[p 29 ] PROBLEM VII. TO DRAW ANY RECTILINEAR QUADRILATERAL FIGURE, GIVEN IN POSITION AND MAGNITUDE, IN A HORIZONTAL PLANE .

[Geometric diagram]
Fig.19.

Let ABCD (Fig.19.) be the given figure.

Join any two of its opposite angles by the line BC.

Draw first the triangle ABC. (ProblemVI.)

And then, from the base BC, the two lines BD, CD, 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 AC or BC.

COROLLARY.

It is evident that by this application of ProblemVI. 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.