The book introduces the reasoning used to derive information about geometric objects. The development uses 3 basic steps and is repeated in 4 settings. First, the essential assumptions or axioms are identified from geometric activity like drawing on a page; next first-level properties are derived from the axioms; and finally 10 key theorems are proved based on the first two steps. Thus, inductive logic establishes a foundation and deductive logic hammers out the consequences. These steps are carried out for Plane, Solid, Spherical, and Hyperbolic Geometries. The first two Geometries, termed...