Leibniz's Early Calculator

If you were not yet convinced of the versatility of his expertise, Gottfried Wilhelm von Leibniz was also talented in technics, or the mechanical and industrial arts. In 1671, Leibniz invented a calculating machine now known as the Step Reckoner, which eventually helped him gain access to the London Royal Society a few years later.  This prestigious group of philosophers and physicians originated in 1660 and still operates today, making Leibniz part of the first generation of thinkers to be inducted into the elite circle. 

Gottfried tells in his manuscript’s from 1685 (after the machine had been invented, prototyped and perfected) that his initial fascination with mathematical instruments was “When, several years ago, I saw for the first time an instrument which, when carried, automatically records the numbers of steps taken by a pedestrian, it occurred to me at once that the entire arithmetic could be subjected to a similar kind of machinery so that not only counting but also addition and subtraction, multiplication and division could be accomplished by a suitably arranged machine easily, promptly, and with sure results.”  It was not until he was in Paris that he became better equipped with an array of knowledge for such an invention.

             When Gottfried Wilhelm von Leibniz was in Paris for his diplomatic missions, he had access to the unpublished works of Parisian masterminds, namely Pascal.  As he became better acquainted with his life’s work, Leibniz took an interest in Pascal’s idea of a machine that computes mathematics.  It is assumed that this is where the inspiration for the Step Reckoner came from, as Leibniz’s designs began as an improvement of Pascal’s “Pascaline.”  Leibniz drew from what he learned about Pascal’s machine which could perform addition and subtraction and made one that could compute matters of multiplication and division.  However, his design was far different from Pascal’s.  The Step Reckoner had the capabilities to work with large numbers, which made calculations simple, quick and reliable.  Leibniz’s goal was to create an apparatus that even young, inexperienced boys could use to do complicated arithmetic.  He succeeded, as the Step Reckoner is "considered a technical marvel of its time and ranks among the most prestigious cultural treasures of the 17th century." 

One of the remaining prototypes of the Step Reckoner

For the purposes of simplicity, the Step Reckoner operated on several step drums which can be twisted by using a crank and cogs of different sizes.  The direction in which the crank is turned determines whether the user is performing addition or subtraction.  Multiplication is performed as a repeated addition and division as repeated subtraction. The Step Reckoner was comprised of a small window for the input mechanisms of the arithmetic, inner workings that performed the computations (think – the machine understood carrying and place values!) and a small output window that read the final answer. 
           In present time, two versions of the machine exist and are viewable in museums today.  One was recovered and preserved at the Deutsches Museum in Munich and the other was stored and forgotten in the attic of the University Church of Gottingen until it was discovered by a work crew who was working on the building's leaky roof.  This machine remains on display at the Gottfried Wilhelm Leibniz Library in Hannover.

A modern day replica of Gottfried Wilhelm von Leibniz's early calculator.

References:

Belaval, Y. & Look, B.C. (2017).  Gottfried Wilhelm Leibniz.  Retrieved from https://www.britannica.com/biography/Gottfried-Wilhelm-Leibniz

Redaktion Hannover.de (2015). Leibniz Calculating Machine. Retrieved from: https://www.hannover.de/en/Tourism-Culture/Event-Highlights/Specials/Year-of-Leibniz-2016/Leibniz-Calculating-Machine

Dalakov, Georgi (2018).  The Stepped Reckoner of Gottfried Leibniz. Retrieved from:

                        http://history-computer.com/MechanicalCalculators/Pioneers/Lebniz.html