[BIBLIOGRAPHY]
American Mathematical Monthly:
Vol. VIII, p. 161, P. Barbarin, for Le Mathematiche, Trans, by Geo. B. Halsted. See also pp. 31-35.
Vol. VIII, 1901, p. 217, Suppl. Report on Non-Euclidean Geometry, Geo. Bruce Halsted.
Vol. IX, p. 59, Geo. B. Halsted.
Idem, pp. 153-159.
Vol.XI, pp. 85-86, Simon's Claim for Gauss.
American Mathematical Society Bulletin, Lancaster, Pa.:
Vol. II, series 1895.
Vol. XX, 1914, pp. 409-412, R. C. Archibald.
Annals of Mathematics, 2d series, 1902:
Vol. XII, F. S. Wood.
Astronomical Society Notices:
Vol. XVI, p. 80, 1856.
Ball's Short Account of the History of Mathematics.br />
Boston Colloquium, for 1903, N. Y. 1905, Forms of Non-Euclidean Spaces, Vols. I-III, pp. 31, et seq., 1891.
Bulletin New York Mathematical Society:
Vol. II, pp. 1-144.
Vol. III, pp. 1, et seq., 1891, G. B. McClintock.
Cambridge Mathematical Journal:
Vol. IV, 1845, Cayley, on Analytical Geometry of n-Dimensions.
Canadian Institute Transactions:
Vol. VIII, pp. 315-339, 1909, August Kirschbaum.
Cayley, A., vide Science, Vol. IX, pp. 59-63:
Amer. Math. Mo., Vol. II, pp. 102-106.
Amer. Math. Mo., Vol. VI, pp. 59-65.
Review of Reviews, June, 1895, pp. 693-694.
Class Book of Non-Euclidean Geometry:
Vide Science, XIII, pp. 462-465.
Cornhill Magazine (n.s.):
Vol. XXXVII, pp. 647-665, C. H. Bryan, on the Fourth Dimension.
Easy Non-Euclid:
Monist, XIX, pp. 399-402.
Educational Review:
November, 1902, issue, pp. 346, et seq.
Euclid's Parallel-Postulate, by John W. Withers.
Flatland, by A. Square.
Foundations of Geometry:
Science, Vol. VI, pp. 487-491.
Foundations of Mathematics, by Paul Carus.
Fourth Dimension:
By Herman Schubert, C. H. Hinton, Claude Bragdon.
Fourth Dimension, Simply Explained:
Edited by H. P. Manning.
Fourth Dimension:
Cornhill Magazine, n.s., Vol. XXXVII, pp. 647-665, by C. H. Bryan.
Fourth Dimension, The Riddle of:
H. A. Bruce, in Scientific American Supplement, Vol. LXVI, p. 146.
Geometry, Foundations of, by O. Veblen:
Popular Science Monthly, Vol. LXVIII, pp. 21, et seq.
Geometry, Lobachevski's:
Theory of Parallels, trans. by Geo. Bruce Halsted.
Geometry, Non-Euclidean:
American Mathematical Monthly, Vol. VII, pp. 123-133.
Geometry, Non-Euclidean, Report on Progress in:
Reprinted from Science, n. s., Vol. X, No. 251, pp. 545, et seq., by Geo. Bruce Halsted.
Geometry, Non-Euclidean, Thesis on:
By M. L. Gerard.
Geometry, Non-Euclidean:
By Roberto Bonola, trans. by H. S. Carslaw, University of Sydney, N.S.W.
Geometry, Non-Euclidean:
Julian Lowell Coolidge, pp. 46, et seq.
Geometry, Non-Euclidean:
By H. P. Manning.
Geometry, Space and, in Light of Physiologic, Psychologic and Physical Inquiry, vide Open Court, 1906, by E. Mach.
Halsted, George Bruce:
Cayley, A., Biog. of, vide Amer. Math. Mo., Vol. II, p. 102.
Four-fold Space in Two-fold Time, vide Science, Vol. XIX, p. 319.
Hoüel, Biog. of, American Math. Mo., Vol. IX, pp. 99-101.
Lambert's Non-Euclidean Geometry, vide N. Y. Math. Soc. Bull., Vol. III, p. 79.
Lobachevski, N., Biog. of, vide Amer. Math. Mo., Vol. II, pp. 137-139; Open Court, Vol. XIII, pp. 411-415.
Message of Mathematics to Natural and Rational Theology, vide Hibbert's Journal, Vol. VII, 1809.
Non-Euclidean Geometry, Inevitable, vide Monist, Vol. IV, p. 483.
Non-Euclidean Geometry, Historical and Expository, American Mathematical Monthly:
Vol. I, pp. 70-72; 112-115; 149-152; 188-195; 222-223; 259-260; 301-303; 345-346; 378-379; 421-423 (1894).
Vol. II, pp. 10; 42-43; 67-69; 108-109; 144-145; 181-214; 256-257; 309-313; 346-348 (1895).
Vol. III, pp. 13-14; 35-36; 67-69; 109; 132-133 (1896).
Vol. IV, pp. 10; 77-79; 101-102; 170-171; 200; 247-249; 269-270; 307-308 (1897).
Vol. V, pp. 1-2; 67-69; 127; 218; 290-291 (1898).
Review of Reviews, Vol. II, 1895, pp. 693-694.
Space, New Ideas About, Popular Science Monthly, Vol. XI, p. 364.
Helmholtz, H., On Origin and Meaning of Geometric Axioms:
Vide Mind, Part I, No. 3, July, 1876. For replies and discussions of the above, vide Nature, Jevons, Vol. IV, p. 481;
J. L. Tupper, Nature, Vol. V, p. 202;
Helmholtz, in Academy, Vol. III, p. 52;
Mind, Part II, April, 1878.
Hermathena, Vol. XIII, pp. 491, et seq., 1906.
Higher Space, A Primer of, by Claude Bragdon.
Ingleby, C. M.:
A Non-Mathematical Criticism of a Part of Professor Clifford's Lecture on "Curved Space," Macmillan's Magazine, October, 1872;
also Nature, Vol. VII, 1873.
Journal of Mathematics, American:
Vol. I, pp. 262, 276, 384, 386; Halsted (1878).
Jour. Philos., Psychol. and Scientific Methods:
Vol. VI, pp. 617, et seq.
Kant, Emmanuel, trans. by Fred. Paulsen.
Kant, Emmanuel, Prolegomena, trans. by J. P. Mahaffy and J. H. Bernard, pp. 35-39.
