Publisher's Synopsis
Excerpt from Analytic Geometry of Space
In this book, which is planned for an introductory course, the first eight chapters include the subjects usually treated in rectangular coordinates. They presuppose as much knowledge of algebra, geometry, and trigonometry as is contained in the major requirement of the College Entrance Examination Board, and as much plane analytic geometry as is contained in the better elementary textbooks. In this portion, proofs of theorems from more advanced subjects in algebra are supplied as needed. Among the features of this part are the development of linear systems of planes, plane coordinates, the concept of infinity, the treatment of imaginaries, and the distinction between centers and vertices of quadric surfaces. The study of this portion can be regarded as a first course, not demanding more than thirty or forty lessons.
In Chapter IX tetrahedral coordinates are introduced by means of linear transformations, under which various invariant properties are established. These coordinates are used throughout the next three chapters. The notation is so chosen that no ambiguity can arise between tetrahedral and rectangular systems. The selection of subject matter is such as to be of greatest service for further study of algebraic geometry.
In Chapter XIII a more advanced knowledge of plane analytic geometry is presupposed, but the part involving Plucker's numbers may be omitted without disturbing the continuity of the subject. In the last chapter extensive use is made of the calculus, including the use of partial differentiation and of the element of arc.
The second part will require about fifty lessons.
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