Book Summary: The front cover shows the figure from page 101 about the geometric proof of the law a(bc) = b(ac). This line of reasoning does not presuppose Pappus' theorem, instead we use properties of circles in a Pythagorean plane. A decade long experience of teaching the course Fundamental of Geometry at the University of North Carolina at Charlotte, many notes for exercises, reading and research are the bases for this bulky work. Retired I could find the time and leisure to prepare several volumes. My heartfelt thanks go to everyone involved, this means famous authors as well as my former students. The present second volume starts with Euclidean geometry, and the text gets a more educational and even more elementary flavour. Here I start with Thales theorem about the angle in a semicircle, and continue with Euclid's related theorems about angles in a circle. The most simple parts of the Euclidean geometry are given in detail, as well as the later parts about similarity, and finally area in Euclidean geometry with the theorem of Pythagoras and trigonometry, and the measurement of the circle. Too, the lens equation from geometrical optics is treated. In several sections is recalled the strictly modern view of the first volume, beginning with Hilbert's axioms from the Foundations of Geometry. After some discussion of logic and axioms in general, we go on with a short section about incidence geometries in two dimensions. The theorems from neutral geometry which have been proved in the first volume and are needed again, are cited. The relation of analytic and synthetic geometry is treated on Hilbert's rigorous account. Authors Bio: Franz Rothe has received his doctoral degree in mathematics from the university of T ̈ubingen, Germany. He has been professor at the University of North Carolina at Charlotte, and has published about 40 articles and a lecture note in mathematics, and two further books on number theory, modern algebra, and graph theory. Dr. Rothe is retired since several years, and is now emeritus professor

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