The Fifth Figure.
Plans of Squares, with their Elevations.
Besides what has been already said of the fore-short’ning of Squares in Perspective, it is convenient to observe, That the Foot of the first Square is here set within the Line of the Plan, as much as the Space BA optically contracted; because the Line BD has the Distance BA from the Visual AO: And in like manner, the second Square is distant from the Line of the Plan the Space EA; and so for the rest.
I would have you observe in all these Squares, That by the Length I always understand part of the visual Lines, and by the Breadth those parallel to the Ground-line; which in the first Square are drawn from the Points in which the Lines BD, CD, tending to the Point of Distance, intersect the Visual AO.
Under the Plans of these Squares are described three others just like them, which are easily converted into three Bases, by erecting, at pleasure, the two first Perpendiculars of equal Height, and thence drawing two Visuals to the Point of Sight O, which also bound the rest, as in the Figure. Observe also, That the Geometrical Height of every thing is to be set perpendicularly from the Ground-line, or Line of the Plan, as the Geometrical Length and Breadth are also placed on the same Line.
The three other Bases below are form’d without the Help of Occult Lines, by making use only of the Heights and Breadths of the Angles, taken from the Perspective Plan and Upright. By Height I understand the Distance of each Angle, or Corner, from the Ground-Line; By Breadth, the Distance of an Angle, or Corner, from any Line perpendicular to the Ground-line; provided these Lines have always the same Place in respect of the Bases, as they have in respect of the Perspective Plan and Upright. And as, by the Help of two Compasses, the Height FG, and the Breadth HI determine the Corner of the first Base; so, in like manner, are found the Corners of the other Bases.
Fig. vi.