The drawing also shows that the edges appear of unequal length and make unequal angles with a horizontal line and illus trates the following rule : Rule 8. When two sides of a square retreat at unequal angles, the one which is more nearly parallel to the picture plane (the slate) appears the longer and more nearly horizontal.
Exercise 5. The Appearance of Equal Spaces on Any Line.
Cut from paper a square of three inches and draw its diagonals. Place this square horizontally in the.middle of the back of the table; with its edges parallel to those of the table, and then trace its appear ance and its diagonals upon the slate. (Fig. 8.) Note.—The diagonals of a square bisect each other and give the center of the square.
CompareThedistance from the nearer end,1, of either diagonal to the centerof the square, 2,with that from the centerof the squaretothe farther end of the diagonal, 3, for an illustration of the following rule: Rule 9. Equal distances on any retreating line appear unequal, the nearer of any two appearing the longer.
Exercise 6. The Triangle. Draw upon an equilateral tri angular tablet a line from an angle to the center of the opposite side. (This line is called an altitude.) Connect the triangular tablet with the square tablet, and place them on the table so that the base of the triangle is foreshortened, and its altitude is vertical. Trace the triangle and its altitude upon the slate. The tracing illustrates the fact that the nearer half of a re ceding line appears longer than the farther half (see Rule 9), and also the following rule: • Rule 10. The upper angle of a vertical isosceles or equilateral triangle, whose base is horizontal, appears in a vertical line erected at the perspective center of the base.
Exercise 7. The Prism. Connect two square tablets by a rod to represent a cube, and hold the object so that one tablet only is visible, and discover that it must appear its real shape, A, Fig. 10. This illustrates the following rule: Rule 11. When one face only of a prism is visible, it appears its veal shape.
' Place the cube represented by tablets (Fig. 10) in the middle of the back of the desk, and trace its appearance. First, when two
faces only cf the solid would be visible (B); and, second, when three faces would be seen (C). These tracings illustrate the fol lowing rule: Rule 12. When two or more faces.of a cube are seen, 'none of them can appear their real shapes.
Place the cubical form on the desk, with the tablets vertical, and one of them seen edgewise (D) and discover that the other tablet does not appear a straight line. This illustrates the follow ing rule: Rule 13. Only one end of a prism can appear a straight line at any one time.
Exercise 8. The Cylinder. Connect two circular tablets by a 2k-inch stick, to represent the cylinder. Bold the object so that one end only is visible, and see that it appears a circle (Fig. 11).
Place the object on the table, so that its axis is horizontal but appears a vertical line, and trace its appearance. The tracing illustrates the following rule: Rule 14. When an end and the curved surface of a cplin der are seenat the same time, the end -must appear an ellipse (Fig. 12).
Place the object horizontally, and so that one end appears a vertical line, and trace to illustrate the following rule: Rule 15. When one end of a cylinder appears a straight line, the other appears an ellipse. (Fig. 13.) .
Place the object upright on the table, and trace its ends and axis. Draw the long diameters of the ellipse, and discover that they are at right angles to the axis of the cylinder. This illustrates the following rule: Rule 16. The bases of a vertical cylinder appear horizontal ellipses. The nearer base always appears the narrower ellipse. (Fig. 14.) Place the object with its axis horizontal and at an angle, so that the surfaces of both tablets are visible. Trace the tablets and the rod, and then draw the long diameters of the ellipses, and discover that they are at right angles to the axis of the cylindrical form. The axes of the ellipses are inclined,. and the drawing illus trates the following rules: Rule 17. The bases of a cylinder appear ellipses, whose long diameters are at right angles to the axis of the cylinder, the nearer base appearing the nar rower ellipse.