What characterized the series of teeth on Leibniz's stepped drum for multiplication?
Answer
Varying lengths corresponding to numbers one through nine
The defining physical feature of the stepped drum, which enabled the concept of the Leibniz multiplier, was the arrangement of its teeth. Unlike simpler notched wheels, Leibniz designed this crucial component so that it featured teeth of differing lengths. Specifically, these lengths corresponded numerically to the values one, two, three, all the way up to nine. This allowed the mechanical system to instantaneously know how far to advance the result gear based on the multiplier digit engaged, fundamentally tying the physical structure of the cylinder directly to base-ten arithmetic for multiplication.
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Gottfried Wilhelm Leibniz, 1672, demonstration video - YouTube
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