he diagonals _Go_
draw lines from the vanishing point _V_ to base. These will give us the
outlines of the squares lying between them and also guiding points that
will enable us to draw as many more as we please. These again will give
us our measurements for the widths of the arches, &c., or between the
columns. Having fixed the height of wall or dado, we make use of _V_
point to draw the sides of the building, and by means of proportionate
measurement complete the rest, as in Fig. 128.

LXX

HOW TO DRAW LINES WHICH SHALL MEET AT A DISTANT POINT,
BY MEANS OF DIAGONALS

This is in a great measure a repetition of the foregoing figure, and
therefore needs no further explanation.

[Illustration: Fig. 133.]

I must, however, point out the importance of the point _G_. In angular
perspective it in a measure takes the place of the point of distance in
parallel perspective, since it is the vanishing point of diagonals at
45 deg drawn between parallels such as _AV_, _DV_, drawn to a vanishing
point _V_. The method of dividing line _AV_ into a number of parts equal
to _AB_, the side of the square, is also shown in a previous figure
(Fig. 120).

LXXI

HOW TO DIVIDE A SQUARE PLACED AT AN ANGLE INTO A GIVEN NUMBER
OF SMALL SQUARES

_ABCD_ is the given square, and only one vanishing point is accessible.
Let us divide it into sixteen small squares. Produce side _CD_ to base
at _E_. Divide _EA_ into four equal parts. From each division draw lines
to vanishing point _V_. Draw diagonals _BD_ and _AC_, and produce the
latter till it cuts the horizon in _G_. Draw the three cross-lines
through the intersections made by the diagonals and the lines drawn to
_V_, and thus divide the square into sixteen.

[Illustration: Fig. 134.]

This is to some extent the reverse of the previous problem. It also
shows how the long vanishing point can be dispensed with, and the
perspective drawing brought within the picture.

LXXII

FURTHER EXAMPLE OF HOW TO DIVIDE A GIVEN OBLIQUE SQUARE
INTO A GIVEN NUMBER OF EQUAL SQUARES, SAY TWENTY-FIVE

Having drawn the square _ABCD_, which is enclosed, as will be seen, in a
dotted square in parallel perspective, I divide the line _EA_ into five
equal parts instead of four (Fig. 135), and have made use of the device
for that purpose by measuring off the required number on line _EF_, &c.
Fig. 136 is introduced here simply to show that the square can be
divided into any number o