[10] Abhandlungen d. Königl. Ges. d. Wiss. zu Göttingen, Bd. xiii.; Ges. math. Werke, pp. 254-269; translated by Clifford, Collected Mathematical Papers.
[11] Cf. Gesamm. math. und phys. Werke, vol. i. (Leipzig, 1894).
[12] Wiss. Abh. vol. ii. pp. 610, 618 (1866, 1868).
[13] Mind, O.S., vols. i. and iii.; Vorträge und Reden, vol. ii. pp. 1, 256.
[14] His papers are “Saggio di interpretazione della geometria non-Euclidea,” Giornale di matematiche, vol. vi. (1868); “Teoria fondamentale degli spazii di curvatura costante,” Annali di matematica, vol. ii. (1868-1869). Both were translated into French by J. Hoüel, Annales scientifiques de l’École Normale supérieure, vol. vi. (1869).
[15] Beltrami shows also that this definition agrees with that of Gauss.
[16] “Sur la théorie des foyers,” Nouv. Ann. vol. xii.
[17] Math. Annalen, iv. vi., 1871-1872.
[18] For an investigation of these and similar properties, see Whitehead, Universal Algebra (Cambridge, 1898), bk. vi. ch. ii. The polar form was independently discovered by Simon Newcomb in 1877.
[19] For an analysis of Leibnitz’s ideas on space, cf. B. Russell, The Philosophy of Leibnitz, chs. viii.-x.