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Lessons in geometry. I. Plane geometry. Transl. from the French by Mark Saul. (English) Zbl 1156.51012
Providence, RI: American Mathematical Society (AMS); Newton, MA: Education Development Center (ISBN 978-0-8218-4367-3/hbk). xiv, 330 p., with CD-ROM. (2008).
The present book is the English translation of the thirteenth French edition from 1947 (Zbl 1152.51303) printed by Librairie Armand Colin, Paris which has also published the original book from 1898 (JFM 29.0428.14).
The book includes a disk for use with the Texas Instruments TI-NSpire$$^{\text{TM}}$$ software.
Here some words to 1. the author Jacques Hadamard, 2. the creation of the book, 3. the content of the book.
1.
Concerning Jacques Hadamard’s life (1865–1963) read the excellent biography ‘Jacques Hadamard, a universal mathematician’ (1998; Zbl 0906.01031) by V. Maz’ya and T. Shaposhnikova.
2.
From the translator’s Preface: In the late 1890s, Gaston Darboux, the editor of a set of textbooks for teaching of mathematics, commissioned several mathematicians to write these books. So Jacques Hadamard as a high school teacher was asked to prepare the materials for geometry. Two volumes resulted: one on plane geometry in 1898 and a volume on solid geometry in 1901.
Hadamard revised his book ‘Plane geometry’ twelve times, the last (thirteenth) edition appearing in 1947 (see above).
3.
The style and structure of the book is dominated by the aim of the author to awaken and encourage the student’s interest in the field of mathematics. This aim results in big parts of exercises and problem sections of gradually different difficulty.
Special chapters, called “Constructions”, reflect the author’s intention of “learning by doing”.

Contents: The Introduction gives basic definitions.
Book I ‘On the straight line’ deals with properties of lines (angle, triangle).
Book II ‘On the cirlce’ concerns elementary properties with circles.
Book III ‘On similarity’ includes (among others) metric relations in a triangle and regular polygons.
Book IV ‘On areas’ deals mainly with calculations of areas.
Note A–D include more theoretical questions (the background) of mathematical methods and basic notions.
Neither references nor an index are given.
Summarizing, the book is a rich source of elementary constructions in plane (Euclidean) geometry, recommended for students and teachers for self-study.

##### MSC:
 51M04 Elementary problems in Euclidean geometries 51-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry 01A75 Collected or selected works; reprintings or translations of classics 51-03 History of geometry 51N05 Descriptive geometry
##### Keywords:
straight line; circle; similarity; area
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