The line _AB_ being the base of the picture, it is at the same time a perspective line and a geometrical one, so that we can use it as a scale for measuring given lengths thereon, but should there not be enough room on it to measure the required number we draw a second line, _DC_, which we divide in the same proportion and proceed to divide _cf_. This geometrical figure gives, as it were, a bird's-eye view or ground-plan of the above.
Draw squares of given dimensions at given distances from the base line to the right or left of the vertical line, which passes through the point of sight.
Let _ab_ (Fig. 55) represent the base line of the picture divided into a certain number of feet; _HD_ the horizon, _VO_ the vertical. It is required to draw a square 3 feet wide, 2 feet to the right of the vertical, and 1 foot from the base.
First measure from _V_, 2 feet to _e_, which gives the distance from the vertical. Second, from _e_ measure 3 feet to _b_, which gives the width of the square; from _e_ and _b_ draw _eS_, _bS_, to point of sight. From either _e_ or _b_ measure 1 foot to the left, to _f_ or _f·_. Draw _fD_ to point of distance, which intersects _eS_ at _P_, and gives the required distance from base. Draw _Pg_ and _B_ parallel to the base, and we have the required square.
Square _A_ to the left of the vertical is 2½ feet wide, 1 foot from the vertical and 2 feet from the base, and is worked out in the same way.
_Note._--It is necessary to know how to work to scale, especially in architectural drawing, where it is indispensable, but in working out our propositions and figures it is not always desirable. A given length indicated by a line is generally sufficient for our requirements. To work out every problem to scale is not only tedious and mechanical, but wastes time, and also takes the mind of the student away from the reasoning out of the subject.
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.