0820 Complex Numbers 



Imaginary powers of quantities, geometrical 

 representation. Warren, J. Phil. Trans. 

 (1829) 339-. _ 



e zkir *~ l , paradox. Catalan, E. C. 



N. A. Mth. 8 (1869) 456-. 



radicals, principle of fundamental substitu- 

 tion in. Saporetti, A. Bologna Ed. (1878) 

 126-. 



and real forms, contiguity in approximate 

 solutions. Valles, F. N. A. Mth. 13 (1854) 

 449-. 



Involution and evolution of imaginaries con- 

 sidered geometrically. Henkle, W. D. Des 

 Moines Anal. 1 (1874) 149-. 



Logarithms of negative quantities, and on 

 imaginaries. Fontana, G. Verona S. It. 

 Mm. 1 (1782) 183-. 



Numbers, irreducible with complex numbers. 

 Formenti, C. Mil. I. Lomb. Ed. 16 (1883) 

 981-. 



Partitions of complex numbers (theorem con- 

 tained in theorem of Jacobi's). Sylvester, 

 J. J. C. E. 96 (1883) 1276-. 



Position of chessmen defined by complex 

 variables. Gochmann, C. Fschr. Mth. (1897) 

 426. 



Power with complex base and exponent, 

 geometrical representation. Durege, . 

 Ziir. Vjschr. 5 (1860) 297-. 



Powers with imaginary exponents. Ballauff", L. 

 Grunert Arch. 6 (1845) 409-. 



Prime factors, ideal, of complex numbers, 

 formed rationally from roots of an irredu- 

 cible equation. Selling, E. Z. Mth. Ps. 

 10 (1865) 17-. 



Product of complex factors, reduction. Schiappa 

 Monteiro, A. Lisb. J. Sc. Mth. 5 (1898) 

 209-. 



Quadratic forms, number. Eisenstein, G. 

 Crelle J. 27 (1844) 311-. 



, belonging to real determinant. 

 Eisenstein, G. Crelle J. 27 (1844) 80. 



Quaternions, proof of Frobenius' theorem on 

 their relation to complex numbers. Grisse- 

 mann, F. X. Mh. Mth. Ps. 11 (1900) 132-. 



Eeality of quantities called imaginary, of form 

 a + W-1, etc. Desmousseaiuc de Givre", 

 F. X. E. Par. Ing. Civ. Mm. (1877) 389-. 



Eelative Abelian number-fields. Hilbert, D. 

 Gott. Nr. (1898) 370-. 



. Wiman, A. Lund. Un. Acta 36 



(1900) (S. Psgr. No. 6) 17 pp. 



quadratic "fields" (Korper). Hilbert, D. 

 [1897-99] D. Mth. Vr. Jbr. 6 (1899) (Heft 1) 

 88-; Mth. A. 51 (1899) 1-. 



Boots of e 2 = -1. Plarr, G. Edinb. E. S. P. 



15 (1889) 93-. 

 unity. Cayley, A. Mess. Mth. 4 (1875) 



171. 

 Seventh roots of unity. Cayley, A. Mess. 



Mth. 7 (1878) 177-. 



Symbols, imaginary, geometrical interpreta- 

 tion. Franqais, J. F. Gergonne A. Mth. 



4 (1813-14) 61-. 

 Theory, means of extending without use of 



imaginaries. Saltel, L. C. B. 94 (1882) 



166-. 



Quaternions 0830 



Triangle, figure of, regarded as a complex 



quantity. Frege, G. [1878] Jena. Sb. (1879) 



xviii. 



Triple algebra and application to solid geo- 

 metry. Graves, C. Ph. Mg. 34 (1849) 



119-. 

 Triplets, functions of two variables employed in 



interpreting. Graves, C. Ir. Ac. P. 5 (1853) 



423-. 

 Twenty -third roots of unity. Cayley, A. 



Crelle J. 55 (1858) 192; 56 (1859) 186-. 

 Units in rationality domain of 5th roots of 1. 



Gmeiner, J. A. Mh. Mth. Ps. 9 (1898) 184-. 

 Zero, imaginary and real. Eiccati, G. Verona 



S. It. Mm. 4 (1788) 116-. 

 , . Fontana, G. [1798] Mod. S. It. 



Mm. 8 (1799) 174-. 

 Zeros, imaginary. Young, J. R. Ph. Mg. 27 



(1845) 91-. 



0830 Quaternions. 



Analogue to quaternions in 4 dimensions. 



Wijthoff, W. A. Amst. Ak. Vs. 6 (1898) 



520-. 

 Conditions of integrability of Suadp, Suftdp, 



Suydp, elimination of o, /3, 7 from. Plarr, 



G. [1874] Edinb. B. S. T. 27 (1876) 251-. 

 Conjugate numbers in general, solution of 



quadratics by quaternions in particular. 



Studnicka, F. J. Casopis 23 (1894) 72-; 



Fschr. Mth. (1893-94) 149. 

 Coordinates versus quaternions. Cayley, . 



Edinb. B. S. P. 20 (1895) 271-. 

 Coplanarity and homoconicism, quaternion 



expressions. Spottiswoode, W. Ph. Mg. 36 



(1850) 379-. 

 Curves cutting plane into squares, systems. 



Tail, P. G. Edinb. Mth. S. P. 7 (1889) 2-. 



of inversion. Raimondi, R. G. Mt. 26 

 (1888) 181-. 



Determinants of quaternions. Peirce, <7. M. 



N. Y. Am. Mth. S. Bll. 5 (1899) 335-. 

 Differentiation of power of a quaternion. 



M'Aulay, A. [1889] Edinb. E. S. P. 16 



(1890) 201-. 

 . Note on M'Aulay's paper. 



Tait, . [1889] Edinb. E. S. P. 16 (1890) 



205-. 



in the quaternion analysis. MacFarlane, A. 

 Ir. Ac. P. 6 (1900-02) 199-. 



Displacements, finite, of system of points 

 whose mutual distances remain invariable; 

 quaternion expression. Plarr, G. (xi) [1883] 

 Edinb. E. S. P. 12 (1884) 151-. 



Dupin's theorem [on intersection lines of three 

 systems of orthogonal surfaces] by quater- 

 nions. Hamilton, (Sir) W. R. Ir. Ac. P. 6 

 (1853-54) 86-. 



and its converse, geometrical proof. 

 Sommerfeld, A. D. Mth. Vr. Jbr. 6 (1899) 

 (Heft 1) 123-. 



Electrodynamics and magnetism, quaternion 

 investigations. Tait, P. G. QJ. Mth. 3 

 (1860) 331-. 



Elementary universal geometry, new terms. 

 Sylvester, J. J. Nt. 32 (1885) 576-. 



56 



