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##### Gottfried Wilhelm Leibniz and his calculating machine

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**Gottfried Wilhelm Leibniz and his calculatingmachine**report by Torsten Brandes**Chapter 1**• Construction of mechanical calculating machines**Structure of a mechanical calculating machine**• counting mechanism two counting wheels**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.**counting mechanism**S – lever Zi – toothed wheel dealing with the carry between two digits**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. • 1670 - 1700 Leibniz is working on his calculator. • 1774 Philipp Matthäus Hahn (1739-1790) contructed the first solid machine.**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.**stepped drum**A configuration of staggered teeth. The toothed wheel can be turned 0 to 9 teeth, depending of the position of this wheel.**Skizze**• H – crank • K – crank for arithmetic shift • rotation counter drawing: W. Jordan**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.**Subtraction.**• Similar to adding. • The orientation of rotating the crank has to be turned.**Multiplication (excampel)**• was possible by interated additions • 32.448*75 • Input of 32.448 in the adjusting mechanism. • Input of 5 in the rotation counter. • Rotating the crank H once. The counting mechanism shows 162.240. • 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 2.433.600.