Excerpt from The Elements of Geometry
In the revision of the author's work on Plane and Solid Geometry, many important improvements have been effected.
With a class just commencing the study of Geometry, too much emphasis cannot be laid on the form in which an oral or written demonstration should be presented.
The beginner requires a certain amount of practice before he can acquire the art of putting a proof in a clear and logical form.
To give this drill, the author has, through the whole of Book I., placed directly after each step in the proof the full statement of the reason, in smaller type, enclosed in brackets.
But too much assistance of this nature is open to serious objections, as it has a tendency to make the pupil a mere automaton, and confirm him in indolent habits of study. It has seemed advisable, therefore, in Books II. to V., inclusive, to give only the number of the section where the required authority is to be found.
The above plan has been submitted to a large number of representative teachers, and in nearly every case has met with the most unqualified approval.
In the Solid Geometry, references are given in full in the first sixteen propositions of Book VI., and by section numbers only through the remainder of the work. On pages ix, x, and xi of the Introduction will be found a few propositions put in a form which is recommended for blackboard work.
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