Fifth. We must now find the focal points of the ellipse. If the line A on each side of the cross line B is divided into four parts, the outer marks E may be used for the foci, and will be the places where the point of the compass, or bow pen, is to be placed.
Sixth. Describe a circle F, so it passes through the mark C, and move the point of the compass to the center of the ellipse, at the star, and describe a circle line G, from the mark C to the line B. This will give a centering point H. Then draw a line I from H to E, and extend it through the circle F.
Seventh. If the point of the compass is now put[p. 107] at H, and the pencil or pen on the circle line F, the curve J can be drawn, so the latter curve and the curve F will thus merge perfectly at the line I.
The Focal Points.—The focal points can be selected at any arbitrary point, between C and the line B, and the point H may be moved closer to or farther away from the line A, and you will succeed in making the ellipse correct, if you observe one thing, namely: The line I, which must always run from H to E, and intersects the circle F, is the starting or the ending point for the small curve F or the large circle J.
Isometric and Perspective.—A figure may be drawn so as to show an isometric or a perspective view. Thus, a cube can be drawn so as to make an isometric figure, as in [Fig. 115], where the three sides are equal to each other.
Isometric means a method of drawing any object in such a manner that the height, length and[p. 108] breadth may be shown in the proportion they really bear to each other. [Fig. 115] has the sides not only equal to each other, in appearance to the eye, but they have the same outlines and angles.
Contrast this figure with [Figs. 116] and [117]. In [Fig. 116] two of the sides are equal in angles and outline; and in [Fig. 117] each side has a different outline, and different angles. Nevertheless, all the cubes are, in reality, of the same dimension.
The Protractor.—This is a most useful tool for the draughtsman. It enables the user to readily find any angle. [Fig. 118] shows an approved form of the tool for this purpose.