[1] For Egyptian geometry see [Egypt], § Science and Mathematics.
[2] Cf. A.N. Whitehead, Universal Algebra, Bk. vi. (Cambridge, 1898).
[3] Cf. A.N. Whitehead, loc. cit.
[4] Cf. A.N. Whitehead, “The Geodesic Geometry of Surfaces in non-Euclidean Space,” Proc. Lond. Math. Soc. vol. xxix.
[5] Cf. Klein, “Zur nicht-Euklidischen Geometrie,” Math. Annal. vol. xxxvii.
[6] On the theory of parallels before Lobatchewsky, see Stäckel und Engel, Theorie der Parallellinien von Euklid bis auf Gauss (Leipzig, 1895). The foregoing remarks are based upon the materials collected in this work.
[7] See Stäckel und Engel, op. cit., and “Gauss, die beiden Bolyai, und die nicht-Euklidische Geometrie,” Math. Annalen, Bd. xlix.; also Engel’s translation of Lobatchewsky (Leipzig, 1898), pp. 378 ff.
[8] Lobatchewsky’s works on the subject are the following:—“On the Foundations of Geometry,” Kazañ Messenger, 1829-1830; “New Foundations of Geometry, with a complete Theory of Parallels,” Proceedings of the University of Kazañ, 1835 (both in Russian, but translated into German by Engel, Leipzig, 1898); “Géométrie imaginaire,” Crelle’s Journal, 1837; Theorie der Parallellinien (Berlin, 1840; 2nd ed., 1887; translated by Halsted, Austin, Texas, 1891). His results appear to have been set forth in a paper (now lost) which he read at Kazañ in 1826.
[9] Translated by Halsted (Austin, Texas, 4th ed., 1896.)