Lambert, Biography of:
American Math. Mo., Vol. II, pp. 209-211.
Lie, Sophus:
Science, Vol. IX, pp. 447-448.
Lobachevski, N.:
Open Court, Vol. XII, pp. 411-415,
Amer. Math. Mo., Vol. II, pp. 137-139.
London, Edinburgh and Dublin Philosophical Magazine:
Vol. V, series 6, p. 559.
Mathematics, Foundations of: Paul Carus.
Mathematical Papers of Chicago Congress, p. 92.
Mathematical Papers, pp. 55-71.
Mathematics (a brochure):
By C. J. Keyser, Adrian Professor of Mathematics, Columbia Univ.
Mathematics, Higher:
Edited by Mansfield Merriam and Robert S. Wood, 1902, pp. 508, et seq.
Mathematics, Spiritual Significance of:
C. J. Keyser, reprinted from Columbia Univ. Quar., December, 1911.
Memorial Volume of Scientific Papers:
Pub. by Univ. of St. Andrews, pp. 3-45, D. M. Y. Somerville.
Mind (Magazine):
Vol. I, 1876, pp. 303, et seq. J. N. P. Land.
Vol. II, 1877, p. 40, J. N. P. Land.
Vol. IX, pp. 522, et seq. 1900.
Monist (Magazine):
Vol. II, pp. 50, 321, Paul Carus.
Vol. IV, 1894, Articles by G. B. Halsted and J. Delboeuf.
Vol. VI, 1895, Herman Schubert.
Vol. VII, G. B. Halsted, on Saccheri.
Vol. XIII, pp. 80-102; 218-234.
Vol. XIV, Article by E. Mach.
Vol. XV, p. 127, Paul Carus.
Vol. XVI, 1906, p. 433, David P. Abbott.
Idem, 1906, p. 65, C. J. Keyser, on Mathematical Emancipations.
Nature (Magazine):
Vol. VIII, pp. 8, 14-17, 36-37 (1873).
Vol. XV, pp. 533-537 (1877).
Vol. XLV, P. 404 (1891).
Newcomb's Philosophy of Hyperspace:
Science, Vol. VII, p. 212.
New York Math. Soc. Bulletin:
Vol. III, p. 79 (1893), F. S. Wood on Forms of Non-Euclidean Space.
Open Court (Magazine):
Vol. XVI, pp. 513-521.
Vide December, 1913 edition, p. 757.
Philosophy of Mathematics, by Paul Carus.
Philosophical Review:
Vol. V, 1896, p. 175, F. C. S. Schiller.
Idem, p. 357, J. H. Hyslop.
Vol. VII, p. 615.
Vol. X, pp. 113, 229, 314, 375, 488, 579, 583.
Vol. XII, p. 493.
Popular Science Monthly:
No. 66 (1905), pp. 639-646.
Vol. LXVII, pp. 639, et seq.
Vol. LXVIII, pp. 21, et seq.
Vol. LXXVIII. p. 554 (1911), Samuel Moffat Weyer.
Popular Astronomy:
Vols. VII and VIII (1900), G. B. Halsted.
Vol. XVIII, pp. 42, et seq. (1910), W. H. Pickering.
Vol. LXXV, p. 179, W. W. Payne, on Attraction and Figure of the Earth.
Vide No. 84 (1901), pp. 187-190.
Popularization, The, of Non-Euclidean Geometry:
Amer. Math. Mo., Vol. VIII, pp. 31-35.
Psychological Bulletin:
Vol. VIII, p. 22 (1911).
Queen's Quarterly:
Vol. XX, pp. 431-446, A. L. Clark (1913).
Revue Generale des Sciences:
No. 23, trans. Nature, Vol. XLV, 1892.
Royal Astronomical Society Proceedings:
Vol. XVI, pp. 80-85.
Royal Society Proceedings, London:
Obituary Notices of Deceased Fellows, Vol. XVI, p. 69 (1867-68).
Royal Society of N. S. W. Journal and Proceedings:
Vol. XXXV, p. 243 (1902), G. H. Knibbs.
Science (Magazine):
Vol. III (new series), No. 58, 1896.
Vol. VI, pp. 487-491 (1897).
Vol. VII, pp. 1-7, Philosophy of Hyperspace, S. Newcomb.
Idem, p. 861 (1898).
Vol. XIII, pp. 462-465.
Vol. XIV (new series), pp. 711-712, G. B. Halsted.
Vol. XIX, pp. 401-413.
Vol. XX, pp. 353-456, Josiah Royce.
Vol. XXII, pp. 270-271.
Vol. XXXV, No. 906 (1912).
Vol. XXXVII, pp. 885, et seq., C. J. Keyser, on Concerning the Figure of the Universe of Space.
Science et L'Hypothese, R. Poincaré.
Scientific American Supplement:
Vol. LXVI, pp. 14-16 (1908).
Scientific Romances, C. H. Hinton.
Thought, New Era of, C. H. Hinton.
Westminster Review:
Vol. CLII, pp. 675, et seq.
Zollner, J. C. F., On Space of Four Dimensions:
Quar. Jour. of Science, Vol. VIII (1878), pp. 227-237.
