Published online by Cambridge University Press: 24 October 2008
In the Transactions of the American Math. Society, vol. I, 1900, and vol. IV, 1904, Mr E. Kasner treats exhaustively the (2, 2) double binary form and discusses the theory connected with double binary forms and multiple binary forms in general terms. He shows the relations between the systems of multiple binary forms with digredient variables and the forms with cogredient variables. Hitherto nothing seems to have been written on systems of triple binary forms (with regard to higher forms see a paper on the (1, 1, 1, 1) form by C. Segre); so here I propose to discuss the complete system of a (1, 1, 1) binary form which consists of six forms connected by one syzygy. When two of the variables are the same we naturally get the (2, 1) form and when the three are the same We get the (3) or cubic binary form.
* Annali di Mat. (3), 29, 105–140 (1920).Google Scholar
† The necessary x, y, z factors are to be added.
* Grace, and Young, , Algebra of Invariants, pp. 85–100Google Scholar; Peano, , Battaglini, vol. 20 (1882).Google Scholar
† In Φ2, Φ1, and in what follows, indicates the implied necessary x, y, z factors.