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**Foundations of geometry (Festschrift 1899). Edited and commented by Klaus Volkert.
(Grundlagen der Geometrie (Festschrift 1899).)**
*(German)*
Zbl 1321.01034

Klassische Texte der Wissenschaft. Heidelberg: Springer Spektrum (ISBN 978-3-662-45568-5/pbk; 978-3-662-45569-2/ebook). xix, 268 p. (2015).

There are many editions and translations of David Hilbert’s [Grundlagen der Geometrie. Leipzig: B. G. Teubner (1899; JFM 30.0424.01)] first published in 1899 as a Festschrift on the occasion of the unveiling of the Gauss-Weber monument in Göttingen. However, the author’s idea is new, he wants to present Hilbert’s Festschrift to the modern reader in a form that is easy to read. Therefore, the author took the perspective of a historian of mathematics. In the introduction, the author presents a description of the construction and contents of his book as well as a biography of Hilbert. There are the following six chapters:

1. A short history of the axiomatics especially of geometry.

2. Hilbert’s way to his “Foundations of geometry”.

3. Text of the Festschrift.

4. Presentation of the text.

5. The reception of Hilbert’s Festschrift.

6. The time after the Festschrift.

The next chapter is devoted to the classical theorems in Hilbert’s “Foundations” as well as in Hilbert’s lectures, the last pages having the title “Hilbert’s models”.

Of course, the book contains a bibliography, an index of names and a subject index.

The author was successful, his presentation is what he wanted it to be, an easy-reading classical text with lots of information. This book is a must for everybody interested in the history of geometry, it is highly recommended.

1. A short history of the axiomatics especially of geometry.

2. Hilbert’s way to his “Foundations of geometry”.

3. Text of the Festschrift.

4. Presentation of the text.

5. The reception of Hilbert’s Festschrift.

6. The time after the Festschrift.

The next chapter is devoted to the classical theorems in Hilbert’s “Foundations” as well as in Hilbert’s lectures, the last pages having the title “Hilbert’s models”.

Of course, the book contains a bibliography, an index of names and a subject index.

The author was successful, his presentation is what he wanted it to be, an easy-reading classical text with lots of information. This book is a must for everybody interested in the history of geometry, it is highly recommended.

Reviewer: Karin Reich (Berlin)

### MSC:

01A55 | History of mathematics in the 19th century |

01-00 | General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to history and biography |

01A70 | Biographies, obituaries, personalia, bibliographies |

01A75 | Collected or selected works; reprintings or translations of classics |

51-03 | History of geometry |

51A05 | General theory of linear incidence geometry and projective geometries |