[INDEX]
A
Abeyance, higher faculties held in, until lower are fully developed, 334
— intuition kept in, [338], ff
Ability, to sense the inaudible and the invisible, [342]
Absolute, no room for the, [101]
Abstract thought, invigorating power of, [33], [40]
Abstractions, realizing, [144], [294]
Absurdity, analysis inevitably ends in an, [319]-[20]
Acrobatics, mathetic, [146]
Acromegaly, [347]
Action, automatic, of the intellect, [253]-[4]
— engendering, of life on the form, [330]
Activities, space, as physical and chemical phenomena, [229]-[30]
Actualities of the physical world pushed over into the conceptual, [119]
Actuality imperceptible to the intellect, [126]
Adaptability of life, [330]
— — mathematical laws, [37]-[39]
Adaptation, purpose of, [327]-[8]
Adaptations made by an organism, [162]
Additional freedom bestowed by higher faculties, [334]
Affinity, zones of, [22], [124]
Agency, interpretative, intellect as an, [166]-[7]
Agent, ego as an, of the Thinker, [243], ff
— engendering, life as an, [331]
— of creation, life as an, [343]
Ahmes, an Egyptian priest, [44]
Alchemy of psychogenesis, [225]
Alcohols, eight different, from one formula, [155]
Algebraic quantities and space, [125]-[7]
Allowability of the rules of logic, [163]
Aloofness, the, of scientific dogmatism, [340]
Alphabet of space-genesis, [237]
— the geometric, [193]
Amenability of mind to the laws of evolution, [28]-[31]
Analogies, use of, to popularize the four-space, [128]-[9]
Analogy, difference between two processes illustrated by, [74]
Analysis incapable of dealing with life, [319]
— the manifold, the fiat of, [77]
Analyst and the manufacture of the space-manifold, [77]
— disregards the conformity of the nature of things, [84]
Analytics and the mechanical origin of the universe, [40]-[1]
— perisophical nature of, [320], ff
— the four-space, a curiosity of, [40]
Anchorage, fourth dimension denied, [265]
Angularity of consciousness, [120]
Answer of the senses to new needs, [332]
— the, of consciousness to realism, [97]
Anti-Euclidean geometry, [69]
Apotheosis of the definition, [78]
Apparatus, man's perceptive, [357]
Apparent vassalage of life, [329]-[30]
Appearance, dynamic, space as, [104]-[7]
Appetences, materialistic, of empiricists, [340]
Appulses of life against matter, [328]
Appurtenances of materiality, [331]
A priori, [185], ff
— — knowledge, [110]-[5]
Aprioriness, [112], [116]
Apriority, the principle of, [113], [223]
Arbitrariness of the common mensurative quantities, [41]
Archeological evidences, [332]
Archimedes, [70]
Aristotle, [322]
Arrangement of the contents of the kosmos, [317]-[8]
Art and the criterion of truth, [323]
— — — higher consciousness, [181]
— evidences of new faculties in the field of, [335]
Assemblage of mathetic contrivances, [335]
Assumptions, category of, [189]
— procedure based upon, disadvantages of, [163]
At-one-ment, [224], [252], [270]
— defined as the end of evolutionary activity, [1]
Attachment of the consciousness to the order of becoming, [305]
Attainment, the difficulty of, by the intellectual method, [206]
— of space-consciousness, [225]
Attitude, the need of a more liberal, [340]
— towards things spatial, [306]
Audital nerves, notes that transcend the grasp of, [355]
Aura, pulsating, [348]
Automatism of the intellect, [253], ff; [338]
Avenues of knowledge opened to inner perceptive faculties, [353]
Awakening of the faculty of awareness in a new domain, [90]
— — — pituitary body and the pineal gland, [353]
— pituitarial, general results of, [355]-[8]
Awareness, a determinant of conception, [120]
— as a gauge of the existence of things, [161]-[202]
— degrees of, [165]
— hyperspace, a symbol of a more extensive, [180]
— progress in, [171]
— Thinker's sphere of, [274], [283]
B
Baltzer, [66]
Barrier, the, to the Thinker's certitude, [186]-[8]
Barriers, freedom determined by absence of, [280]
Becoming, endless labyrinth of, [220]
— the kosmos, in a state of, [265]
— the order of, [305]
Becomings, infinity of, [234]
Becquerel rays, [336]
Being, identification of consciousness with, [205]
— kathekotic, [210]
Being, the interiority of, [290]
— the numericity of, [309]
— the range of, co-extensive with reality, [168]
Beings, discarnate, [154]
Beltrami, Eugenio, [1]-[2], [63]-[5], [66]-[7]
— — and the manifold, [317]
— — and the pseudosphere, [64]-[5]
Besiegement of matter by life, [329]-[30]
Bessel, on geometry as incomplete, [58]
Bewilderment, new realities cause, [169]-[70]
— of the mind, [182]
Biogenetics, passage from mechanics to, [357]
— turning to, from mechanics, [322]
Birth, as a fourth dimensional process, [159]
Blind men and the elephant, [257]
Bolyai, Janos, [2]-[3], [46], [60], [66], [83], [87]
Boundaries of a hypercube, [136]-[8]
Brain, the physics of, [292]
Brain-consciousness, [184], [186]
— standards of, [190]
Brotherhood, and the tendencies of the Thinker's consciousness, [301]
— the keynote of the intuition, [252]
Bulwarks, the formal, of geometry, [77]-[9]
C
Carpet, the sensible world as a, [196]
Carus, Paul, on four-dimensional space, [254]
— — on metageometricians, [102]
— — on space, [110]
— — on the representation of the tesseract, [136]-[7]
Cayley, [3]-[4], [54]-[5], [66]-[7]
Cell-activity as a performance a priori, [114]
Cell-colony, [250], [301]
Cell-consciousness as an aposterioristic phenomenon, [185]
Centers, pyknotic, [232]
Certainty, geometric, the basis of, [77]-[8]
— of mathetic conclusions, provisional, [37]
Chaogenic period of involution, [208], ff
Chaogeny, [231], [233]
— the evolution of chaos into order, [4]
— the laboratory of, [193]
Chaomorphogeny, defined, [4], [231]-[2]
Chaos, as egg-plasm, [265]
— duration of, [268]
— movement of life in, [307]
— shores of, [307]
Chaos-geometricity, [307]
— -intellectuality, [307]
— -materiality, [307]
— -spatiality, [307]
— -Theos-Kosmos, [215], 233-4, [237]
— — — a triglyph symbolizing kathekos, [11]-[2]
Character of the universe, fixed by consciousness, [162]
Characteristics, changes in the, of reality, [169]
— fourth dimensional, of the ether, [157]
— minds of similar, fall into zones of affinity, [124]
— of non-Euclidean space, [72]-[3]
