‎"CAYLEY, ARTHUR. - A FUNDAMENTAL PAPER ON INVARIANT THEORY.‎
‎An Introductory Memoir upon Quantics. received April 20, - Read may 4, 1854.‎

‎(London, Richard Taylor and William Francis, 1854). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1854, Vol. 144 - Part I. Pp. 245-258.‎

Reference : 49410

‎First printing of the first paper in Cayley's famous memoirs on 'quantics', a term he coined for algebraic forms. In this paper Cayley throughout remodelled the whole basis for Invariant Theory.""In addition to his part in founding the theory of abstract groups, Cayley has a number of important theorems to his credit: perhaps the best known is that every finite group whatsoever is isomorphic with a suitable group of permutations (see the first paper of 1854). This is often reckoned to be one of the three most important theorems of the subject, the others being the theorems of Lagrange and Sylow. But perhaps still more significant was his early appreciation of the way in which the theory of groups was capable of drawing together many different domains of mathematics: his own illustrations, for instance, were drawn from the theories of elliptic functions, matrices, quantics, quaternions, homographic transformations, and the theory of equations. If Cayley failed to pursue his abstract approach, this fact is perhaps best explained in terms of the enormous progress he was making in these subjects taken individually.""(DSB)‎