Perpendicular and Vertical.—A few words now as to terms. The boy is often confused in determining the difference between perpendicular and vertical. There is a pronounced difference. Vertical means up and down. It is on a line in the direction a ball takes when it falls straight toward the center of the earth. The word perpendicular, as usually employed in astronomy, means the same thing, but in geometry, or in drafting, or in its use in the arts it means that a perpendicular line is at right angles to some other line. Suppose you put a square upon a roof so that one leg of the square extends up and down on the roof, and the other leg projects outwardly from the roof. In this case the projecting leg is perpendicular to the roof. Never use the word vertical in this connection.
Signs to Indicate Measurements.—The small circle (°) is always used to designate degree. Thus 10° means ten degrees.
Feet are indicated by the single mark '; and two closely allied marks " are for inches. Thus five feet ten inches should be written 5' 10". A large cross (×) indicates the word "by," and in expressing the term six feet by three feet two inches, it should be written 6' × 3'2".
The foregoing figures give some of the fundamentals necessary to be acquired, and it may be said that if the boy will learn the principles involved in the drawings he will have no difficulty in producing intelligible work; but as this is not a treatise on drawing we cannot go into the more refined phases of the subject.
Definitions.—The following figures show the various geometrical forms and their definitions:
151. Abscissa.—The point in a curve, A, which is referred to by certain lines, such as B, which extend out from an axis, X, or the ordinate line Z.
152. Angle.—The inclosed space near the point where two lines meet.
153. Apothegm.—The perpendicular line A from the center to one side of a regular polygon. It represents the radial line of a polygon the same as the radius represents half the diameter of a circle.