Chasm, kosmic, between the real and the ideal, [107]
Chemists, speculative, and the ourth dimension, [155]
Chrism, sacred, of creative mentality, [91]
Circle, significance of process of squaring, [109]
Circle, the symbology of, [309]
Circuits, closed, our interests as, [167]
Clairaudience, [352]
Clairvoyance, [352]
Clairvoyant perception, [349]
Clause, enabling, of metageometry, [76]-[7]
Clavius, Christoph, [46], [52], [83]
Clifford, [66]
Code, psychic, for systematizing cognitions, [190]-[1]
Cognition, instantaneous, organ of, [258]
— intimacies of direct, [205]
— the method of, [186]-[8]
Cognitions, intuitive, [145], [192]-[3]
— psychic code for systematizing, [190]-[1]
Commensurable quality, dimension as, [140]
Communal consciousness, [270], ff
Communalization and the intuition, [301]
Conarium, the, [345]
Conceivability and evolution of mind, [24]
— ultimate range of, [278]
Conceiving, power of, derived from sense-experience, [26]
Concept, as a shadow, [119]
— the hyperspace, gradual rise of, [27]-[8]
Conception and awareness, [120]
— every, based upon prior experience, [25]
— freedom, the, of the mind from, [28]
Conceptions, symbolic, dependence placed upon, [147]
Concepts, and the Thinker, [244]
— intuitograms as, [248]
— quality of, dependent upon sense-experience, [26]
Concepts, the perception of, [255]
Conceptual, related to the objective, [291]
— the, and mathematicians, [71]
Conceptualization, the act of, [4]
— the power of, dependent upon evolution of mind, [25]
Conclusions, mathetic, complex dependence of, [37]
Concrete hewn into shape by the intellect, [295]
Congruency, the, between intellect and the universe, [319], ff
Congruity, the, between concepts and objects, [120]
Connection, the, traced out between reality and object, [126]
Co-originality of things, [303]
Consciousness and kosmos, graph representing, [271]
— — the character of the sensible world, [166]
— — — wake of life, [205]
— — time, [224]
— angularity of, [120]
— a priori, [185]
— a replica of, and judgments, [205]
— as a scale, [165]
— — barrier to ultimate knowledge, [207]
— — determinant of dimension, [145]
— — life, [295]
— — variable quantity, [171]
— attachment of, to the order of becoming, [305]
— dawn of, and dimension, [179]
— degrees of, [162]
— deprived of the validity of notions, [314]
— evolution of, [250]
— expansion of, [164], [272]
— extended, [89]-[90]
— focus of, [290]
Consciousness and the planes of the kosmos, [163]
— fragmentary view of, [260]
— freedom of, in the genus homo, [332]
— habitation of, [278]
— higher, and art, [181]
— — planes of, [178]
— history of, [298]-[9]
— identification of, with objects, [189]-[90]
— intuitional, [255]
— keyed to the entire range of reality, [167]-[8]
— kinds of, [270], ff
— kosmic, Elysian fields of, [235]
— of the primitive man, [253]
— organ of, [184], ff; [90]
— psychics of, [292]
— raised from the sensuous to the conceptual, [72]
— recipient of truths from dual sources, [26]
— sensible world as instrument of, [199]
— triple presentation of notions of space to, [72]
— turned inward, [283]
— unification of the states of, [192]
— youthful, of mankind, [122]
Consequences, the science of, [85]
Considerations, mathematical, and reality, [128]
Consistency, kosmic, [174]
— self, of hyperspatial hypotheses, [67]
— the criterion of geometry, [86]
— — inconsistence of, [173]
— — metageometrician curtailed by, [85]
Construction, idealized, cannot be objectified, [144], [276]
— ideal, the meaning of, [4]
— mental, trafficking in, [154]
Consubstantiality of intellectuality and spatiality, [331], ff
Continuity of the psychic plasm, [260]
Contrivances, mathetic, the passing of, [241]
Convergence of parallel lines, [315]
Convolutions, duplex, [146]
Coördinates, as spatial determinants, [203]
— of hyperspace, [94], [97], [99], [115]-[6]
— systems of, [301], ff
— three, [132], [232]
Copolarity of ideas and objects, [127]
Corpora quadrigemina, [345]
Corpuscular orbits of particles, [152]
Cosmos, significance of, [4]
Creation, impregnated screen of, [232]
Creations, the, of the intellect, [173]
Criterion of geometry as consistency and convenience, [86]
— — truth, [323]-[4]
Crookes, [344]
Cube, as succession of planes, [148]
— generation of the, [144]
— illustrated, [133]
— the generating, [134]
Curiosities, analytic, energy spent in elaborating misappropriated, [39]
Current, electric, as component in the fourth dimension, [153]
Curvature of space, the doctrine of, formulated by Riemann, [5]
— — — valid element in the notion of, [305]
— the measure of, [61]
Curved space and metageometricians, [316]
D
D'Alembert, note, [51]
Dante, [181]
Darwin, [181]
Day, the Great Kosmic, [213]
De Tilly, [66]
Death, as fourth dimensional unity, [159]
— of the intellect, [195]
Decrement of the diametrical ratio to the circumference of circle, [312]
Deeps, fearful, of kosmic mind, [71], [91]
Definition, apotheosis of, [77]-[8]
— as an arbitrary determination, [100]
— the deification of, [37]
Degrees of realism, [164]-[5]
Deiform, basic idea of the, [5]
Demarkation between reality and phantasy, the line of, [173]
Deposits of life, [173]
Descartes, [322]
Designs, cut out in materiality by life, [264]
Details, the power to dispose of innumerable, [303]
Determinations, geometrical, the necessity of, inheres in logical deductions, [78]
— the factors of conscious, [162]
Determinative period of mental development, [31]
Development of the intuitive faculty, future, [188]
Diacritics of life, [286]
Diameter, the ratio of, to the circumference, [311]-[2]
Difference between concept and thing, [121]-[2]
— between mathematical and perceptual space, [120]
— between the ideal and the actual is dynamic, [108]
Differential, among minds, [124]
Difficulty of imagining the fourth dimension, [90]
— of propagating an intuition, [315]
Difficulties in the acquisition of real knowledge, [325]
— of hyperspace, the logical, [139]-[41]
Dilemma of metageometricians, [97]-[8]
Dimension, a distinct stage in psychogenesis, [27]
— — system of space measurement, [5]
— and analysis, [163]
— — D'Alembert, note, [51]
— — the action of a tartrate in, [156]
— as an arbitrary contrivance, [262]
— — — assemblage of elements, [93]
