6410 



Principles of Geometry 



6410 



straight lines. Petersen, J. Kjtfb. Ov. (1900) 



305-. 

 and teaching. Andrade, J. Ens. Mth. 2 



(1900) 114-. 



theorems. Simon, M. Mth. A. 48 (1897) 607. 

 volume of a body, expression for. Mansion, P. 



Brux. S. Sc. A. 21 (1897) (Pt. 1) 118-. 



Numbers and ratios in geometry. Maiziere, A. 



Lille Mm. S. (1833) 1-. 

 Paradoxes connected with mathematics of in- 



finity. DomenechyEstapd, J. [1894] Barcel. 



Ac. Mm. 1 (1892-1900) 315- . 

 Plane angle, definition. Bonnel, J. Lyon Ac. 



Mm. (Sc.) 31 (1892) 39-. 



, concept, fundamental. Gerling, C. L. 

 Crelle J. 20 (1840) 332-. 



, definition, and axiom raised to theorem. 

 Valeriani, V. G. Mt. 7 (1869) 376. 



, general theory. Crelle, A. L. Berl. Ab. 

 (1834) 23-. 



in infinite dimension space, concept. 

 Pincherle, S. Bologna Ed. 2 (1898) 71-. 



polygons and angles as system of absolute 

 magnitudes. Stolz, 0. Mh. Mth. Ps. 5 

 (1894) 233-; 7 (1896) 296. 



triangle, extension of elementary theorems 

 to general space. Mehmke, B. Arch. Mth. 

 Ps. 70 (1884) 210-. 



Point pairs, and circles in space, treated by 

 Grassmann's method. Mttller, E. Mh. Mth. 

 Ps. 7 (1896) 77-. 



, power of, with regard to five circles or six 

 spheres. Lucas, E. Em. B. Ac. Line. Mm. 

 2 (1878) 449-. 



, straight line and circle, concepts. R., F. 

 Bv. Ligure 2 (1843) 132-. 



Problems, methods of solution. Egidi, G. 

 Em. N. Line. At. 40 (1887) 9-. 



, --- not based on proportions. Airy, 

 (Sir) G. B. [1857] Camb. Ph. S. T. 10 

 (1864) 166-. 



Products of numbers, properties. Teixeira, 



J. P. G. Teix. J. Sc. 14 (1900) 179-. 

 Projections, areas of, applications of Tinseau's 



theorem. Cabreira, A. [1897] Lisb. J. Sc. 



Mth. 5 (1898) 93-. 

 Project! ve relations of space of various dimen- 



sions. Veronese, G. Mth. A. 19 (1882) 



161-. 

 Proportion, equimultiples in ancient theory. 



Trudi, N. Nap. G. Mt. 1 (1863) 337-. 



, Euclid's theory. Hitt, M. J. M. [1897] 

 Camb. Ph. S. T. 16 (1898) 227-. 



, -- . Gibson, G. A. Edinb. Mth. S. P. 

 16 (1898) 99-. 



, , filling a gap in. Nordmark, Z. 

 Ups. N. Acta S. Sc. 6 (1799) 174-. 



, reduced to formulae. Peano, G. 

 Mathesis 10 (1890) 73-. 



, geometrical. Marrat, W. Tilloch Ph. Mg. 

 33 (1809) 426-. 



and ratio, Euclid's theory; and nature of 

 quantity. Powell, B. [1836] Ashmol. S. 

 T. 1 (1838) No. 5, 64 pp. 



, theory. Chelini, D. G. Arcad. 73 (1837) 



166-. 



Proportion, theory. Gibson, G. A. Edinb. 



Mth. S. P. 18 (1900) (App.) 26 pp. 

 , , geometrical. Hoppe, R. Arch. Mth. 



Ps. 62 (1878) 153-. 

 Pseudospherical functions and their applications 



to pseudospherical geometry. Jakovkin, 



A. F. Kazan S. Ps.-Mth. Bll. 9 (1900) 



(Prot.) 45-. 



geometry. Cayley, A. E. S. P. 37 (1884) 

 82-. 



, theorem. Beltrami, E. G. Mt. 10 



(1872) 53. 

 Quantities, geometrical and hyper-geometrical. 



Polignac, A. (Prince de). G. E. 52 (1861) 



24-. 

 , hyper-geometrical. Polignac, A. (Prince 



de). C. E. 56 (1863) 381-. 

 , positive and negative, in geometry. 



Pourtales, L. A. de. Neuch. Bll. 2 (1846-47) 



127-. 

 , principles applicable to geometry. Valat, 



. Bordeaux Act. Ac. Sc. (1849) 535-. 

 Eadical axis, existence demonstrated without 



Euclid's postulate. Reyes Prosper, V. Fschr. 



Mth. (1895) 571. 

 Eatio, Archimedes' principle. Terquem, 0. 



N. A. Mth. 3 (1844) 586-. 

 Eatios, arithmetical and geometrical. Bianchi, 



G. Palomba Eac. 3 (1847) 155-. 

 , duplicate. Hain, E. Arch. Mth. Ps. 60 



(1877) 404-. 

 Eectangle, geometrical existence. Collignon, 



E. As. Fr. C. E. (1899) (Pt. 2) 87-. 

 Eiemann planes and Euclidean spheres, 



identity. Lechalas, G. Brux. S. Sc. A. 20 



(1896) (Pt. 2) 167-. 



, non-identity. Mansion, P. 

 Brux. S. Sc. A. 20 (1896) (Pt. 2) 178-. 



Eiemann's geometry, fundamental principle. 



Mansion, P. Mathesis 14 (1894) 180- ; B. 



A. Ep. (1894) 579-. 

 , interpretation of a theorem. Dauge, F. 



Mathesis 18 (1898) 5-. 

 and metageometry, principles. Mansion, 



P. Mathesis 15 (1895) 63-. 

 Segment, postulate of, deduced from that of 



angle. Sbrana, S. Bv. Mt. 3 (1893) 179-. 

 Signs of distances. Fontene, G. Ens. Mth. 



1 (1899) 272-. 

 , rule of. Laguerre, . N. A. Mth. 9 (1870) 



175-. 

 , use. Fontene, G. Ens. Mth. 1 (1899) 



123-. 



+ and - . Haillecourt, A. N. A. Mth. 7 

 (1848) 83-. 



. De Morgan, A. Camb. and 

 Dubl. Mth. J. 6 (1851) 156- ; 7 (1852) 242-. 



Space and body, knowledge. Wedgwood, H. 



[1850] Camb. Ph. S. T. 9 (1856) 157-. 

 , concept. Hoppe, . D. Nf. Tbl. (*1875) 



142-. 

 , , and application to natural science. 



Harnack, A. [1878] Dresden Isis Sb. (1879) 



178-. 

 , , empirical and ideal. Kapke, . Hamb. 



Mth. Gs. Mt. 1 (1889) 274-. 

 , , an extension of concept of length. 



Graberg, F. Ziir. Vjschr. 31 (1886) 339-. 



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