Certain theorems in analysis, of which a demonstration is thus far desired
The three theorems are: Clearly all imaginary [complex] quantities whatsoever which can occur in analytic calculus can be renamed to this most simple form a + b √(-1), such that the letters a and b denote real quantities; Except for the circle, there is no algebraic curve whose individual arc lengths can be expressed simply by circular arcs; There is absolutely no algebraic curve whose individual arc lengths can be expressed simply by logarithms.
Original Source Citation
Opuscula analytica, Volume 2, pp. 76-90.
Opera Omnia Citation
Series 1, Volume 21, pp.78-90.