— — direction, [140]
— — extent, [98]
— — lying near the surface of things, [159]-[60]
— — space,
[96]
— current definitions of, [98]-[100]
— denied legitimate anchorage, [265]
— determined by consciousness, [145]
— does not explain spiritualism, [155]
— evolution of the fourth, [44]
— fourth, direction of, [134]
— as "jack of all trades," [156]
— impossible to actualize, [124]
— key, to non-Euclidean geometry, [90]
— movement of a plane into, [147]-[8]
— no motion of material masses into, [125]
— not a priori, [116]
— proof of the existence of the fourth, [136]
Dimensionality, and the intellect, [200]
— as dependent upon the will of the investigator, [95]
Dimensionality, conception of, purely conventional, [92]
— logical difficulties which beset, [97]
— of perceptual space, [72]
— — space, the four, [142]-[3]
Dimensions, four, no basis in consciousness for, [172]
— piled upon one another, [300]
— vanity, the, of segmenting space into many, [299]
Direction as dimension, [99]
Disappointment with the sensible world, [120]-[1]
Discoveries, metageometrical, as excrescences of mental unfoldment, [131]
— never the result of methodic reflection, [29]-[30]
Disorder, the edict of, and space, [230]
Disorderliness, the fringe of, [277]
Dispossessal of the intellect by the intuition, [195]
Dissimilarities, besetment of, [291]
Distinctions, between conceptual and perceptual space, fundamental, [73]-[5]
Diversity, a result of the fragmentative tendency of life, [6]
— as transfinite quantity, [42]
Divinity, prize of, won by the intellect, [43]
Duadic phase of evolution, [210]-[1]
Duodim, defined, [6]; [128], [129], [134], [177]
— consciousness, [163]
Duopyknon, [212], [213]
— the meaning of, [6]
Duopyknosis, [208]-[10], [218]
— as a stage in the evolution of space, [6]
Duration and space, [224]
— eternal, [234]
Dynamic appearance, space as, [104], [107]
Dynamism, of the intellect, functional, [303]
E
Earth, the nebulous youth of, [335]
— a new, [358]
East effloresces as West, [306]
Ego, the, [270]
— and percepts, [244]
— as sovereign, [244]
— Thinker's dependence upon, [245]
— — treatment of, [246]
Egopsyche, [265]
— as an agency of self-consciousness, [258]
— defined, [7]
Egos, compared to choppy sea, [256]-[7]
Egypt, birth-place of geometry, [44]
Eisenlohr, [44]
Elaborative period of the non-Euclidean geometry, [66]-[70]
— — of mental development, [31]-[32]
Element of evolution, basal, [259]
Elements of the non-Euclidean geometry, [79]-[80]
Elephant and blind men, [257]
Ellis, Wilmot E., on ether as four-dimensional, [157]-[9]
Embrace of direct cognition, [205]
Engenderment of space, [260]
Ensoulment of the world-plasm, [329]
Entities, hyperspace, and the phenomenal world, [128]-[130]
Enumeration, reformation of the system of, [38]
Enveilment of consciousness, [273]-[4]
Environment, artificial and natural, [162]
Epiphysis, the, [345]
Equidistantial, described by hyperspatial perpendicular, [80]
Essence, elemental, as world-plasm, [329]
Ether as possessing fourth dimensional characteristics, [157]
Ethics recast in a new mold, [358]
Euclid, [46], [70], [83], [263]
— and the parallel-postulate, [45]
— never-dying elements of, [53]
Evidences, mathematical, exemplifies intellectual evolution, x
— the vanity of fragmentary, [204]
Evolution, a continuous process, [327]
— and the norms of reality, [175]
— basal element of, [259]
— commencement of, [232]-[3]
— intellectual, forward movement of, [184]
— kosmic, vicissitudes of, [215]
— laws of, govern mind, [28]
— mental, results of, [122]
— of faculties, synchronous with evolution of matter, [332]
— — material characteristics of the earth, [335]
— — organs, time required for, [188]
— preparation of the field of, [218]
Exaltation of matter into spirit, [329]
Examples of new perceptive evidences, [341]-[3]
Existence on a higher plane, states of, [162]
Experience, corroborative testimony of, denied hyperspace, [263]
— prior, and conception, [25]
Experiences, spatial, systematization of, [78]
Extension, space as an unbounded, [61]
Extra-spatiality, degraded into spatiality, [261]
Extravaganza, mathematical, and the fourth dimension, [156]
Eyes, as Roentgen rays, [353]
F
Fact-mass, [289]
Factors of conscious determinations, [162]
— four, of the criterion of truth, [324]-[5]
Facts as facets of truth, [284]
— attempts to reform, [304]
— logic as symbolism of, [287]
— — the modeler of, [288]
Faculties, dual derivation of, [162]
— evolution of, synchronous with evolution of material qualities, [332], ff
— extended, [239]
— foreshadowed by the hyperdimensional, [131]
— higher, man must win his way to, [357]
— new faculties evidenced by four-space, [24]-[29]
— rudimentary nature of, [341], ff
— the source of, [349]
Faculty and the intellect, [247], ff
— as transmissible character, [251]
— determined by function, [336]
— greatly extended, [117]
— higher than the intellect, [126]
— I-making, self-consciousness as, [243]
— intuitive, [185]
— of perception in higher worlds, [353]
— — awareness, the awakening of, [89]-[91]
— overshadowed by the intellect, [188]
— of perception in higher worlds, [353]
— rudimentary condition of, [192], ff
Faculty, outcropping of, [249]-[51]
Failure of efforts to justify the objective existence of four-space, [125]-[6]
Failures at solving the parallel-postulate, outcome of, [48], [83]
Faith, dispossessed by knowledge, [358]
Fay, mathetic, [160]
Fechner, [39]
Finity and unboundedness of space, [76]
Flammarion, Camille, [341]-[2], [344]
Flexity, as property of hyperspace, [63]
Flexure, space as a, [305]
Fluxional, between sense objects and ideal representations, [122]-[3]
Fluxion, psychic, as difference between memory image and object, [7]-[8]; [122]
Focus of consciousness, [163], [290]
— — the intellect, [310]
Fohat, and the creation of morphons, [219]
— as creative energy, [213]
— Creator, [8]
Fohatic energy, [226]
Form, as vehicle of life, [330]
— definition of, [8]
— driven back over the path of its genesis, [327]
— pure, cannot exist in nature, [294]
— the idealty of, [110]
— the universe not a pure, [108]
Formative period of mental development, [31]
— — of non-Euclidean geometry, [55]
