^{note * page 61} The full name is Alexis Fontaíne des Bertins. The very same collection was issued in 1770 under the less appropriate title Traité de calcul différentiel εt intégral. Vandermonde is said to have been a pupil of Fontaine's (v. Nouv. Annales de Math., v. p. 155).

^{note * page 65} Jacobi writes it with the caution that the two parts are not to be taken as cancelling one another. Of course, also, lower down he does not write |a ₀b ₁| but a ₀b ₁ − a ₁b ₀ or later (a ₀b ₁).

^{note * page 75} See Rothe's paper of the year 1800.

^{note * page 76} See Sylvester's paper of 1840.Google Scholar

^{note * page 78} As the memoir of Lagrange which Cayley refers to is not one of those brought into notice in the early part of our history, but is one bearing the title “Sur le problème de la détermination des orbites des comètes d'après trois—Nouv. Mém. de l'Acad. Roy (Berlin), ann. 1778, p. 160.Google Scholar

^{note * page 83} See Postscript to Cayley's paper “On the Theory of Permutants,” Camb. and Dub. Math. Journ., vii. pp. 40–51; or Collected Math. Papers, ii. pp. 16–26.

^{note * page 84} This is stated to be a translation of the preceding paper, with certain additions by the author; and as such it is not reprinted in Collected Math. Papers. It also contains the substance of the paper which follows, the latter having been delayed in publication.

^{note † page 84} And indeed the covariants also.

^{note * page 85} In Liouville's Journal brackets, [ ] or { }, were used in Cayley's own papers of the year 1845. See vol. x.Google Scholar

^{note * page 91} The date 1833 has been assigned to this “rule “in a recent German textbook on determinants (Weichold's): if 1833 be the correct date the “rule “probably will be found in a publication by Sarrus entitled Nouvelle méthode pour la résolution des équations, which appeared at Strasbourg in that year.Google Scholar