The text describes a method for determining dimensions and drawing geometrically correct depictions of pillars and their components, such as capitals, using specific mathematical ratios and geometrical techniques. It explains how to use geometrical and perspective planes to understand and depict elements in drawing, utilizing the example of a box figure from a reference plate. The instructions include measuring and comparing angles, dimensions, and lines to achieve accurate perspective representations, with a focus on practical execution techniques for artists.
Starting from point G, a height GH is equal to one twelfth of the total height. We also compare the height of the base with the height FH. Here, FJ equals one sixth of FH. Therefore, we find FJ on the drawing by taking a sixth of FH from point F.
To find the widths, observe that the visible part of the pillar consists of two planes, a geometrical plane and a perspective plane. It is, in essence, the same figure as the box in Plate 3, Figure 10, with the only difference being that the perspective plane, placed to the right for the box, is placed here to the left of the pillar.
We start with the geometrical plane. We compare the width represented by H1, with the height FH of the pillar excluding the capital. Here, the width HL is one fifth of the height FH. On the drawing, a width HL equal to one fifth of the height FH is taken. From point H1, a horizontal line is drawn to point L, and from this point, a perpendicular line is lowered completing the geometrical plan of the pillar, represented here by FHL, and whose fourth angle is hidden by the stairs.
The perspective plan of the pillar is found in the same way as the perspective or vanishing side of the house in Plate 5, Figure 7. The distance from line FH to line ab is found by comparing it with the width HL of the geometrical plan FHL. Then, holding the pencil horizontally, we see at what height angle b cuts the line FJ or FH. We also see at what height angle a cuts the line FH (see Plate 3, Figure 10).
This side being found, it remains to draw the capital. Its height is already represented here by HG. Holding the pencil upright, we see how much the portion of the capital represented by Ed exceeds the line represented by FH. Here, it is one third of the line fe, which exceeds the line FH. Similarly, by lowering a plumb line from the angle represented by f, we see that this point is still above a point situated one third of the line LH. These points f and e, being found on the drawing, form the line represented here by fe. Next, the profile cd is drawn, etc., completing the cornice, by comparing the molds with the height of the capital. To finish, the viewpoint, which will be here the point V where the extended lines Ha and Fb will meet, and which is located opposite the observer and at eye level (see Plate 3, Figure 10), will be used. Now, by drawing lines from points c, d, e, to the viewpoint, the cornice can be completed, provided one knows how much the angle represented here by f exceeds the line represented by b. It is found here that it is an amount equal to the width of the perspective plan FHaI. Point h, having been found, a vertical parallel to cd is lowered. Then the curve corresponding to the curve of ed is drawn, leading to point a. Another drawing of the profile represented here as f2 is then made. Using the rule at the point e and the points f, f1, etc., the lines f1, ga are drawn.
To find the second pillar, its height could be compared to that of the first pillar. These pillars are all the same height in reality, though they rise just as much. Here, it will not be simple to use a viewpoint to find their height reductions. Extend the lines Fb and ch to point of view V, and these two lines will show the decreases in the heights of all the pillars as they recede.
Next, the width of these pillars will be sought. The position of the line represented by OM is found by comparing its distance to the line FH with the width of the geometrical plan of the first pillar. Next, the width of the perspective plan MOPR is found by comparing it with the extent of the geometrical plan IOMS. The other pillars will be similarly discovered. By extending the lines ch, Ha to each pillar, the height of its capital is given: similarly, by extending to the viewpoint lines starting from points c, d, e, etc., reductions in the molds of each capital are noted. It then only remains to check how far the capitals extend on the pillars, which is found by holding the pencil upright, as with the first pillar. With points N, m, ... etc., having been found, a line is drawn from point N horizontally to meet the line ab; from point m, another horizontal is drawn to meet RP, and similarly for the other capitals.
We assumed that on the other side of the gallery, instead of pillars, there would be a suite
Translation Notes:
- "Geometrical plane" and "perspective plane" are artistic and technical terms referring to projection techniques used in drawing to convey three-dimensional objects on two-dimensional surfaces.
- "Capital" refers to the topmost part of a pillar or column.