Formula, eight different alcohols from one, [155]
Four-dimensionality, justification of, [176]
Four-space, a curiosity of analytics, [40]
— and Riemann, [27]
— as a divertisement, [175]
— consciousness does not act in the, [172]
— existence of, denied, [171]-[2]
— movement of matter in, [157]
— reality of, glibly proclaimed, [154]
— the, [8], [240]
— — denizens of, [353]
— — domain of, [154]
— — study of, [124]
— use of analogies to popularize, [128]
Fourth dimension, analogical reasoning of, [177]-[9]
— as a transcendental problem, [140]
— — an attitude of the intellect, [200]
— electric current as a component in, [153]
— imaginability of, [106]-[7]
— Simon Newcomb on, [125]
Fragmentariness of the intellectual method, [164]
Fragmentary view of the universe, [260]
Fragmentation, tendency to, [296]
— harks back to cell-division, [301]
Freedom, a new, [338]
— determined by absence of bonds, [280]
— mathematical, [60]
— mental, [66]-[7]
— now dawning for the mind, [32]
— of consciousness in genus homo, [332]
— regal freedom of the mind, [118]
— three degrees of, [125]
— unrealizable, for the Thinker, [255]
Fringe, chaogenetic, [308], [309]
— of disorderliness, [257]
— — kathekosity, [229]
Frischauf, [66]
Full, the universe as a, [310]
Function determines faculty, [336]
Functions back of latent faculties, indefinite, [343]
— cellular and histologic, [253]
Functioning, instinctive, of the intellect, [289]
Fundamentals, totality of, kosmic, [265]
G
Gamut of realism, [169]
Gauge, awareness as a, [161]-[202]
Gauss, Charles Frederick, [8]-[9], [56]-[8], [59], [174]
— — — as formulator of the non-Euclidean geometry, [57]
Geminos of Rhodes, [45], [52]
Generability, as property of space, [62]
— of hyperspace, Keyser on, [144]
— — space by lines, [143]
Generation, the, of the hypercube, [134]
— of the hypertetrahedron, [135]-[6]
Genesis, of space, [211], [227], ff
— — the earth, its nebulous youth, [335]
— — — form, [327]
— — — sensible world, [167]
Genus homo, freedom of consciousness in, [332]
Geometricity, [266]
Geometries, non-Euclidean, based upon a negation of the latent geometrism, [262]-[3]
— three possible, [54]
Geometrism, engenderment of, [262]
— established by life, [264]
— kosmic geometrism, establishment of, [231]
— latent, [257]
— native geometrism of space, [262]
— rediscovered by the intellect, [9]-[10]
Geometrism, the basis of, [237], [261]
Geometry, anti-Euclidean, [69]
— and the study of magnitudes in space, [203]
— artificial, [262]-[4]
— a two-fold, [59]
— breakdown of, [266]
— determinative period of the non-Euclidean, [61]-[4]
— diverse systems of, [323]
— Euclid's Elements of, [53]-[4]
— formal bulwarks of, [77]-[9]
— Imaginary Geometry, The, [60]
— natural geometry, [261]
— Plato and the divine geometry, [193]
— possible systems of, [174]
— radical essence of pure, [85]
Geometry, non-Euclidean, at variance with the parallel-postulate, [83]-[5]
— — based upon a misconception, [91]
— — determined by qualitative differences, [140]
— — elaborative period of, [66]-[70]
— — first published treatise on, [60]
— — formative period of, [55]
— — the final issue of, [88]-[9]
— — growth and development of, [92]
— — invalidation of, [174]
— — key to, [90]
— Lambert's Non-Euclidean geometry, note, [51]
— — popularization of, [66]-[7]
— — Schweikart's treatise on, [59]
— — self-consistence of, [57]
— — some elements of, [79]-[80]
— — superperceptual knowledge of, [72]
Geometry, non-Legendrean, [70]
— symbolic, and commensurable quality, [145]
Gerling, as correspondent of Gauss, [58]
Germ-plasm, continuity of, [260]
Giantism, [347]
Glimpse, a, of the reality of space, [314]
Glorification of the flesh, [227]
Groups, transformation, discovery of, [30]
Guide-posts to a new domain, [273], [277]
Gulf, interposed between manifestation and non-manifestation, [206]
H
Halley, memoir of, mastered by La Grange, [50]
Halstead, G. B., note, [49], [66]; note, [79]
Heindel, Max, note, [353]
Helmholtz, [39], [66]
Hewer, the, of the concrete, the intellect as, [295]
Hinton, C. H., [154]
— on the fourth dimension, [153]
History, the, of mind, three great epochs of, [31]-[32]
Homogeneity, the, of realism, [165]
Hoüel, J., [60], [66]
Hudson, [344]
Humanity and the exalting power of life, [331], ff
Hypercube, boundaries of, and mirrors, [136]-[9]
— the generation of, [134], [145]
Hyperdimensional, as a prophecy of new faculties, [131]
Hyperspace, [175]
— a monument to the intellect, [356]
— and the involved procedure of arriving at a recognition of its relations, [73]
— and the passage thither, [293], ff
Hyperspace as a figurative mountain-peak, [200]
— — — movement, [44]-[68]
— — an all-powerful something, [160]
— — — idealized construction, [10]
— — evidence of new faculties, [24]
— — ignes fatuii, [154]
— — illusion, [202]
— a symbol of higher consciousness, [180]-[4]
— concept of, as an evolutionary quantity, [44]-[5]
— confounded with real space, [91]
— creation of, [335]
— denied the corroborative testimony of experience, [263]
— direction of, baffling to mathematicians, [146]
— discovery of, a sign of mental evolution, [180]
— domain of, a fairy-land, [239]
— magnitudes of, the non-sensuous, [72]
— mysterious hiding place in, [129]
— the logical difficulties of, [139]-[141]
— the six pillars of, [62]-[3]
Hyperspatiality as the toys of childhood, [241]
Hypertetrahedron, the, [135]
Hypertrophy of the pituitary body, [347]
Hypervolume, the, [134]
Hypothesis, a superfoetated, [141]
— four-space, utility of, [129]; [154]
Hypotheses, admissibility of, [118]
— incompatibility of the non-Euclidean, [67]; [71]
— Riemannian, [80]
— solution of, Bolyai, [31]
Hyslop, James H., on the logical difficulties of hyperspace, [139]-[141]
I
Icosahedron, examination of the, [285]
Ideal, and the real, kosmic chasm between, [107]
— perceptual value of, [275], ff
Ideas and words as symbols, [126]-[7]
— Malebranche on, [222]
— realism of, [24]-[35]
— the symbolism of, [205]
Identification of consciousness with being, [205]-[6]
— with the objects of study, [189]-[90]
Identity of things-in-themselves,
[353]
Ignes fatuii and hyperspaces, [154]
Illustration of plane-rotation, [148]-[150]
