Miscellanea mathematica 10. Ed. by Bob van Rootselaar and Anna van der Lugt. (Miscellanea mathematica 10. Hrsg. von Bob van Rootselaar und Anna van der Lugt.) (German) Zbl 0833.01035

Bolzano, Bernard

Bernard Bolzano-Gesamtausgabe. Reihe II: Nachlaß. B. Wissenschaftliche Tagebücher. 6.2. Stuttgart - Bad Cannstatt: Friedrich Frommann Verlag - Günter Holzboog. 225 S. (1995).

The volume under review continues the critical edition of Bernard Bolzano’s mathematical diary, his Miscellanea Mathematica [vol. 6.1 (1994), see Zbl 0799.01032], with the portions written especially between 14 September 1814 and 29 October of the same year. It contains the results of Bolzano’s examination of mathematical textbooks, especially of G. S. Klügel’s Mathematisches Wörterbuch. Among the themes discussed are topics from elementary geometry including considerations on the project to write a textbook of his own on geometry aiming not at a scientific presentation but at certainty as such, which shows Bolzano’s stress on the philosophical side of mathematics (MM 876, p. 119).
Other topics are from general geometry (e.g., the direction of a line), higher geometry (e.g., the curvature of curves in space), general mathematics (e.g., the discussion of Klügel’s definition of mathematics as the science of the forms of magnitudes, and of the notion of number), analysis, and the mathematical method. The interplay between excerpts, comments and the attempts to develop own conceptions gives a lively impression of Bolzano doing mathematics at his desktop.
The volume documents an enormous amount of editorial work, mastered with excellent skill. The useful introduction written by B. van Rootselaar (pp. 11–32) gives not only a summary of treated topics, but also helpful information on the mathematics used, and hints on those ideas which found their way into Bolzano’s publications. The volume is closed by a bibliography, and useful indices including basic biographical data of all persons mentioned.

Reviewer: Volker Peckhaus (Erlangen)

MSC:

01A75	Collected or selected works; reprintings or translations of classics
01A55	History of mathematics in the 19th century

Keywords:

Bolzano; complete works; Klügel’s dictionary

Citations:

Zbl 0799.01032