1. The substance of this theorem was given byA. M. Cauchy,Memoire sur les fonctions qui ne peuvent obtenir que deux valeurs égales et de signes contraires par suite des transpositions opérées entre les variables qu’elles renferment (lu à ľInstitut le 30 novembre 1812) [Journal de ľÉcole Polytechnique, XVIIe Cahier (1815), pp. 29-112]. It is (XVIII. 5) ofTh. Muir,The Theory of Determinants in the Historical Order of Development (London, Macmillan and Co.), Part. I (Second Edition, 1906):General Determinants up to 1841; Part. II (Second Edition, 1906):Special Determinants up to 1841, hereafter referred to as: MujrHistory. — Compare: Binet (MuirHistory, Part I, p. 83).
2. J. Binet,Mémoire sur un systéme de formules analytiques, et leur application a des considerations géométriques (lu à ľInstitut le 30 novembre 1812) [Journal de ľÉcole Polytechnique, XVIe Cahier (1813), pp. 280–354]; MuirHistory (XXX.), Part I, p. 85.
3. A. L. Cauchy, loc. cit. I); MumHistory (XXX. 2), Part I, p. 121. Compare:Th. Muir,The Sum of the r-line Minors of the Square of a Determinant [Proceedings of the Royal Society of Edinburgh, Vol. XXVI (1906), pp. 533–539].
4. J. J. Sylvester,On the Relation between the Minor Determinants of Linearly Equivalent Quadratic Functions [Philosophical Magazine, Vol. I (1851), pp. 295–305].
5. Compare:Th. Muir, loc. cit. 3), arts 6 and 5.