GEOMETRICAL RELATIONS
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The dimensions and proportions set forth in the previous paragraphs, and recapitulated in the Tables, enable one to draw the Five Orders, according to Vignola, with great accuracy and sufficiently in detail for all the ordinary purposes of the draftsman and designer. The figures for the larger features are easily remembered, and the smaller divisions and subdivisions can for the most part be obtained by dividing the larger into two, three, four, or five equal parts.
But besides these arithmetical proportions some geometrical relations may be pointed out, which are calculated greatly to facilitate the work of draftsmanship, drawing being naturally more closely related to Geometry than to Arithmetic.
LINES AT 45 DEGREES
The proportions of any figure that is as wide as it is high, and which can accordingly be included within a square, are most easily determined by drawing the diagonal of the square, that is to say, by drawing a line with a 45-degree triangle. Such figures are, as is shown in the Illustrations, the projections of:
- The Echinus, in the Tuscan, Doric, and Ionic Capitals, Figs. 84 and 85.
- The Abacus, in the Tuscan and Doric Capitals, Figs. 84 and 85.
- The Astragal, in all the Orders, Fig. 86.
- The Architrave, including the Taenia, in the Tuscan and Doric Orders, counting from the axis of the Column, Figs. 84 and 85.
- The Taenia itself, and the Cymatium that takes its place, Figs. 84 and 85.
- All the Cornices, except the Doric, Fig. 84.
A line drawn at 45 degrees through the Doric Cornice from the top of the Frieze gives, where it cuts the upper line of the Cornice:
- The face of the Corona, in the Denticulated Doric, Fig. 85.
- The face of the Mutule, in the Mutulary Doric, Fig. 85.
A line drawn at 45 degrees through the Doric Architrave and Frieze, from a point on the axis of the Column and of the Triglyph, taken either at the bottom of the Architrave or at the top of the Frieze, gives:
- The Axis of the next Triglyph, and so on, Fig. 85.
