[20] Cf. Hon. Bertrand Russell, “Is Position in Time and Space Absolute or Relative?” Mind, n.s. vol. 10 (1901), and A.N. Whitehead, “Mathematical Concepts of the Material World,” Phil. Trans. (1906), p. 205.
[21] Cf. Critique of Pure Reason, 1st section: “Of Space,” conclusion A, Max Müller’s translation.
[22] Cf. Ernst Mach, Erkenntniss und Irrtum (Leipzig); the relevant chapters are translated by T.J. McCormack, Space and Geometry (London, 1906); also A. Meinong, Über die Stellung der Gegenstandstheorie im System der Wissenschaften (Leipzig, 1907).
[23] Cf. Russell, Principles of Mathematics, § 352 (Cambridge, 1903).
[24] Cf. A.N. Whitehead, The Axioms of Projective Geometry, § 3 (Cambridge, 1906).
[25] Cf. Russell, Princ. of Math., ch. i.
[26] Cf. Russell, loc. cit., and G. Frege, “Über die Grundlagen der Géométrie,” Jahresber. der Deutsch. Math. Ver. (1906).
[27] This formulation—though not in respect to number—is in all essentials that of M. Pieri, cf. “I principii della Geometria di Posizione,” Accad. R. di Torino (1898); also cf. Whitehead, loc. cit.
[28] Cf. G. Peano, “Sui fondamenti della Geometria,” p. 73, Rivista di matematica, vol. iv. (1894), and D. Hilbert, Grundlagen der Geometrie (Leipzig, 1899); and R.F. Moulton, “A Simple non-Desarguesian Plane Geometry,” Trans. Amer. Math. Soc., vol. iii. (1902).
[29] Cf. “Sui postulati fondamentali della geometria projettiva,” Giorn. di matematica, vol. xxx. (1891); also of Pieri, loc. cit., and Whitehead, loc. cit.