Excerpt from Treatise on the Principles and Applications of Analytic Geometry
The following treatise, designed as a text-book upon Analytic Geometry, has been written with the most practical ends in view, and is intended to meet the wants of classes in Scientific and Technological Schools, Colleges and Universities. While the needs of the student of Mechanics, Astronomy and Civil Engineering have never been forgotten, it has been found possible to so select the material and to put it in such shape as to adapt the work to the student who pursues the subject merely as a part of a liberal education.
The prime difficulty the ordinary student meets in the study of analytic geometry is in the use of variables, since with these he has had no previous acquaintance.
No pains has been spared to make the introduction to their use clear and free from all other complexities. To this end a thorough knowledge of co-ordinates has been first secured by the study of the relations of points, the transformation of co-ordinates, etc.
Again, the entire subject of the general relation of constant and variable quantities is postponed to Chapter V, at which point the student will have attained a sufficient acquaintance with the processes and notation peculiar to analytic geometry to grasp the ideas advanced and use them in after work.
To secure an accurate knowledge of the meaning of the general equations, it is essential that the student should solve numerous numerical examples. They should be illustrations, and of such simple character as to be readily solved by any one who understands the preceding text.
Such are the examples interspersed through the work, which should in no case be omitted. Indeed, if the class is numerous, the teacher is advised to largely increase the number of examples as class-room work by substituting other numbers than those used, and giving each example to a sufficient number of different computers to ensure correct results.
The Exercises are much more difficult than the examples, and have two objects in view: first, as original work for the more ambitious students; and secondly, as results to be referred to in the students subsequent studies. They may be omitted by the ordinary student.
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