n: Fig. 50.]

XII

GEOMETRICAL AND PERSPECTIVE FIGURES CONTRASTED

As at first there may be a little difficulty in realizing the
resemblance between geometrical and perspective figures, and also about
certain expressions we make use of, such as horizontals, perpendiculars,
parallels, &c., which look quite different in perspective, I will here
make a note of them and also place side by side the two views of the
same figures.

[Illustration: Fig. 51 A. The geometrical view.]

[Illustration: Fig. 51 B. The perspective view.]

[Illustration: Fig. 51 C. A geometrical square.]

[Illustration: Fig. 51 D. A perspective square.]

[Illustration: Fig. 51 E. Geometrical parallels.]

[Illustration: Fig. 51 F. Perspective parallels.]

[Illustration: Fig. 51 G. Geometrical perpendicular.]

[Illustration: Fig. 51 H. Perspective perpendicular.]

[Illustration: Fig. 51 I. Geometrical equal lines.]

[Illustration: Fig. 51 J. Perspective equal lines.]

[Illustration: Fig. 51 K. A geometrical circle.]

[Illustration: Fig. 51 L. A perspective circle.]

XIII

OF CERTAIN TERMS MADE USE OF IN PERSPECTIVE

Of course when we speak of +Perpendiculars+ we do not mean verticals
only, but straight lines at right angles to other lines in any position.
Also in speaking of +lines+ a right or +straight line+ is to be
understood; or when we speak of +horizontals+ we mean all straight lines
that are parallel to the perspective plane, such as those on Fig. 52, no
matter what direction they take so long as they are level. They are not
to be confused with the horizon or horizontal-line.

[Illustration: Fig. 52. Horizontals.]

There are one or two other terms used in perspective which are not
satisfactory because they are confusing, such as vanishing lines and
vanishing points. The French term, _fuyante_ or _lignes fuyantes_, or
going-away lines, is more expressive; and _point de fuite_, instead of
vanishing point, is much better. I have occasionally called the former
retreating lines, but the simple meaning is, lines that are not parallel
to the picture plane; but a vanishing line implies a line that
disappears, and a vanishing point implies a point that gradually goes
out of sight. Still, it is difficult to alter terms that custom has
endorsed. All we can do is to use as few of them as possible.

XIV

HOW TO MEASURE VANISHING OR RECEDING LINES

Divide a vanishing line which is at