All horizontal lines which are at right angles to the picture plane are drawn to the point of sight.
All horizontals which are at 45° to the picture plane are drawn to the point of distance.
All horizontals forming any other angles but the above are drawn to some other points on the horizontal line.
Lines which incline upwards have their vanishing points above the horizon, and those which incline downwards, below it. In both cases they are on the vertical which passes through the vanishing point of their ground-plan or horizontal projections.
The farther a point is removed from the picture plane the nearer does it appear to approach the horizon, so long as it is viewed from the same position.
Horizontals in the same plane which are drawn to the same point on the horizon are perspectively parallel to each other.
In the foregoing book we have explained the theory or science of perspective; we now have to make use of our knowledge and to apply it to the drawing of figures and the various objects that we wish to depict.
The first of these will be a square with two of its sides parallel to the picture plane and the other two at right angles to it, and which we call
From a given point on the base line of the picture draw a line at right angles to that base. Let _P_ be the given point on the base line _AB_, and _S_ the point of sight. We simply draw a line along the ground to the point of sight _S_, and this line will be at right angles to the base, as explained in Rule 5, and consequently angle _APS_ will be equal to angle _SPB_, although it does not look so here. This is our first difficulty, but one that we shall soon get over.
In like manner we can draw any number of lines at right angles to the base, or we may suppose the point _P_ to be placed at so many different positions, our only difficulty being to conceive these lines to be parallel to each other. See Rule 10.
From a given point on the base line draw a line at 45°, or half a right angle, to that base. Let _P_ be the given point. Draw a line from _P_ to the point of distance _D_ and this line _PD_ will be at an angle of 45°, or at the same angle as the diagonal of a square. See definitions.
Draw a square in parallel perspective on a given length on the base line. Let _ab_ be the given length. From its two extremities _a_ and _b_ draw _aS_ and _bS_ to the point of sight _S_. These two lines will be at right angles to the base (see Fig. 43). From _a_ draw diagonal _aD_ to point of distance _D_; this line will be 45° to base. At point _c_, where it cuts _bS_, draw _dc_ parallel to _ab_ and _abcd_ is the square required.