[40] Cf. O. Veblen, “On the Projective Axioms of Geometry,” Trans. Amer. Math. Soc. vol. iii. (1902).
[41] Cf. P. Stäckel and F. Engel, Die Theorie der Parallellinien von Euklid bis auf Gauss (Leipzig, 1895).
[42] Cf. Pasch, loc. cit., and R. Bonola, “Sulla introduzione degli enti improprii in geometria projettive,” Giorn. di mat. vol. xxxviii. (1900); and Whitehead, Axioms of Descriptive Geometry (Cambridge, 1907).
[43] The original idea (confined to this particular case) of ideal points is due to von Staudt (loc. cit.).
[44] Cf. Critique, “Trans. Aesth.” Sect. I.
[45] Cf. loc. cit.
[46] Cf. Über die Grundlagen der Geometrie (Leipzig, Ber., 1890); and Theorie der Transformationsgruppen (Leipzig, 1893), vol. iii.
[47] Cf. A. Cayley, “A Sixth Memoir on Quantics,” Trans. Roy. Soc., 1859, and Coll. Papers, vol. ii.; and F. Klein, Math. Ann. vol. iv., 1871.
[48] Cf. loc. cit.
[49] For similar deductions from a third set of axioms, suggested in essence by Peano, Riv. mat. vol. iv. loc. cit. cf. Whitehead, Desc. Geom. loc. cit.