— — the tesseract, [133]
Images, totality of, recoils upon us, [167]
Imaginability of the fourth dimension, [90], [106]-[7]
Imagination, premises of, the mathematical, [146]
Impossibility of plane-rotation, the structural, [151]-[3]
Impressions, the symbolism of, neurographic, [186]
Impulse, the satisfaction of the original creative, [310]-[1]
Incomprehensibility of reality to the intellect, [126]
Incongruity, life estranged by a radical, [325]
Individual as space, [223]
Ineptitude of intellectual determinations for vitality, [314]
Infinite, interpreted in the terms of the finite, [82]
Infinitesimals of unity, numbers as, [41]
Infinity as a process, [109]
— of becomings, [234]
Infinity of parallels through a given point, [70]
— — space, a capital illusion, [195]
— the concept of, [277]
— — innate dread of, [103]
— — relativity of, [194]
Influence of abstract thought, [33]
— — Kant on the non-Euclidean geometry, [49]-[50]
— — La Grange, [51]-[2]
— — the intellect, [315]
Infundibulum, the, [345]
Inner organs of perception, [352]
Innermost, the, realities of things, [356]
Insouciance of the geometer, [96], [294]
Instant-exposure and intellect, [311]
Instrument, intellect likened to a color-bearing, [313]
— for the measurement of the passage of space, [297]
— of consciousness, the sensible world as, [199]
— — life, form as an, [328]
Integers, as fractional parts of unity, [41]
Intellect and its domination of the intuition, [333]
— — — final union with the space-mind, [194]
— — — topography, [312]
— — spatiality, [263]
— — the deposits of life, [173]
— — — designs cut by life in materiality, [264]
— — — dictum of Sensationalists, [26]
— — — instant-exposure, [311]
— — — intuitive faculty, [247], ff
— — — prize of divinity, [43]
— as a color-bearing instrument, [313]-[4]
— — — searchlight, [168]
Intellect as a fashioner of phenomena, [199], ff
— — hewer of the concrete, [295]
— — sole interpretative agency, [166]-[7]
— automatism of, [253], [338]
— cannot seize life, [282]
— crowned by a diadem of gold, [338]
— dominated by the intuition, [250]
— fashioned for matter only, [231]
— follows in the grooves of logic, [294]
— hyperspace as a monument to, [356]
— in the field of vitality, ix
— its aptitude for starts and stops, [292], [302]
— — instinctive tendency to fragmentate, [296]
— quality, determined by mathematics, [337]
— makes for individuality, [252]
— misses the ceaselessness of life, [201]
— modus vivendi of, its influence upon knowledge, [184]
— the constitution of, [291]
— — cut and mode of, [167]
— — focus of, [310]
— — illusion of, [246]
— — illusionary character of, [323]
— — incomprehensibility of reality to, [126]
— — instinctive functioning of, [289]
— — judgments of, [302]
— — moods of, [202]
— — predominating tendency in, [320]-[1]
— — scientific tendence of, [165]-[6]
— — struggle of, against dispossessal, [195]
— unsuited to deal with reality, [322], ff
Intellectuality and reality, [304]
— — spatiality, consubstantial, [331]
Intellectuality as co-extensive with spatiality and materiality, [236]
— the source of, [260]
— — Thinker makes his own, [242]
Intelligence and automatism, [253], ff
— the Thinker as a pure, [243]
— transfinite intelligence and the degrees of realism, [164]
Intent, the kosmic, of the intellect, [326]
Interests, the sphere of our, as closed circuits, [167]
Interior, the great, [290]
Interiority of being, [290]
Interpretation, the standards of, vary as consciousness varies, [171]
Interstices of materiality, [264]
Intuition and brotherhood, [252]
— — communalization, [301]
— — the riddle of spatiality, [325]
— as dispossessor of the intellect, [195]
— cannot be served by mathematics, [337]
— dominated by the intellect, [333]
— held in abeyance, [338], ff
— its domination of the intellect, [250]
— the development of a spatial, not absurd, [145]
— — need of a sympathetic attitude towards, [249]
— — results of the development of, [357]
Intuitional consciousness, [255]
— the superiority of, over the rational, [187]
Intuitions and the lead of life, [191]
— — — Thinker, [27]
— free, mobile and formless, [166]
— the conceptualization of, [248]
— — humility of, [165]
— — nature of, [185]
Intuitograms, as concepts, [248]
Intuitograph as means of contacting the egopsychic consciousness by the Thinker, [10]
— as super-concepts, [255]
— the difficulty of transmitting, [315]
Invariability, the vaunted, of the laws of mathesis, [37]
Invariants, psychological, [24]
Investigations, metageometrical, and the new sense-organs, [354]
Involution, as antithesis of evolution, [10]-[11]
— kosmic involution, [226]
— of matter, [328]
— the movement of, [219]
— — seven stages of, [208]-[12]
Ions, creation of, [219]
— magnitude of a hydrogen ion, [225]
J
Judgments a priori, Kant on, [85]-[6]
— and the faculty a priori, [190]-[1]
— — zones of affinity, [124]
— based upon a replica of consciousness, [205]
— no trustworthy, can be predicated upon fragmentary knowledge, [282]
— of the intellect, [302]
— the lessening of error in, [256]
— — more complex the more at variance with the nature of things, [75]
— — synthesis of, [257]-[8]
— valid judgments long delayed, [170]-[1]
Judicative power of mathematics, [180]
Justification for a multi-dimensional quality in space, [262]
— of four-dimensionality, [176]
Justification of sense-deliveries by one another, [76]
— — the existence of the fourth dimension, [125]
K
Kant, [85], [181], [182], [322]
— and the faculty of thinking, [261]
— — — idea of space, [322]-[3]
— influence of, on the hyperspace movement, [49]-[50]
— on the nature of things, [119]
— — space as an intuition, [115]
Kathekos, [233]-[4]
— as chaos, [266]
— — symbol of Chaos-Theos-Kosmos, [11]-[12]
— symbology of, [234]
Kathekosis, note, [227]
Kathekosity, fringe of, [229]
— rock-bound coast of, [267]
— significance of, [12]
Kathekotic consciousness, [272]
— period, [209]
Key to the mysteries of nature, the fourth dimension as, [131]
Keyser, Cassius Jackson, and freedom of the mind, [33]
— — — on attitude of metageometricians, [71]
— — — — dimensionality, [94]-[5]
— — — — four-dimensionality of space, [142]-[3]
— — — — generability of hyperspace, [144]
