S_,
and are therefore at right angles to the base _AB_. _AD_ being drawn to
_D_ (the distance-point), is at an angle of 45 deg to the base _AB_, and
_AC_ is therefore the diagonal of a square. The line 1C is made
parallel to _AB_, consequently A1CB is a square in perspective. The
line _BC_, therefore, being one side of that square, is equal to _AB_,
another side of it. So that to measure a length on a line drawn to the
point of sight, such as _BS_, we set out the length required, say _BA_,
on the base-line, then from _A_ draw a line to the point of distance,
and where it cuts _BS_ at _C_ is the length required. This can be
repeated any number of times, say five, so that in this figure _BE_
is five times the length of _AB_.

[Illustration: Fig. 31.]

RULE 7

All horizontals forming any other angles but the above are drawn to some
other points on the horizontal line. If the angle is greater than half a
right angle (Fig. 32), as _EBG_, the point is within the point of
distance, as at _V"_. If it is less, as _ABV""_, then it is beyond the
point of distance, and consequently farther from the point of sight.

[Illustration: Fig. 32.]

In Fig. 32, the dotted line _BD_, drawn to the point of distance _D_,
is at an angle of 45 deg to the base _AG_. It will be seen that the line
_BV"_ is at a greater angle to the base than _BD_; it is therefore drawn
to a point _V"_, within the point of distance and nearer to the point of
sight _S_. On the other hand, the line _BV""_ is at a more acute angle,
and is therefore drawn to a point some way beyond the other distance
point.

_Note._--When this vanishing point is a long way outside the picture,
the architects make use of a centrolinead, and the painters fix a long
string at the required point, and get their perspective lines by that
means, which is very inconvenient. But I will show you later on how you
can dispense with this trouble by a very simple means, with equally
correct results.

RULE 8

Lines which incline upwards have their vanishing points above the
horizontal line, and those which incline downwards, below it. In both
cases they are on the vertical which passes through the vanishing point
(_S_) of their horizontal projections.

[Illustration: Fig. 33.]

This rule is useful in drawing steps, or roads going uphill and
downhill.

[Illustration: Fig. 34.]

RULE 9

The farther a point is removed from the picture plane the nearer does
its perspectiv