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. 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.

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.

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.