The Mathematical Works of Bernard Bolzano

Steve Russ9780198539308, 0-19-853930-4

Bolzano’s (1781-1848) interests mirrored those of the 19th century, including theology, philosophy, ethics, politics, logic and mathematics. His work was all of a piece, so to study one discipline requires studying his complete works. In an effort to make more of Bolzano’s work available in English, this new translation offers a representative selection of the mathematical work. In geometry and foundations the titles include Considerations on Some Objects of Elementary Geometry and Contributions to a Better-Grounded Presentation of Mathematics. Early works of analysis include such topics as the binomial theorem and as a consequence from it the polynomial theorem, purely analytic proof of the theorem and three problems of rectification, complanation and cubature (“as a sample of a complete organization of the science of space”), with later analysis and the infinite represented by pure theory of numbers, theory of functions and improvements, and paradoxes of the infinite. The editors provide notes on translation issues and a list of selected works”

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Table of contents :
Contents……Page 8
List of Illustrations……Page 10
Abbreviations……Page 11
Preface……Page 13
Note on the Texts……Page 21
Note on the Translations……Page 24
Introduction……Page 32
GEOMETRY AND FOUNDATIONS……Page 42
Considerations on Some Objects of Elementary Geometry (BG)……Page 56
Contributions to a Better-Grounded Presentation of Mathematics (BD)……Page 114
EARLY ANALYSIS……Page 170
The Binomial Theorem, and as a Consequence from it the Polynomial Theorem, and the Series which serve for the Calculation of Logarithmic and Exponential Quantities, proved more strictly than before (BL)……Page 186
Purely Analytic Proof of the Theorem, that between any two Values, which give Results of Opposite Sign, there lies at least one real Root of the Equation (RB)……Page 282
The Three Problems of Rectification, Complanation and Cubature, solved without consideration of the infinitely small, without the hypotheses of Archimedes and without any assumption which is not strictly provable. This is also being presented for the scrutiny of all mathematicians as a sample of a complete reorganisation of the science of space (DP)……Page 310
LATER ANALYSIS AND THE INFINITE……Page 376
Pure Theory of Numbers Seventh section: Infinite Quantity Concepts (RZ)……Page 386
Theory of Functions (F)……Page 460
Improvements and Additions to the Theory of Functions (F+)……Page 604
Paradoxes of the Infinite (PU)……Page 622
Selected Works of Bernard Bolzano……Page 710
Bibliography……Page 716
L……Page 722
Y……Page 723
C……Page 724
F……Page 725
L……Page 726
P……Page 727
S……Page 728
Z……Page 729