The mystery of space

[1] Vide Popular Science Monthly, vol. 78, p. 554, 1911.

[2] Vide New York Mathematical Society Bulletin, Vol. III, 1893-4, p. 79, G. B. Halstead on Lambert's Non-Euclidean Geometry.

[3] Prolegomena, Kant, p. 37, Trans. by J. P. Mahaffy and J. H. Bernard.

[4] In 1754 D'Alembert (1717-1783) published an article in the famous old Encyclopedia edited by Diderot and himself on Dimension. In this article the idea of the fourth dimension is dwelt upon at length. The view which he expressed in this article, of course, served greatly to popularize the conception among the learned men of the day, and owing to the close relationship existing between D'Alembert and La Grange, it is not surprising that the latter should have been very much enamored of the idea.

[5] Vide Nature, Vol. VIII, pp. 14-17; 36, 37 (1873); also Mathematical Papers, pp. 65-71.

[6] Mathematics, by C. J. Keyser, Adrian Professor of Mathematics, Columbia University.

[7] The science of pure mathematics is perhaps indebted to no one in so great a degree as to George Bruce Halstead, formerly of the University of Texas, whose labors in connection with the popular exposition of the non-Euclidean geometry have been most untiring and effectual. Vide Popular Astronomy, Vol. VII and VIII, 1900, Dr. G. B. Halstead.

[8] Note.—M may be any point on the line BA indefinitely produced.

[9] Vide Non-Euclidean Geometry, p. 91.

[10] Vide Nature, Vol. XLV, 1892.

[11] Vide Monist, Vol. XVI, 1896, Mathematical Emancipations.

[12] Vide Monist, Vol. XIX, p. 402 (1909).

[13] Philosophical Review, Vol. VII (1898).

[14] Vide Foundations of Mathematics, p. 107.

[15] Vide Foundations of Mathematics, p. 42.

[16] Vide Science, Vol. VII, p. 2, No. 158, 1898.

[17] Vide Foundations of Mathematics, pp. 93-94.

[18] Vide Philosophical Review, Vol. V, 1896, p. 352, et. seq.

[19] Vide Monist, Vol. XVI, 1896, Mathematical Emancipations.

[20] Vide Fourth Dimension, Simply Explained, edited by H. P. Manning, p. 28.

[21] Vide Fourth Dimension, p. 75, C. H. Hinton.

[22] Q. v., p. 242, edited by H. P. Manning.

[23] Vide Science, Vol. VII, 158, 1898, p. 4.

[24] See Fig. 18.

[25] Vide Recherche, Chap. VII, also Philosophical Review, V. 15, p. 401.—Malebranche.

[26] Kathekosis (from Chaos-Theos-Kosmos) is to evolution what "chaogeny" is to involution. It is the end of evolution, but also the beginning of involution, and in the latter function is known as "chaogeny." See diagram No. 17.

[27] See The Germ Plasm; A Theory of Heredity, by A. Weissman.

[28] Figure 20.

[29] See pp. 338, 341.

[30] See Unknown, p. 485, et. seq.

[31] Rosicrucian Cosmo-Conception, p. 477, Max Heindel

[32] Foundations of Mathematics, p. 90.