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**Gottfried Wilhelm Leibniz and his calculating machine**

report by Torsten Brandes

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Chapter 1 Construction of mechanical calculating machines

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**Structure of a mechanical calculating machine**

counting mechanism two counting wheels

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**counting mechanism Every counting wheel represents a digit.**

By rotating in positive direction it is able to add, by rotating in negative direction it is able to subtract. If the capacity of a digit is exceeded, a carry occurs. The carry has to be handed over the next digit.

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**counting mechanism S – lever Zi – toothed wheel**

dealing with the carry between two digits

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**Chapter 2: calculating machines bevore and after Leibniz**

1623 Wilhelm Schickard developes a calculating machine for all the four basic arithmetic operations. It helped Johann Kepler to calculate planet‘s orbits. 1641 Blaise Pascal developes an adding- and subtracting machine to maintain his father, who worked as a taxman. Leibniz is working on his calculator. 1774 Philipp Matthäus Hahn ( ) contructed the first solid machine.

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**Leibniz‘ calculating machine.**

Leibniz began in the 1670 to deal with the topic. He intended to construct a machine which could perform the four basic arithmetic operations automatically. There where four machines at all. One (the last one) is preserved.

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stepped drum A configuration of staggered teeth. The toothed wheel can be turned 0 to 9 teeth, depending of the position of this wheel.

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**four basic operations performing machine by Leibniz**

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**Skizze H – crank K – crank for arithmetic shift rotation counter**

drawing: W. Jordan H – crank K – crank for arithmetic shift rotation counter

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**Functionality Addition: partitioning in two tacts**

Addition digit by digit, saving the occuring carries with a toothed wheel. Adding the saved carries to the given sums, calculated before.

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**Subtraction. Similar to adding.**

The orientation of rotating the crank has to be turned.

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**Multiplication (excampel)**

was possible by interated additions 32.448*75 Input of in the adjusting mechanism. Input of 5 in the rotation counter. Rotating the crank H once. The counting mechanism shows Rotating the crank K. The adjusting mechanism is shifted one digit left. Input of 7 in the rotation counter. Rotating the crank H once. The counting mechanism shows

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