wheels from misaligning during the calculation process, which could lead to errors. This increased the precision and reliability of the device.

The Aritmometers manufactured by Pascal and Leibniz revolutionized the world of mathematical calculations and laid the groundwork for the development of the first mechanical and electrical calculators in the 19th and 20th centuries. Although still a primitive machine compared to today’s calculators, the Aritmometer demonstrated that it was possible to automate mathematical processes using gears and wheels, paving the way for modern calculators


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