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Leibniz's Calculating Machine

William Gottfried Leibniz (1646-1716) was the co-inventor of Calculus (along with Newton), and a practical mathematician. He was the inventor of a mechanical calculating machine that could add, subtract, multiply, and divide -- these latter two features were revolutionary in Leibniz's day. A faintly similar machine had been built by Pascal (a model which Leibniz had seen and been inspired by), but lacked the capability to multiply and divide.

The most innovating and curious feature of Leibniz's machine is the stepped drum that it uses to accumulate a sum of multiple digit numbers in a single rotation of a crankshaft. Not surprisingly, the machine is named after this feature, the "Stepped Reckoner." To illustrate this and the general operation of the machine, I would like to share a simple animation that I have been working on this semester (as part of independent extra Calculus project) of the interior of the machine as it performs a simple addition.

Here are the steps (I know it's a bit hard to follow in 20 seconds):

  1. The first number to be added, 23, is dialed in using the two dials at the top. Turning these dials move the steps drums underneath a smaller gear (see above right image).
  2. The crank is turned one full rotation. The stepped drums rotate and catch the smaller gears -- attached to the counting dials -- the specified number of times, by catching the correct amount of teeth arranged around the stepped drum that was aligned in step 1.
  3. The second number to be added (42) is dialed in at the top, as in step 1.
  4. Once again the crank is turned; the left drum (ten's place) catches its gear 4 times, incrementing to 6; and the right drum (one's place) increments twice, equaling 5.
  5. The number shown on the counting dials is the result: 23+42=65.

For more information on the Stepped Reckoner, you may find these resources (not my own) to be of use: