Mathematics of the 19th Century: Geometry, Analytic Function TheoryAndrei N. Kolmogorov, Adolf-Andrei P. Yushkevich 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). |
Contents
3 | |
PROJECTIVE GEOMETRY | 27 |
NONEUCLIDEAN GEOMETRY | 47 |
J Bólyais Absolute Geometry | 61 |
3 | 63 |
Beltramis Interpretation | 67 |
Elliptic Geometry | 73 |
The Multidimensional Geometry of Klein and Jordan | 81 |
Multidimensional Surface Theory | 94 |
TOPOLOGY | 97 |
GEOMETRIC TRANSFORMATIONS | 106 |
CONCLUSION | 115 |
26 | 139 |
36 | 146 |
273 | |
283 | |
Other editions - View all
Common terms and phrases
Abelian functions Abelian integrals algebraic functions analysis analytic function analytic function theory angles Berlin Bólyai called Cauchy Cauchy's Cayley Chasles coefficients complex numbers complex variable computation concept conformal mapping congruence conic connected convergence coordinates corresponding curvature curve defined derivatives differential equations differential geometry Dirichlet principle elliptic functions elliptic integrals entire function Euclidean space Euler expression finite formulas Gauss geodesic Grassmann hyperbolic geometry hyperbolic plane hyperelliptic integrals hypergeometric Ibid ideas imaginary infinite intersection intrinsic geometry introduced Jacobi Kazan Klein linear lines Lobachevskii manifold mapping Math mathematical mathematicians mentioned methods metric Möbius multi-dimensional geometry n-dimensional obtained osculating paper Paris Plücker Poincaré points polyhedra polynomial Poncelet power series problem professor projective geometry properties proved published Puiseux Riemann surface Riemannian Schläfli single-valued sphere term theorem theory of elliptic theory of functions three-dimensional topology transformations triangle trigonometric University values vector Weierstrass wrote zero