the mind of the student away from the
reasoning out of the subject.

XVI

HOW TO DRAW PAVEMENTS, &C.

Divide a vanishing line into parts varying in length. Let _BS'_ be the
vanishing line: divide it into 4 long and 3 short spaces; then proceed
as in the previous figure. If we draw horizontals through the points
thus obtained and from these raise verticals, we form, as it were, the
interior of a building in which we can place pillars and other objects.

[Illustration: Fig. 56.]

Or we can simply draw the plan of the pavement as in this figure.

[Illustration: Fig. 57.]

[Illustration: Fig. 58.]

And then put it into perspective.

XVII

OF SQUARES PLACED VERTICALLY AND AT DIFFERENT HEIGHTS,
OR THE CUBE IN PARALLEL PERSPECTIVE

On a given square raise a cube.

[Illustration: Fig. 59.]

_ABCD_ is the given square; from _A_ and _B_ raise verticals _AE_, _BF_,
equal to _AB_; join _EF_. Draw _ES_, _FS_, to point of sight; from _C_
and _D_ raise verticals _CG_, _DH_, till they meet vanishing lines _ES_,
_FS_, in _G_ and _H_, and the cube is complete.

XVIII

THE TRANSPOSED DISTANCE

The transposed distance is a point _D'_ on the vertical _VD'_, at
exactly the same distance from the point of sight as is the point of
distance on the horizontal line.

It will be seen by examining this figure that the diagonals of the
squares in a vertical position are drawn to this vertical
distance-point, thus saving the necessity of taking the measurements
first on the base line, as at _CB_, which in the case of distant
objects, such as the farthest window, would be very inconvenient. Note
that the windows at _K_ are twice as high as they are wide. Of course
these or any other objects could be made of any proportion.

[Illustration: Fig. 60.]

XIX

THE FRONT VIEW OF THE SQUARE AND OF THE PROPORTIONS OF FIGURES
AT DIFFERENT HEIGHTS

According to Rule 4, all lines situated in a plane parallel to the
picture plane diminish in length as they become more distant, but remain
in the same proportions each to each as the original lines; as squares
or any other figures retain the same form. Take the two squares _ABCD_,
_abcd_ (Fig. 61), one inside the other; although moved back from square
_EFGH_ they retain the same form. So in dealing with figures of
different heights, such as statuary or ornament in a building, if
actually equal in size, so must we represent them.

[Illustrati