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