In adding another text-book on analytic geometry to the large list of such books now available, the authors feel that a statement of the reasons for this one is desirable. In compiling the work they have endeavored to keep constantly in view the needs of that large class of students in our colleges and technical schools who, though in a way sympathetic toward mathematical study, are yet lacking in that quick appreciation of the mathematical point of view which is a characteristic of the so-called mathematical mind. The assimilation of new ideas, or even of new combinations and applications of ideas already familiar, in which the study of analytic geometry especially abounds, is not easy even for the trained mind, and for the student approaching the subject for the first time is the source of most of his difficulties. The attempt here is to make this approach by easy gradations so that the student may not lose himself on the way, but may feel sure of his ground as he advances. To try to gain this end by the lack of rigorous demonstration would be to lose sight of an important object of such study, which, rightly viewed, is to assist the student to an acquaintance with correct principles of mathematical reasoning and the accompanying scientific attitude of mind. The aim has been therefore to preserve mathematical rigor throughout.