Klein, Felix, [12], [54]-[5], [66]-[7]
Knowledge, all, relative, [101]
— barrier to the certitude of the Thinker's, [186]-[7]
— fabric of, [196]
— hypothetical nature of, [189], ff
— immeasurable realm of, laid bare by the telescope, [298]
Knowledge, mathematical, apriority of, questioned, [37]
— nature of the non-Euclidean, superperceptual, [72]
— real, difficulties of acquiring, [325]
— related to the stream of life and to the shore of materiality, [323]
— relative, degrees exist for, [164]
— sphere of, [184]
— systematization of, [126]
— ultimate, consciousness as a barrier to, [207]
— unification of, [256]
Kosmogenesis, the latent geometrism of, [264]
— — scope of, [237]
Kosmometer, the, [297]
Kosmos, and consciousness, graph representing, [271]
— arrangements of the contents of, [317]-[8]
— in a state of becoming, [265]
— magnitude of, [308]
— moods of, [311]
— space as the consistence of, [239]
— see Cosmos, [12]
L
Labor, division of, between the tuitional and the intuitional faculties, [193]-[4]
— mathematical labors, significance of, [176]
La Grange, Joseph Louis, [12], [39], [50]-[3], [321], [322]
— — — — and the parallel-postulate, [51]-[2]
Lambert, John, [58]
— — and the theory of parallels, [48]-[9]
Language, the passing of, [357]
Legendre, [70]
Leibnitz' dictum, [26]
Leonard rays, [336]
License, mathematic, permissibility of, [38]
Lie, Sophus, [12], [67]
— — and transformation groups, [30]
Life, analysis incapable of dealing with, [319]
— and consciousness as one, [224]
— — form rooted in pyknosis, [214], [328]
— — the fourth dimension, [172]
— — — inaptitude of mathematics for, [179]
— — — power to create, [297]
— as agent of creation, [343]
— — creative agent, [264]
— — expression, [303]
— — vassal of materiality, [329]-[30]
— causative agencies in prolonging, [123]
— current of, as engendering element, [331]
— deposits of, and the intellect, [173]
— estranged by a radical incongruity, [325]
— exalting power of, and humanity, [331], ff; [342]
— exhibition of its remains, [282]
— flow of, [265], [297]
— form as an instrument of, [328]
— indescribable signs of, [219]
— infinitive action of, [327]
— intellect has no aptitude for, [231]
— intuitive, values of, x
— larger life of the Thinker, [196]
— lead of, followed by intuition, [191]
— limits of, fixed by consciousness, [198], ff
— most solid facts of, as shadows, [195]
— motility of, admits of endless variations, [35]
Life, movement of chaos in, [307]
— passage of, [201]
— passage through spatiality, [288]
— power to manipulate, [303]
— recurrent movement of, [307]
— totality of egoic, [243]
— undulations in the current of, [329]
— uniqueness of, [41]
— wake of, and consciousness, [205], [288]
Life-cycle, evolutionary results of the, [259]
Life-stream, the, [278]
Light, polarized, and the fourth dimension, [156]
— consciousness as a spreading, [168]
Light-years and space, [278]
Limits, the sphere of, consciousness as, [163]
Line, as generating element, [144]
— the straight, a curved, [76]
Lineage of every principle runs back to monopyknosis, [213]
Lines, perpendicularity of, in four space, [130]
Lobachevski, [55], [60], [66], [87]
Lodge, Sir Oliver, [340]-[1]; [344]
Logic as architect, [118]
— conventional forms of, [262]
— data of, [286]
— intellect follows in the grooves laid out by, [294]
— miracle power of, over facts, [288]-[9]
— rules of, allowability under, [163]
— — — the game of, [164]
— as symbolism of facts, [287]
Logos and the limits of space, [193]
— being of, [218]
— body of being of, [214]
— consciousness of, [204]
— creative, [12], [213]
— the, [216]-[7]
Lorenz, [83]
Luther, Martin, [181]
M
Magnitudes, geometry, a study of, [203]
— non-sensuous, of hyperspace, [72]
Makrokosmic consciousness, [270]
Malebranche, N., [222]; see note
Manifestation and non-manifestation, [206]
Manifold, finite, though unbounded, [70]
— manufactured by the analyst, [77]
— the, [61]-[2], [172]
Manifoldness, analytical manifoldnesses, as mental excitants, [89]-[90]
— as a conventional construction, [262]
— — an intuition, [318]
— of space, as a near-truth, [317]
Manning, [82], [157]
— and maneuvers in the fourth dimension, [152]
Manvantara, [213], [228]-[9], [232]
— as evolution and involution combined, [13]
Mask, logic as a, [288]-[9]
Mass-termini, of lines, [236]
Mastery of life over matter, [330]
— of the sensible world, [196]-[7]
Materiality as a deposit of life, [295]
— — consubstantial with spatiality, [331], ff
— becoming spatialized, [261]
— characteristics of, [260]
— engendered by kosmic mind, [261]
— engenderment of, [294]
— interpenetrative with spirituality, [236]
— interstices of, [264]
— neglect of, [320]
Materiality, shore of, [323]
— transmuted into spirituality, [328]
Mathematicians and the definition, [37]
— — — limitations of consciousness, [178]
— — — phenomenal world, [118]-[9]
— as prophets, [336]
— respected by humanity, [337]
— the gods of mathesis, [84]
Mathematics, a determinant of the quality of the intellect, vii
— and the criterion of truth, [323]
— — — kosmic intent of the intellect, [326]
— as symbology, [184]
— Euclidean, [140]
— fails when it encounters life, [337]
— its inaptitude for life, [179]
— — kingdom yielded to kinetics, [358]
— possesses no judicative power over life, [180]
— the orthodoxy of, [34]
Mathesis, and conceptional space, [203]
— conduct of the intellect in the field of, vii
— definition of, [13]
— domain of, as origin of fourth dimension, [130]
— gods of, [84]
— marvelous domain of, [118]
— realm of, not submissive to laws of sensible space, [34]
— things of, as emblems of kosmic forces, [239]
— world of, [67], [127]
Matter and mind, syncretization of, [299]
— appulses of life against, [328]
— as a deposit of life, [330]
— honeycombs of, [339]
Matter metamorphosed by life, [328]
— mind as wedded to, [249]
— movement of, in four-space, [157]
— qualities of, and faculties, [332]
— seven planes of, [212]
— spiritualization of, as end of evolution, [327]
— totality of, acted upon by totality of life, [328]
— unity of, with space, [260]
— universum of, [261]
Matutinal ceremonials of creation, [221]
Measurability, as property of space, [62]-[3]