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XXIV.—The Theory of Bigradients in the Historical Order of Development up to 1860
Published online by Cambridge University Press: 15 September 2014
Extract
As we have already pointed out (Hist., i. p. 487), bigradients were first brought to light by Sylvester in 1840 in the paper in which he made known his so-called “dialytic“ method of eliminating the unknown from two equations of the same or different degrees. Shortly afterwards Richelot and Cauchy recalled attention to Euler's and Bezout's method of 1764, as giving substantially the same result as Sylvester's, the fact being that the determinant obtained by Sylvester differs from that obtainable in the other case merely by being its conjugate. The details of these papers and of others related to them have already been given.
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- Copyright © Royal Society of Edinburgh 1910
References
page 396 note * Crelle's Journ., xxvii, pp. 105–106, 319–321.
page 397 note * This short paper of Cayley's teems with misprints, both in the original and in the Collected Math. Papers.
page 399 note * The signs require verification.
page 401 note * This identity Heilerman published again separately in 1860 (see Zeitschrift f. Math. u. Phys., v. pp. 262–263). It is included, however, in a result given by Stern in 1883 (see Grelle's Journ., x. p. 156); and a still more general identity will be found in the Proc. Edin. Math. Soc., xxiii, p. 37.
page 401 note † The expression for R4,4 is full of inaccuracies.
page 402 note * Three misprints being corrected.
page 403 note * In the expression for R4,4 there is at least one misprint, namely, a 2 c 2 for a 2 b 2 outside the third square of the chain.
page 406 note * The expression for R4,4 though now given more accurately than before, is still disfigured by at least ten misprints.