In this book the main theorems of plane euclidean geometry are proved on a university level. In the opinion of the writer, a reasonable training of high-school teachers must present them with a good working knowledge of geometry before starting to speak about foundations, i.e., about geometry.
The approach to geometry chosen in this book goes back to some papers by Ch. Wiener in the early 1890's. In particular also, I am indebted to the great book on plane geometry by Jacques Hadamard, and to modern works by G. Thomsen, H. Freudenthal, and F. Bachmann. Freudenthal has remarked that geometry today suffers from a low level of formalization as compared to other parts of mathematics. I am trying to remedy the situation by the use of a consistent formalism which is in keeping with the notations both of set theory and of traditional geometry. The deviations from the usual notations are kept to a minimum. Sometimes, however, they are unavoidable; for example, to untangle the different notions of angle that appear in elementary geometry, or, to distinguish between the point set of a segment and the vector which is its length.