Plane and Solid Analytic Geometry
An Elementary Textbook (Classic Reprint)

Excerpt from Plane and Solid Analytic Geometry: An Elementary Textbook

The present work is intended as a text-book for classroom use, and not as an exhaustive treatise on the subject. This object has been kept constantly in mind in writing the book, and every subject has been treated from this point of view. A large part of the book was mimeographed and tested by use for several years in the author's classes in Harvard University.

The author has tried to meet the needs of a class which occupies from sixty to seventy recitation hours upon the subject, and it is thought that the book ought to be completed by the average class in that time. Necessarily some subjects which usually find a place in books on Analytic Geometry have been omitted; but it is thought that nothing has been omitted which has an important bearing on future mathematical study.

The conies have been treated from their ratio definition, and much space and time have been gained by not repeating proofs which are identical, or very similar, for the three forms of the conic. Analytic methods are used throughout the book, and the author has attempted to give proofs which are concise and easily understood by the average student, but, at the same time, mathematically rigorous. In this connection he would call attention to the proofs in oblique coordinates (Arts. 12, 28), which are usually given without reference to the directions of the lines, and, therefore, do not hold if the positions of the points are changed.

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