The book we are proposing here to the English-speaking reader is one that would have qualified at the beginning of the previous century as a book of “Modern Geometry” of the triangle and quadrilateral. Most of the results were obtained in the second half of the 19th century and the first half of the 20th century. The author was a retired artillery colonel and an enthusiastic amateur mathematician. This should come as no surprise, as for any artillery officer mathematics (and, especially, geometry) plays an important part in his formation.
As the title surely suggests, this book is a rich collection of some of the most important properties of numerous points, lines, and circles related to triangles and quadrilaterals, as they were known by the mid-1950s. These include the nine-point circle, the Simson line, the orthopolar triangles, the orthopole, the Gergonne and Nagel points, the Miquel point and circle, the Carnot circle, the Brocard points, the Lemoine point and circles, the Newton-Gauss line, and many others. It was, probably, one of the most complete descriptions of the subject at the moment of the writing. The book was primarily addressed to young students but will be of interest to problem solvers in elementary geometry as well. Even geometers will find here new problems to inspire them.
- Titu Andreescu, Dorin Andrica, Paul Blaga, and Dan Bränzei
- Hardcover: 580 pages
- Publisher: XYZ Press (2016)
- Language: English
- ISBN-10: 0996874518
- ISBN-13: 978-0996874519