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vanishing, system and lines

NOTE: The vanishing point for the base of the isosceles triangle always becomes the measure point for the side of the isosceles triangle which does not lie in HPP.

96. All lines belonging to the same system will have the same measure point. Thus, if the line be, which is parallel to ad, be continued to meet HPP, and an isosceles triangle (cku) con strutted on it, as indicated by the dotted lines in the figure, the (Or) of this isosceles triangle will be parallel to de, and its vanishing point will be coincident with v".

97. There is a constant relation between the vanishing point of a system of lines and the measure point for that system. Therefore, if the vanishing point of a system of lines is known, its measure point may be found without reference to a diagram, as will be explained.

In constructing the vanishing points vad and ved, fh was drawn parallel to ad, fy was drawn parallel to ed, and since hg is coinci dent with HIT, the two triangles ead and fhy must be similar.

As ae was made equal to ad in the small triangle, hf must be equal to by in the large triangle ; and consequently ed, which is as far from vad as g is from h, must be as far from v" as the point f is from the point h.

If the student will refer back to Figs. 8, 9, and 9a, he will see that the -point is bears a similar relation in Fig. 26 to that of the point mH in Figs. 8, 9, and 9m- and that the point Is in Fig. 26 is really the horizontal projection of the vanishing point (See also 32.) Therefore, as ed is as far from ed as the point Is is from the point f, we may make the following statement, which will hold for all systems of horizontal lines.

98. The measure point for any system of horizontal lines will be found on VII as far from the vanishing point of the system as the horizontal projection of that vanishing point is distant from the hori zontal projection of the station point.