On the Art of Building

...the rest of that same kind, about which we shall speak more distinctly in their proper place. For one thing is owed to the forum, another to the theater, another to the wrestling school, and another to the temple in terms of space and location. Therefore, according to the reason and use of each, the situation and size of the area will be determined. But in this place, so that we may pursue these matters generally as we have begun, we shall touch upon only those things which we judge to be necessary, if I first relate something concerning lines, which may assist in expressing the matter conveniently. For it is fitting for those dealing with the description of an area that we settle those things by which the description itself is annotated. Every description, therefore, is made by lines and angles. Lines, indeed, are the outermost description by which the space of the entire area is enclosed. That part of a surface substituted for the description, which is contained within two lines mutually intersecting each other, is called an angle. And from the mutual intersection of two lines, four angles are written out. If each of these is equal to each of the other three, they shall be called right angles. Those that are smaller than a right angle will be called acute, just as those that are larger than a right angle will be called obtuse. Furthermore, one line is straight, another is curved; I need not mention here helical or vortex-like lines. A straight line is a length-wise description from point to point, drawn in such a way that no shorter one can be made. A curved line is a part of a circle. A circle is that description made from one of two points, which is moved around in the same surface in such a way that, throughout the entire course of the description, it is neither farther nor closer to the immobile middle point around which it revolves than it was when it first began to be moved around. But it must be added that the curved line, which we said is a part of a circle, is called an arc among us architects for the sake of similarity. And that line which is drawn directly from the two extreme points of a curved line will be called a chord by equal similarity. And that line which is brought out from the point of the middle of the chord at equal angles on both sides to the arc will be called a sagitta (arrow). And that line which is drawn from the immobile point, which is inside the circle, to the curved and outermost line of the circle, will be called a radius. And the point that resides within the circle immobile in the middle will have the name of center. And that straight line passing through the center and cutting the curved line of the circle in two places will be called a diameter. Furthermore, there is a difference between arcs...