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Turn the wheels one way and one performs an addition, the other way a subtraction. As part of a redesign of the arithmometer , [ 1 ] they reduced by an order of magnitude the cost and the size of mechanical calculators on which one could easily do the four basic operations (add, subtract, multiply and divide).
A diagram of a wheel, as the real projective line with a point at nullity (denoted by ⊥). A wheel is a type of algebra (in the sense of universal algebra) where division is always defined. In particular, division by zero is meaningful. The real numbers can be extended to a wheel, as can any commutative ring.
Schickard's machine used clock wheels which were made stronger and were therefore heavier, to prevent them from being damaged by the force of an operator input. Each digit used a display wheel, an input wheel and an intermediate wheel. During a carry transfer all these wheels meshed with the wheels of the digit receiving the carry.
Now the user pressed the multiplication 1 key. The machine cycled once. To see the total the user was required to press a Total key and the machine would print the result on a paper tape, release the locked down keys, reset the adding mechanism to zero and tabulate it back to its home position. Modern adding machines are like simple calculators.
In the position shown, the counting wheel meshes with three of the nine teeth of the Leibniz wheel. In 1672, Gottfried Leibniz started working on adding direct multiplication to what he understood was the working of Pascal's calculator. However, it is doubtful that he had ever fully seen the mechanism and the method could not have worked ...
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