Bolzano, Bernard Russ, Steve (ed.) The mathematical works of Bernard Bolzano. Edited by Steve Russ. Translated from the German. (English) Zbl 1065.01015 Oxford: Oxford University Press (ISBN 0-19-853930-4/hbk). xxx, 698 p. (2004). This is the first collection of English translations of several key Bolzano works and it combines scholarly care with an easily readable text. Five of the works are translations of texts published by Bolzano that have appeared in facsimile in Bernard Bolzano (1781-1848), Bicentenary, Early mathematical works (1981; Zbl 0534.01024). An earlier translation of these five also formed the appendix to the translator’s 1980 dissertation. These are: Betrachtungen über einige Gegenstände der Elementargeometrie, (Elementary Geometry, 1804); Beyträge zu einer begründeteren Darstellung der Mathematik Erste Lieferung, (A Better-Grounded Presentation of Mathematics, 1810); Der binomische Lehrsatz, (The Binomial Theorem, 1816); Rein analytischer Beweis des Lehrsatzes, dass zwischen je zwey Werthen, die ein entgegensetztes Resultat gewähren, wenigstens eine reelle Wurzel der Gleichung liege, (A 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, 1817); Die drey Probleme der Rectification, (Three Problems of Rectification, Complanation and Cubature, 1817). The remaining works were left by Bolzano in manuscript form only and can be classed under the headings: Unendliche Grössenbegriffe, (Infinite Quantity Concepts, 1830s); Functionenlehre, (Theory of Functions, 1830s); Paradoxien des Unendlichen, (Paradoxes of the Infinite, posthumous 1851). Of these latter the first two are based on texts appearing in Gesamtausgabe. Reihe II: Nachlass. A. Nachgelassene Schriften. Band 8: Grössenlehre II (1976; Zbl 0323.01033) and Gesamtausgabe. Reihe II: Nachlass. A. Nachgelassene Schriften. 10.1 (2000; Zbl 0961.01038), while the last has appeared in various editions and translations.The smooth-reading translation is faithful to the wording and details of notation, adopting, for example, the astronomical signs used by Bolzano to label equations. Even Greek quotations are silently corrected for accuracy and their sources and translations given in footnotes. Original diagrams are redrawn in the text in a clearer, but still very faithful, fashion, while also reproducing in facsimile the original single plate, back-of-the-book diagrams. The only thing this reviewer found lacking was a consistent attention to quote marks. Though they are hardly essential they are left out of a number of passages (e.g. p. 80, §43, and p. 136) where the original appears to use them to good effect. In some instances quote marks are retained and, in addition, the quoted passage is indented as a block (p. 160).Helpful introductions are given to the volume and to each of the three sections. There is a thorough annotated bibliography of those of Bolzano’s works most relevant to the present volume. This is complemented by a bibliography of works consulted and of further reading. There are separate name and subject indexes, with the name index, however, covering only Bolzano’s text. Reviewer: Albert C. Lewis (Indianapolis) Cited in 2 ReviewsCited in 12 Documents MSC: 01A75 Collected or selected works; reprintings or translations of classics Keywords:Bernard Bolzano Citations:Zbl 0534.01024; Zbl 0323.01033; Zbl 0961.01038 × Cite Format Result Cite Review PDF