Numerical Solution of Algebraic Equations

Abstract

IN his account of Newton's work in pure mathematics (NATURE, Mar. 26, Suppt. p. 42), Prof. Mordell directs attention to the method of solving the cubic equation introduced by him. This method is in principle precisely that usually attributed to Horner; but the form quoted by Prof. Mordell is much more convenient in application than that given in most modern works on algebra. In the original form of the method, when we want to reduce the equation by 2, we replace y by p + 2, and rearrange in powers of p. In the usual form we divide three times by y 2; thus in finding the coefficient of the second term we add 2 to the original coefficient three times instead of simply adding 6. The introduction of division resulted in a great increase in labour instead of a reduction. If there is any doubt, try it both ways and see!