A calculating machine is a machine, with those assistance determined mathematical computations to be automated implemented can. A calculating machine is thus a device for calculation, which supports the computation of mathematical tasks, as as little as possible cognitive expenditure is demanded from the user of the machine. Which computations are possible, depends on the machine and the algorithms offered for this machine.

The first calculating machines were mechanical. Far common above all the relatively inexpensive adding machines into the 70's-years, which controlled only the addition and subtraction (therefore also two-species machines called, were), which however in many ranges of application was sufficient. Three-species machines more or less automatically could implement additionally the multiplication and four-species machines also the division.

Three and four-species machines were designed particularly according to two principles: Staffelwalze and sprocket wheel.

Historical development

The first documentary mentioned calculating machine was scarcely described 1623 by William sending pool of broadcasting corporations in a letter at Johannes Kepler. The machine consists of an adding and a subtracter according to kind of the Napier as well as a device for multiplying and dividing. Sending pool of broadcasting corporations reports that it also realized this machine. One assumes that this machine was lost later during a fire of its house.

1645 demonstrated the Frenchman Blaise Pascal its calculating machine "“Pascaline"”, which functions with gear wheels and pawls. Pascal manufactured some these machines and dispatched it to European prince houses. For this reason today also still some original Pascalinen exist apart from many reproductions.

Between Germans and French historians gladly about one argues who nation brought now the first calculating machine out. As so often this question cannot be answered objectively. By sending pool of broadcasting corporations the first construction design is provable and the first Machine received from Pascal.

Both machine types have a common problem. They are not suitable for the everyday employment as calculating machines. They contain important operational principles, not however of devices, which make daily safe work possible.

Thus the possibility is missing to the machine of William sending pool of broadcasting corporations of storing energy for the decimal carry of each decimal place. That means that the calculation 9+1 is to be mastered simply, however 9999+1 high energy expenditure required and probably to blocking the machine led.

In the machine of Blaise Pascal prevent pawls a free swivellingness of the gear wheels, these by the force of gravity are down held. This leads to the fact that the machine under the phenomenon of the "“over hurling"” suffers. The problem is that gear wheels or whole transmissions move on as slow-acting mass also without drive with the result that the result of computation is falsified, since the machine counts with addition 1 or more too much.

1673 presented developed relay roller machine of the Royal Society in London to Gottfried William Leibniz one of it. This calculating machine is today still in the original in the federal state museum Hanover received. How well this machine actually worked, cannot be said unfortunately with absolute certainty. To the end 19. Century the German calculating machine manufacturer Arthur Burkhardt was assigned to repair the Leibniz machine. Today the original machine is not ready for use.

The finishing technique at that time could manufacture gear wheels and other mechanical parts very exactly, was however from an exchange's building far. The individual parts had to be manufactured manually and adapted together by remachining. Even if the construction of the mechanics for the 10er-Stelle were identical to the 100er-Stelle, one could not exchange the mobile parts between both places, without having to do over again.

Therefore is to be assumed the original machine of Leibniz could count the problem examples duly and in the course of the time by changes and false repairs was blocked. The reproductions Heinz Nixdorf museum forum and the German museum function anyhow perfectly. They developed however also using modern finishing techniques.

Leibniz manufactured a calculating machine with all necessary design features, to a quantity production never came it.

1709 publish the Italian mathematician and astronomer Giovanni Poleni (1683-1761) the construction designs of its wooden calculating machine. This functions to the so-called sprocket wheels on basis of gear wheels with changeable number of teeth. The realization of its machine failed because of the manufacturing possibilities at that time, so that Poleni destroyed its machine personally. Reproductions exist e.g. in the Museo di Storia della Scienza Firence (Florenz) and in the Arithmeum Bonn.

1727 become the sprocket wheel calculating machine for the Viennese yard, designed by Antonius brown (1686-1728), finished. It is dedicated to emperors Karl VI and is today in the technical museum Vienna. From this machine exist today only accurate copying in the Arithmeum a Bonn. Over the serviceability of the machine for the everyday life enterprise one stated when measuring and to make a replication that she could work only over three to four places faultlessly: The decimal carry did not function over a larger number of places. Construction and fine-mechanical accuracy nevertheless permit such a development at this time.

1727 publish the German mechanic Jacob Leupold (1674-1727) in its technical encyclopedia "“Theatrum Aritmetico Geometricum"” construction designs of a calculating machine invented by it, which works according to the placing segment principle. One assumes that brown already knew this construction before the and copied the machine around 1727. It was however only placed around 1736 of the French instrument farmer Philippe Vayringe (1684-1746) finished (inscription: "“Brown invenit, Vayringe fecit"”). Therefore the calculating machine of the Antonius brown is called today "“Leupold brown Vayringe machine"”. It is in the German museum Munich.

Starting from 1770 the minister and inventor Philipp cock (1739-1790) design a calculating machine in dose form with concentrically arranged gear wheels, Staffelwalzen and a central operating handle. From this machine it manufactured four or five copies, which partially today still exist federal state museum Stuttgart) and are functional. It is the first fully functional four-species calculator with of several characters and two-stage decimal carry.

The central operating handle inspired by Leupold, the relay roller principle and the improved manufacturing possibilities contribute to the fact that many historians in the machine see minister cock the first everyday life-suited calculating machine.

Although the technical manufacturing possibilities would have to this time a limited production of these machines certified and at least the calculating machines of cock "“useful"” were, no machine of the inventors in series, specified above, was built. This may be justified in it that the calculating machines at the beginning of their development stood, consequently for practical application yet not developed enough and too expensively in the production was. The most relevant reason was however that there was still no market for such machines. National administrations, the military or buyers suffered from no time pressure or lack of worker.

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