Mathematics of the 19th Century: Geometry, Analytic Function Theory
The general principles by which the editors and authors of the present edition have been guided were explained in the preface to the first volume of Mathemat ics of the 19th Century, which contains chapters on the history of mathematical logic, algebra, number theory, and probability theory (Nauka, Moscow 1978; En glish translation by Birkhiiuser Verlag, Basel-Boston-Berlin 1992). Circumstances beyond the control of the editors necessitated certain changes in the sequence of historical exposition of individual disciplines. The second volume contains two chapters: history of geometry and history of analytic function theory (including elliptic and Abelian functions); the size of the two chapters naturally entailed di viding them into sections. The history of differential and integral calculus, as well as computational mathematics, which we had planned to include in the second volume, will form part of the third volume. We remind our readers that the appendix of each volume contains a list of the most important literature and an index of names. The names of journals are given in abbreviated form and the volume and year of publication are indicated; if the actual year of publication differs from the nominal year, the latter is given in parentheses. The book History of Mathematics from Ancient Times to the Early Nineteenth Century [in Russian], which was published in the years 1970-1972, is cited in abbreviated form as HM (with volume and page number indicated). The first volume of the present series is cited as Bk. 1 (with page numbers).
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Mathematics of the 19th Century: Vol. II: Geometry, Analytic Function Theory
Andrei N. Kolmogorov,Adolf-Andrei P. Yushkevich
Vista previa restringida - 1996
Abel Abelian functions Abelian integrals algebraic functions analysis analytic function analytic function theory angles Berlin Bólyai called Cauchy Cauchy's Cayley coefficients complex numbers complex variable computations concept conformal mapping conic constructed continuous convergence coordinates corresponding curvature curve defined derivatives differential equations Dirichlet principle disk dissertation elliptic functions elliptic integrals entire function Euler example expressed finite formulas Funktionen Gauss genus geodesic Grassmann hyperbolic plane hyperelliptic integrals Ibid ideas imaginary independent infinite intersection introduced Jacobi Klein later linear lines Lobachevskii manifold Math mathematical mathematicians mentioned method metric Möbius multi-dimensional geometry multi-valued functions neighborhood nineteenth century obtained paper Paris periods Plücker Poincaré polynomial Poncelet power series problem professor projective geometry proof properties proved published Puiseux rational function Riemann surface Schwarz single-valued sphere term theorem theory of elliptic theory of functions theta functions three-dimensional tions topology transformations triangle Úber University values vector Weierstrass Werke zeros