6410 



Principles of Geometry ; Hyperspace 



6410 



Problem, solution. Kretkowski, W. Par. T. 



Nauk Sc. Pam. 12 (*1882) Art. 4, 3 pp. 

 Projective geometry of hyperspace, postulates. 



Fieri, 31. Ev. Mth. 6 (1896-99) 9-. 

 , theorem. Meyer, . D. Nf. Tbl. 



(1884) 141. 

 Projections of regular "bodies" or cells. 



Schlegel, V. D. Mth. Vr. Jbr. 2 (1893) 



66-. 

 Pythagorean theorem, generalisation. Klug, 



L. Mh. Mth. Ps. 10 (1899) 84-. 

 Quadrics, classification. Wythoff, W. A. N. 



Arch. Wisk. 4 (1899) 162-. 

 Eeciprocal relations. Schubert, H. D. Mth. 



Vr. Jbr. 4 (1897) 158-. 

 Eepresentation by correlative figure of ordinary 



geometry. Konig, Jul. Gott. Nr. (1872) 



157-. 



of figures by correlative figures of ordinary 

 geometry. Spottiswoode, W. C. E. 81 (1875) 

 875-, 961-. 



on plane, of ordinary space by quadric. 

 Aschieri, E. Mil. I. Lomb. Ed. 18 (1885) 

 494-. 



, regular solids. Schlegel, V. Pa- 

 lermo Cir. Mt. Ed. 5 (1891) 1-. 



Six-hundred cell (hyper-polyhedron) and its 

 self-corresponding displacements. Oss, S. L. 

 van. [1899] Amst. Ak. Vh. (Sect. 1) 7 (1901) 

 No. 1, 18 pp.; Nt. 61 (1899-1900) 304. 



Sphere, potential. Giuliani, G. N. Cim. 21 

 (1887) 260-. 



Spheres, ?i-fold linear systems. Del Re, A. 

 Palermo Cir. Mt. Ed. 2 (1888) 124-. 



Theory corresponding to curvature of ordinary 

 space. Lie, S. Gott. Nr. (1871) 191-, 

 535-. 



Volume calculation, three theorems. Hoppe, 

 E. Arch. Mth. Ps. 69 (1883) 385-. 



Direction. Blakslee, T. M. Des Moines Anal. 



9 (1882) 15-, 51-. 

 , arguments against disuse of term. Warren, 



S. E. [1898] N. Y. Am. Mth. S. fill. 5 



(1899) 88, 94-. 

 , geometry of. Laguerre, E. Par. S. Mth. 



Bll. 8 (1880) 196-. 

 Distance, analytical theory. Beltrami, E. 



Mil. I. Lomb. Ed. 5 (1872) 294-. 



relations, theory. Dillner, G. Ups. Vet. 

 S. Arsk. 2 (1861) 1-. 



Divisibility of consecutive integer products, 



geometric analogy. Pincherle, S. Bologna 



Ed. (1892-93) 17-. 

 magnitude. MacWhorter, A. Silliman 



J. 6 (1848) 329-. 

 Equivalence of figures, proof of fundamental 



axiom. Veronese, G. Ven. I. At. (1894-95) 



421-. 



in geometry, concept founded on number. 

 Calinon, A. Nancy S. Sc. Bll. (1900) 85-. 



, definition. Sbrana, S. Ev. Mt. 4 



(1894) 147-. 

 , group of, and its kinematic bases. An- 



drade, J. C. E. 126 (1898) 1775-. 

 Euclid, Bk. xn. Walsh, J. Tilloch Ph. Mg. 



64 (1824) 181-. 



Euclidean geometry, defence. Lagrange, C. 



Brux. Ac. Bll. (1899) 506-. 

 without Euclid's postulate. Delbceuf, J. 



Liege S. Sc. Mm. 19 (1897) No. 3, 116 pp. 



and non-Euclidean geometry. Andrade, J. 

 Ens. Mth. 2 (1900) 298-. 



Euclid's 3rd postulate, substitute for. Muir- 

 head, R. F. Glasg. Ph. S. P. 12 (1880) 

 112-. 



5th postulate and principle of homogeneity. 

 Flauti, V. Nap. Ed. 1 (1842) 61 (161)-. 



Finite equality of two plane figures. Rethy, M. 



Mth. Tennt. Ets. 12(1894)279-; Mth. Nt. 



B. Ung. 12 (1895) 72-. 

 Finitely equal surfaces. Rethy, M. Mth. 



Termt. Ets. 8 (1890) 176- ; 11 (1893) 103- ; 



Mth. Nt. B. Ung. 8 (1891) 170- ; 11 (1894) 



' _ (Eethy). Dobriner, H. Mth. A. 42 



(1893) 275-. 



Functional notation, application to demonstra- 

 tion of fundamental propositions. M., F. 

 Bb. Un. 12 (1819) 85-. 



, geometrical theorems. Anon. 



(vi 534) Gergonne A. Mth. 10 (1819-20) 

 161. 



Fundamental figures in Euclidean space, 



measurement. Doehlemann, K. Z. Mth. Ps. 



41 (1896) 265-. 

 of 1st rank, geometric definition of pro- 



jectivity. Klein, C. F. Mth. A. 17 (1880) 



52-. 



Fundamental Principles. 



Nieuport, C. F. F. de. [1819] Brux. Ac. Sc. 



Mm. 1 (1820) 435-. 



Price, B. Ashmol. S. P. 2 (1843-52) 177-. 

 Wedgwood, H. B. A. Ep. (1845) (pt. 2) 2-. 

 Matthes, C. J. Amst. Ts. Wis. Nt. Wet. 3 



(1850) 35-. 



Gardiner, M. Viet. T. Ph. I. 4 (1859) 76-. 

 Helmholtz, H. [1866] Gott. Nr. (1868) 193-. 

 Riemann, [G. F.] B. Gott. Ab. 13 (1868) 



(Mth.) 133-. 



Lagout, E. Les Mondes 22 (1870) 13-. 

 Konig, G. (xn) Mag. Tud. Ak. Ets. 6 (No. 5) 



(1872) 94-. 

 Cassani, P. G. Mt. 11 (1873) 331- ; (K) Ven. 



Aten. At. 10 (1873) 222-. 

 Worpitzky, (Dr) . Arch. Mth. Ps. 55 (1873) 



405-. 

 Zambelli, A. (xi) Ven. Aten. At. 11 (1873) 



193-. 

 Helmholtz, H. L. F. von. V. Nost. Eng. Mg. 



15 (1876) 501- ; Ev. Sc. 12 (1877) 1197-. 

 Caitani, P. G. Mt. 15 (1877) 284-; 20 (1882) 



143-. 

 Tilly, J. M. de. Bordeaux S. Sc. Mm. 3 (1880) 



Krebs, C. (xn) Ts. Mth. 6 (1882) 81-. 

 Meyer, A. (xn) Ts. Mth. 6 (1882) 113-. 

 Zeuthen, H. G. (xn) Ts. Mth. 6 (1882) 119-. 

 Henrici, 0. Nt. 29 (1884) 453-, 573. 

 (Henrici.) Geoghegan, E. Nt. 29 (1884) 



551. 

 (Helmholtz's paper, 1866.) Lie, S. Leip. 



Mth. Ps. B. 38 (1886) 337-. 



415 



