Excerpt from Plane Analytic Geometry: With Introductory Chapters on the Differential Calculus
Analytic Geometry, if properly taught, is a difficult subject, and concentration on a few of its important principles is necessary if mastery is the aim. I have cut out, or put in small type (or in late chapters which may be easily omitted) what seems to me less essential. With very few exceptions I have used methods so straightforward that they can serve as models for the student in his own work. Neither the notation of determinants nor (except in Chapters XII, XIII) that of the calculus has been used, since a difficult new subject is only obscured by a notation which has not already become thoroughly familiar, and I am old-fashioned enough to believe in handling one difficulty at a time.
It need hardly be said that in teaching it may not be advisable to follow everywhere the order of the book, which is meant to serve not merely as a text-book from day to day but as a permanent book of reference. At Harvard, where most of the work here given is taken up in the Freshman class, a considerable part of Chapter X and the whole of Chapter XI are postponed till the Sophomore year, thus making room for Chapters XII and XIII. This introduction of a little calculus, not hashed fine but put squarely as a new subject, during the last six weeks of the Freshman year has been most successful. The parts of the calculus thus introduced are easier than the parts of analytic geometry they replace, and, to the average student, more interesting; and the student who has got somewhat beyond his depth has a chance for a new start.
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