Fig. 19.
Let A B C D ([Fig. 19.]) be the given figure.
Join any two of its opposite angles by the line B C.
Draw first the triangle A B C. ([Problem VI.])
And then, from the base B C, the two lines B D, C D, to their vanishing-points, which will complete the figure. It is unnecessary to give a diagram of the construction, which is merely that of [Fig. 18.] duplicated; another triangle being drawn on the line A C or B C.
[COROLLARY.]
It is evident that by this application of [Problem VI.] any given rectilinear figure whatever in a horizontal plane may be drawn, since any such figure may be divided into a number of triangles, and the triangles then drawn in succession.
More convenient methods may, however, be generally [p30] ]found, according to the form of the figure required, by the use of succeeding problems; and for the quadrilateral figure which occurs most frequently in practice, namely, the square, the following construction is more convenient than that used in the present problem.