The Elements of Perspective / arranged for the use of schools and intended to be read in connection with the first three books of Euclid :: [p 10 ] PROBLEM I. TO FIX THE POSITION OF A GIVEN POINT. [Footnote 8 ]

[p 10 ] PROBLEM I. TO FIX THE POSITION OF A GIVEN POINT. [Footnote 8 ]

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

[Geometric diagram]
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.][Footnote 9]

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

[p11]
Arrange the three distances of the object on your paper, as in Fig.4.[Footnote 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.

[Geometric diagram]
Fig.5.

And if the point P is to the right instead of the left of the [p12] 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 AppendixI. (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.

[Footnote 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.] Return to text

[Footnote 9: The sentence within brackets will not be repeated in succeeding statements of problems. It is always to be understood.] Return to text

[Footnote 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.] Return to text

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