Deformatio circulorum.
Ut stylobatis imponere liceat columnas cum suis basibus & capitellis, docendus est modus qui servandus est in projectione optica circulorum, tum singularium, tum duplicium aut multiplicium circa idem centrum.
Vestigium geometricum A constat quadrato in quatuor partes æquales diviso, cui circulus inscribitur, additis diagonalibus: & ubi hæ secant circulum, fiunt rectæ parallelæ ad singula latera ipsius quadrati. Deinde quadratum cum omnibus divisionibus opticè imminuitur; ac tum per quatuor puncta ubi tres lineæ rectæ se intersecant, tum per quatuor extrema reliquarum duarum diametrorum circuli, ducetur cum venustate circumferentia circuli B. Si addere velimus alium circulum, vestigio geometrico C inscribetur aliud quadratum; indeque habebitur optica delineatio duplicis circuli D. Inter hos duos quomodo liceat describere tertium, per octo sectiones quadratorum, ostendunt figuræ E & F. Uno verbo, circuli describuntur per quadrata, adhibendo sectiones visualium cum parallelis ad lineam plani; ac nullum est punctum in quadratis & circulis A, C, E, cui per sectiones illas nequeat inveniri punctum correspondens in quadratis & circulis B, D, F. Nihilominus ubi opus habeas pluribus circulis, autor tibi sum ne multiplices quadrata, plus confusionis allatura tibi quam adjumenti.
The Fourteenth Figure.
Circles in Perspective.
That upon Pedestals you may be able to place Columns with their Bases and Capitals, it is requisite you should know the Manner of putting Circles into Perspective; whether single, double, or many concentrick.
The Geometrical Plan A consists of a Square with a Circle inscrib’d, whose Diameters divide it into four equal Parts; and the Diagonals being drawn where they intersect the Circle, continue Lines parallel to each Side of the Square. The Square, with all its Divisions, being put in Perspective; by the four extreme Points of the Diameters, and by those of the Intersection of the Diagonals, you neatly trace by hand the Circumference B. If you would add another Circle, you must inscribe another Square, as in the Plan C; from whence you find in Perspective the double Circle D. Between these two Circles, you may, by the eight Intersections of the Squares, describe a third; as is evident by the Figures E and F. In a word, all Circles are described by the Help of Squares, tracing them by the Intersections of the visual Lines, with those parallel to the Ground-line: Nor is there any Point in either the Squares or Circles A, C, E, whose correspondent Point may not be readily found by such Sections, in the respective Squares and Circles B, D, F. Nevertheless, where your Work requires many Circles, I would advise you to use as few Squares as possible; lest they perplex, rather than assist you.