A Treatise on Special Or Elementary Geometry: University Edition, Including an Elementary, and Also, in Part III. , a Higher Course, in Plane, Solid, and Spherical Geometry, and Plane and Spherical Trigonometry, with the Necessary Tables (Classic Reprint)

Excerpt from A Treatise on Special or Elementary Geometry: University Edition, Including an Elementary, and Also, in Part III., A Higher Course, in Plane, Solid, and Spherical Geometry, and Plane and Spherical Trigonometry, With the Necessary Tables

The order of arrangement in Plane Geometry (chap. L), is thought to be simple, philosophical, and practical. A glance at the table of contents will show what it is. This arrangement secures the very important result, that each section presents some particular method of proof, and holds the student to it, until it is familiar. True, it requires that a larger number of propositions be demonstrated from fundamental truths; but who will consider this an objection?

To such as consider it the sole province of geometrical demonstra tion, to convince the mind of the truth of a proposition, not a few theorems in these and ordinary pages must seem quite superfluous. To them, Pr0p. I., page 121, may afford some merriment. But those who, with myself, consider Geometry as a branch of practical logic, the aim of which is to detect and state the steps which actually lie be tween premise and conclusion, will see the propriety of such demonstra tions; and for each individual of the other class, a separate treatise will be needed, since no two minds will intuitively grant exactly the same propositions.

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