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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).
Now form wheel 3 with length 5 × 6 = 30 by first extending wheel 2 up to 30 and then deleting 5 times each number in wheel 2 (in reverse order!), to get 1 2 3 5 7 11 13 17 19 23 25 29. The first number after 1 for wheel 3 is 7; note it as a prime. Now wheel 4 has length 7 × 30 = 210, so we only extend wheel 3 up to our limit 150. (No further ...
For example, the range 1 to 10 is a single decade, and the range from 10 to 100 is another decade. Thus, single-decade scales (named C and D) range from 1 to 10 across the entire length of the slide rule, while double-decade scales (named A and B) range from 1 to 100 over the length of the slide rule.
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.
Multiplication was a simple process of keying in the numbers one or more columns to the left and repeating the "addition" process. For example, to multiply 34.72 by 102, key in 3472, pull crank, repeat once more. Wheels show 6944. Key in 3472(00), pull crank. Wheels now show 354144, or 3,541.44.
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