CHAPTER LIX

On Lateral (Faceted) Columns, and First on the Three-Sided (Triangular) Column, Called the Serratile Body (Plates XLV–XLVI).

Folio 0052 (f. 18v) Initial

Another species of columns is called lateral or faceted (colonne laterate, prisms), of which the first is the three-sided or triangular column (colonna laterata trilatera, Plates XLV–XLVI):

Structure of the Triangular Column (Corpo Seratile)

  1. Its two opposite bases—the upper (suprema) \(abc\) and the lower (inferiore) \(def\)—are two equal and parallel triangles separated by the height (altitude) of the column (see the marginal diagram 0053.g1.png on Folio 0053).

  2. Our author Euclid (in Campanus Book XI/XII) calls this triangular prism the serratile body (corpo seratile, from serra, a saw, because it is formed by sawing a parallelepiped diagonally in half!).

  3. Visually, when laid horizontally, it resembles the pitched ridge of a house roof (el colmo de vn tecto de vna casa) that slopes down on two sides with two triangular gables at the ends.

  4. Its two triangular bases may be either equilateral or non-equilateral (isosceles or scalene), while its three lateral faces joining the bases are always right-angled parallelograms (rectangles).

  5. Thus every triangular column (corpo seratile) is bounded by 5 plane surfaces in all: 3 quadrangular (rectangular) lateral faces and 2 triangular bases, with 6 solid angles and 9 edges.