Let p, Fig. 4., be the given point.

Let its direct distance be d t; its lateral distance to the left, d c; and vertical distance beneath the eye of the observer, c P.

Fig. 4.

[Let g h be the Sight-line, s the Sight-point, and T the Station-point.]2

1 More accurately, To fix on the plane of the picture the apparent position of a point given in actual position. In the headings of all the following problems the words on the plane of the picture are to be understood after the words to draw. The plane of the picture means a surface extended indefinitely in the direction of the picture.

2The sentence within brackets will not be repeated in succeeding statements of problems. It is always to be understood.

It is required to fix on the plane of the picture the position of the point P.

Arrange the three distances of the object on your paper, as in Fig. 4.1

Fig. 5.

Join c T, cutting G H in Q.

From Q let fall the vertical line Q p'.

1 In order to be able to do this, you must assume the distances to be small; as in the case of some object on the table: how-large distances are to be treated you will see presently; the mathematical principle, being the same for all, is best illustrated first on a small scale. Suppose, for instance, P to be the corner of a book on the table, seven inches below the eye, five inches to the left of it, and a foot and a half in advance of it, and that you mean to hold your finished drawing at six inches from the eye; then T s will be six inches, t d a foot and a half, D c five inches, and c P seven.

Join p T, cutting Q P in p'.

p' is the point required.

If the point p is above the eye of the observer instead of below it, c p is to be measured upwards from c, and Q p' drawn upwards from Q. The construction will be as in Fig. 5.

And if the point P is to the right instead of the left of the observer, d c is to be measured to the right instead of the left.

The figures 4. and 5., looked at in a mirror, will show the construction of each, on that supposition.

Now read very carefully the examples and notes to this problem in Appendix I. (page 277.). I have put them in the Appendix in order to keep the sequence of following problems more clearly traceable here in the text; but you must read the first Appendix before going on.