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Calculemus! New research results and functional models regarding Leibniz' four function calculating machine and binary calculating machine

Stein E., Kopp F. O., Wiechmann K., Weber G.

Foundations of Civil and Environmental Engineering

2006

No. 7

319-332

The decimal carries of Leibniz1 Four Function Calculating Machine have mainly been discussed herein. This machine may not complete the decimal carries which is indicated by the pentagonal discs in skew positions. This can be overcome by setting the input number to zero and turning the crank in idle mode at the end of a calculation. N. J. Lehmann, Dresden, built several replicas in the 1980s with decreasing spreading angels of the twin-horn wheels from right to left in order to complete the decimal carries without post-turning the crank which, however, is not sufficient in general. F. O. Kopp, K. Poppf and E. Stein additionally reduced the pitch angle of the step drums, based on analytical and numerical optimizations, to get the correct decimal carries and built a fully functioning Hannover model in 2004/05, scale 2:1. Moreover, a new construction and functional model of the "machina arithmeticae dyadicac" (a binary calculating machine for adding and multiplying with down-rolling metal balls) after Leibniz' description has been presented.