[kragen]

I didn't know about prosthaphaeresis! Thank you!

Richard Guy developed a single-scale nomogram based on elliptic curves in 01953: https://www.jstor.org/stable/3609499

His explanation is wonderfully simple; quoting the beginning: "Since the equation x³ + ax + b = 0 has zero for the sum of its roots, the x-coordinates of the three intersections of the line y = mx + c and the curve y = x³ + px + q add to zero." It may be entertaining to attempt to derive the rest of the nomogram from that sentence and the use of logarithms before consulting the (one-page) paper.

A nice advantage of Guy's contrivance over slide rules is its facility with squares and square roots. On a conventional Oughtred slide rule you can easily enough read off the square root of a number on the A or B scales by reading across the hairline to the D or C scales, respectively; but if your square had been computed on C or D, you are out of luck. Guy's nomogram has some similar limitations, but you can in general easily take the square root of any point on it.