Terms Of Angles

The relation of the lines to each other, the manner in which they are joined together, and their comparative angles, all have special terms and meanings. Thus, referring to the isometric cube, in Fig. 145, the angle formed at the center by the lines (B, E) is different from the angle formed at the margin by the lines (E, F). The angle formed by B, E is called an exterior angle; and that formed by E, F is an interior angle. If you will draw a line (G) from the center to the circle line, so it intersects it at C, the lines B, D, G form an equilateral or isosceles triangle; if you draw a chord (A) from C to C, the lines H, E, F will form an obtuse triangle, and B, F, H a right-angled triangle.

Circles And Curves

Circles, and, in fact, all forms of curved work, are the most difficult for beginners. The simplest figure is the circle, which, if it represents a raised surface, is provided with a heavy line on the lower right-hand side, as in Fig. 146; but the proper artistic expression is shown in Fig. 147, in which the lower right-hand side is shaded in rings running only a part of the way around, gradually diminishing in length, and spaced farther and farther apart as you approach the center, thus giving the appearance of a sphere.

Irregular Curves

But the irregular curves require the most care to form properly. Let us try first the elliptical curve (Fig. 148). The proper thing is, first, to draw a line (A), which is called the "major axis." On this axis we mark for our guidance two points (B, B). With the dividers find a point (C) exactly midway, and draw a cross line (D). This is called the "minor axis." If we choose to do so we may indicate two points (E, E) on the minor axis, which, in this case, for convenience, are so spaced that the distance along the major axis, between B, B, is twice the length across the minor axis (D), along E, E. Now find one-quarter of the distance from B to C, as at F, and with a compass pencil make a half circle (G). If, now, you will set the compass point on the center mark (C), and the pencil point of the compass on B, and measure along the minor axis (D) on both sides of the major axis, you will make two points, as at H. These points are your centers for scribing the long sides of the ellipse. Before proceeding to strike the curved lines (J), draw a diagonal line (K) from H to each marking point (F). Do this on both sides of the major axis, and produce these lines so they cross the curved lines (G). When you ink in your ellipse do not allow the circle pen to cross the lines (K), and you will have a mechanical ellipse.

Ellipses And Ovals

It is not necessary to measure the centering points (F) at certain specified distances from the intersection of the horizontal and vertical lines. We may take any point along the major axis, as shown, for instance, in Fig. 149. Let B be this point, taken at random. Then describe the half circle (C). We may, also, arbitrarily, take any point, as, for instance, D on the minor axis E, and by drawing the diagonal lines (F) we find marks on the circle (C), which are the meeting lines for the large curve (H), with the small curve (C). In this case we have formed an ovate or an oval form. Experience will soon make perfect in following out these directions.