The First Figure.
Explication of the Lines of the Plan and Horizon, and of the Points of the Eye and of the Distance.
That you may the better understand the Principles of Perspective, here is presented to your View a Temple, on the inner Wall of which, amongst other things, one would paint something in Perspective. The Geometrical Plan of this Church is A, the Geometrical Elevation, or Upright, lengthwise is B, breadthwise is C. In A is the Place from whence a Man beholds the Line DE, which is the Plan of the Wall that is to be painted: In B the same Man, from the same Distance, looks upon the Line FG, that represents the Elevation of the Wall. In Fig. C, the Man is supposed to stand opposite to the said Wall; and this Figure contains, in Little, the very same Proportions of Measures transferr’d from the real Wall.
The first Line therefore HI is call’d the Ground-line, or Line of the Plan, at which the Edifice begins, and on which it stands. The second Line NON, parallel to the former, is call’d the Horizontal Line, wherein is plac’d O the Point of the Eye, and N the Point of the Distance. Two Points of Distance are here laid down, that you may make use of which you please; for that on one Side only is sufficient for the fore-short’ning Figures in Perspective: Neither can any Optick Delineation, or Perspective, be described, without first making two Parallels; one of the Plan, or Ground-line, the other of the Horizon; marking, in the Line of the Horizon, the Point of the Eye, or Sight, and the Point of Distance. It was thought besides expedient to put one and the same Thing into three Schemes or Designs, to let you see, that the Place, from which the Figure C is to be look’d upon, is the Point N, one of the right Lines NO, which must be conceived as fixt at right Angles into O; the Distance ON being the same as that between A and DE in the Plan, or between B and GF in the Upright.
In Pictures taking up a great deal of Room, the Point of Sight ought to be made in the middle of the Horizontal Line; and where the Height of the Picture happens to be greater than the Breadth, the Distance NO must be made equal to the Height. If the Breadth of the Picture exceed the Height, the Distance NO must be made equal to the Breadth: For so will the Extent of the Picture be the better comprehended, or receiv’d, at one View. And altho’ the same Distance may seem to be used in a different manner in the Plan A, and in the Elevation B, from what it is in C; nevertheless the Sections of the visual Rays, with the Wall of the Plan A, and of the Elevation B, have a perfect Correspondence with the Sections of those of the Figure C.
Now, if to the Spectator in A and B, we would have the farthest Part of the Work seem to recede from the Lines DE and GF, as much as the Square P does, whose Elevation is Q; draw from the Points A and B, the visual Rays to the extreme Points of the Square P and Q; noting the Sections they make with the Walls DE and GF; which by some is call’d the Veil, Transparent Medium, Section, Cloth, or Table: and you’ll find RS equal to TV, XZ equal to YK; and so of the rest.
Fig. II.