FOOTNOTES:[1]VidePopular Science Monthly, vol. 78, p. 554, 1911.[2]VideNew York Mathematical Society Bulletin, Vol. III, 1893-4, p. 79,G. B. HalsteadonLambert's Non-Euclidean Geometry.[3]Prolegomena,Kant, p. 37, Trans. byJ. P. MahaffyandJ. H. Bernard.[4]In 1754D'Alembert(1717-1783) published an article in the famous oldEncyclopediaedited byDiderotand himself onDimension. 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 betweenD'AlembertandLa Grange, it is not surprising that the latter should have been very much enamored of the idea.[5]VideNature, Vol. VIII, pp. 14-17; 36, 37 (1873); alsoMathematical Papers, pp. 65-71.[6]Mathematics, byC. 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 toGeorge 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. VidePopular Astronomy, Vol. VII and VIII, 1900, Dr.G. B. Halstead.[8]Note.—Mmay be any point on the lineBAindefinitely produced.[9]VideNon-Euclidean Geometry, p. 91.[10]VideNature, Vol. XLV, 1892.[11]VideMonist, Vol. XVI, 1896, Mathematical Emancipations.[12]VideMonist, Vol. XIX, p. 402 (1909).[13]Philosophical Review, Vol. VII (1898).[14]VideFoundations of Mathematics, p. 107.[15]VideFoundations of Mathematics, p. 42.[16]VideScience, Vol. VII, p. 2, No. 158, 1898.[17]VideFoundations of Mathematics, pp. 93-94.[18]VidePhilosophical Review, Vol. V, 1896, p. 352, et. seq.[19]VideMonist, Vol. XVI, 1896, Mathematical Emancipations.[20]VideFourth Dimension, Simply Explained, edited by H. P. Manning, p. 28.[21]VideFourth Dimension, p. 75, C. H. Hinton.[22]Q. v., p. 242, edited by H. P. Manning.[23]VideScience, Vol. VII, 158, 1898, p. 4.[24]See Fig. 18.[25]VideRecherche, 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]SeeThe Germ Plasm; A Theory of Heredity, byA. Weissman.[28]Figure 20.[29]See pp. 338, 341.[30]SeeUnknown, p. 485, et. seq.[31]Rosicrucian Cosmo-Conception, p. 477,Max Heindel[32]Foundations of Mathematics, p. 90.
[1]VidePopular Science Monthly, vol. 78, p. 554, 1911.
[1]VidePopular Science Monthly, vol. 78, p. 554, 1911.
[2]VideNew York Mathematical Society Bulletin, Vol. III, 1893-4, p. 79,G. B. HalsteadonLambert's Non-Euclidean Geometry.
[2]VideNew York Mathematical Society Bulletin, Vol. III, 1893-4, p. 79,G. B. HalsteadonLambert's Non-Euclidean Geometry.
[3]Prolegomena,Kant, p. 37, Trans. byJ. P. MahaffyandJ. H. Bernard.
[3]Prolegomena,Kant, p. 37, Trans. byJ. P. MahaffyandJ. H. Bernard.
[4]In 1754D'Alembert(1717-1783) published an article in the famous oldEncyclopediaedited byDiderotand himself onDimension. 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 betweenD'AlembertandLa Grange, it is not surprising that the latter should have been very much enamored of the idea.
[4]In 1754D'Alembert(1717-1783) published an article in the famous oldEncyclopediaedited byDiderotand himself onDimension. 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 betweenD'AlembertandLa Grange, it is not surprising that the latter should have been very much enamored of the idea.
[5]VideNature, Vol. VIII, pp. 14-17; 36, 37 (1873); alsoMathematical Papers, pp. 65-71.
[5]VideNature, Vol. VIII, pp. 14-17; 36, 37 (1873); alsoMathematical Papers, pp. 65-71.
[6]Mathematics, byC. J. Keyser, Adrian Professor of Mathematics, Columbia University.
[6]Mathematics, byC. 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 toGeorge 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. VidePopular Astronomy, Vol. VII and VIII, 1900, Dr.G. B. Halstead.
[7]The science of pure mathematics is perhaps indebted to no one in so great a degree as toGeorge 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. VidePopular Astronomy, Vol. VII and VIII, 1900, Dr.G. B. Halstead.
[8]Note.—Mmay be any point on the lineBAindefinitely produced.
[8]Note.—Mmay be any point on the lineBAindefinitely produced.
[9]VideNon-Euclidean Geometry, p. 91.
[9]VideNon-Euclidean Geometry, p. 91.
[10]VideNature, Vol. XLV, 1892.
[10]VideNature, Vol. XLV, 1892.
[11]VideMonist, Vol. XVI, 1896, Mathematical Emancipations.
[11]VideMonist, Vol. XVI, 1896, Mathematical Emancipations.
[12]VideMonist, Vol. XIX, p. 402 (1909).
[12]VideMonist, Vol. XIX, p. 402 (1909).
[13]Philosophical Review, Vol. VII (1898).
[13]Philosophical Review, Vol. VII (1898).
[14]VideFoundations of Mathematics, p. 107.
[14]VideFoundations of Mathematics, p. 107.
[15]VideFoundations of Mathematics, p. 42.
[15]VideFoundations of Mathematics, p. 42.
[16]VideScience, Vol. VII, p. 2, No. 158, 1898.
[16]VideScience, Vol. VII, p. 2, No. 158, 1898.
[17]VideFoundations of Mathematics, pp. 93-94.
[17]VideFoundations of Mathematics, pp. 93-94.
[18]VidePhilosophical Review, Vol. V, 1896, p. 352, et. seq.
[18]VidePhilosophical Review, Vol. V, 1896, p. 352, et. seq.
[19]VideMonist, Vol. XVI, 1896, Mathematical Emancipations.
[19]VideMonist, Vol. XVI, 1896, Mathematical Emancipations.
[20]VideFourth Dimension, Simply Explained, edited by H. P. Manning, p. 28.
[20]VideFourth Dimension, Simply Explained, edited by H. P. Manning, p. 28.
[21]VideFourth Dimension, p. 75, C. H. Hinton.
[21]VideFourth Dimension, p. 75, C. H. Hinton.
[22]Q. v., p. 242, edited by H. P. Manning.
[22]Q. v., p. 242, edited by H. P. Manning.
[23]VideScience, Vol. VII, 158, 1898, p. 4.
[23]VideScience, Vol. VII, 158, 1898, p. 4.
[24]See Fig. 18.
[24]See Fig. 18.
[25]VideRecherche, Chap. VII, also Philosophical Review, V. 15, p. 401.—Malebranche.
[25]VideRecherche, 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.
[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]SeeThe Germ Plasm; A Theory of Heredity, byA. Weissman.
[27]SeeThe Germ Plasm; A Theory of Heredity, byA. Weissman.
[28]Figure 20.
[28]Figure 20.
[29]See pp. 338, 341.
[29]See pp. 338, 341.
[30]SeeUnknown, p. 485, et. seq.
[30]SeeUnknown, p. 485, et. seq.
[31]Rosicrucian Cosmo-Conception, p. 477,Max Heindel
[31]Rosicrucian Cosmo-Conception, p. 477,Max Heindel
[32]Foundations of Mathematics, p. 90.
[32]Foundations of Mathematics, p. 90.
Transcriber's NotesVariations in spelling, punctuation and hyphenation have been retained except in obvious cases of typographical errors. Inconsistencies between the text and index have been resolved in favour of the text.Duplication of the sub title (The Mystery of Space) betwen the table of contents and the introduction has been removed.