# Gottfried Wilhelm Leibniz and his calculating machine

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Gottfried Wilhelm Leibniz and his calculating machine
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. Leibniz is working on his calculator.  1774 Philipp Matthäus Hahn ( ) 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.

four basic operations performing machine by Leibniz

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

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.