Ringenberg L., Presser R. Geometry 1971

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Geometry is one of a series of five mathematics textbooks for junior and senior high schools. It is designed for a one-year course for students with a background of informal geometry and elementary algebra such as that included in Mathematics I, Mathematics II, and Algebra of this series. In its formal development of Euclidean geometry, this textbook features an integrated treatment of plane and solid geometry with an early introduction of coordinates. Coordinates on a line, in a plane, and in space relate numbers and points. They are used to gain knowledge of geometrical figures and to simplify the develop-ment of formal geometry. Students use their knowledge of elementary algebra throughout the book to help them learn geometry. In doing this they maintain and strengthen their competence in algebra. The postulates in this book form the basis of a rigorous, yet plausible, development of a first course in formal Euclidean geometry. In some instances, statements that are proved in more advanced treatments are accepted as postulates here. This has been done to decrease tho length of the development and to make the develop-ment appropriate for high school students. Geometry is an important subject because it is practical and useful and at the same time abstract and theoretical. There arc two main objectives in this geometry textbook. One is to help students learn a body of important facts about geometrical figures. Spherical geometry is the three-dimensional study of geometry on the surface of a sphere. It is the spherical equivalent of two-dimensional planar geometry, the study of geometry on the surface of a plane. A real-life approximation of a sphere is the planet Earth - not its interior, but just its surface