Let _P_, Fig. 4., be the given point.
[Illustration: Fig. 4.]
Let its direct distance be _DT_; its lateral distance to the left, _DC_;
and vertical distance _beneath_ the eye of the observer, _CP_.
[Let _GH_ be the Sight-line, _S_ the Sight-point, and _T_ the
Station-point.][9]
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.[10]
Join _CT_, cutting _GH_ in _Q_.
From _Q_ let fall the vertical line _QP′_.
Join _PT_, cutting _QP_ in _P′_.
_P′_ is the point required.
If the point _P_ is _above_ the eye of the observer instead of below it,
_CP_ is to be measured upwards from _C_, and _QP′_ drawn upwards from
_Q_. The construction will be as in Fig. 5.
[Illustration: Fig. 5.]
And if the point _P_ is to the right instead of the left of the
observer, _DC_ 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 69). 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.
[8] 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.
[9] The sentence within brackets will not be repeated in succeeding
statements of problems. It is always to be understood.
[10] 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 _TS_ will be six inches, _TD_ a foot
and a half, _DC_ five inches, and _CP_ seven.