A Symbolic proof of Euler's Addition Theorem for Elliptic Functions

Proceedings of the Edinburgh Mathematical Society

Proceedings of the Edinburgh Mathematical Society / Volume 44 / February 1925, pp 13-21
Copyright © Edinburgh Mathematical Society 1925
DOI: http://dx.doi.org/10.1017/S0013091500034301 (About DOI), Published online: 20 January 2009

§1. Let S0013091500034301_inline1 be a binary quartic; then I propose to show symbolically that the solution of Euler's differential equation

can be written in the form

where

are otherwise arbitrary.

(Received October 05 1925)

(Accepted June 05 1925)

^{page 14 note *} Grace and Young, Algebra of Invariants, p. 198.

^{page 15 note *} Grace and Young, loco, cit., p. 198.

^{page 17 note *} Prof. Turnbull, H. W., Proc. Roy. Soc, Edinb., 44 (1924), 23–50 [OpenURL Query Data] [Google Scholar].

^{page 19 note *} Proc. R.S.E., loco. cit.

^{page 20 note *} The notation used is that of Peano, quoted in Proc. R. S. E., loco. cit.