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Even in prehistoric times there were no doubt schemes for computation based for example on making specific arrangements of pebbles. Such schemes were somewhat formalized a few thousand years ago with the invention of the abacus. And by about 200 BC the development of gears had made it possible to create devices (such as the Antikythera device from perhaps around 90 BC) in which the positions of wheels would correspond to positions of astronomical objects. By about 100 AD Hero had described an odometer-like device that could be driven automatically and could effectively count in digital form. But it was not until the 1600s that mechanical devices for digital computation appear to have actually been built. Around 1621 Wilhelm Schickard probably built a machine based on gears for doing simplified multiplications involved in Johannes Kepler’s calculations of the orbit of the Moon. But much more widely known were the machines built in the 1640s by Blaise Pascal for doing addition on numbers with five or so digits and in the 1670s by Gottfried Leibniz for doing multiplication, division and square roots. At first, these machines were viewed mainly as curiosities. But as the technology improved, they gradually began to find practical applications. In the mid-1800s, for example, following the ideas of Charles Babbage, so-called difference engines were used to automatically compute and print tables of values of polynomials. And from the late 1800s until about 1970 mechanical calculators were in very widespread use. (In addition, starting with Stanley Jevons in 1869, a few machines were constructed for evaluating logic expressions, though they were viewed almost entirely as curiosities.)
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