THEORY

The element of the line. A multiplied line produces a surface: the simplest of these figures is the triangle, derived from the number three. It is composed of three straight lines that join at their ends. The square comes next; it has as its elements four straight lines equally distant from one another at all points, and which touch at the ends. From this arrangement arises the solid rectangle, called substance or matter. For having placed four points equally distant from each other, if you join them with straight lines, they form the base of a cube that supports all parts and the sides positioned at equal height, through the means of four lines raised perpendicularly on the angles of this base. Now, the cube has six equal sides: one on which it stands: another opposite the base: and four others that form its outline: such is a die for playing.

This cube or perfect square is the primitive element of all strong and vigorous bodies, such as Heroes, Athletes, and everything that should express simplicity, heaviness, firmness, and strength; for the cube has a base on which it can stand without any external help, and it maintains a universal dominance over the human body, especially in the male gender. In contrast, in women, the strength of its angles is weakened and diminished in the form of a sphere.

(1) From the cube, or figure squared on all sides, let everything masculine or virile, and everything heavy, strong, robust; compact, and athletic is. And whatever is taken away from the form of the square will likewise perish in amplitude. Quintil. Book I, chapter X.

Translation Notes:

The term 'rectangle solid' in the original French refers to what we would identify as a three-dimensional rectangle or 'cuboid' in English. The concept of the cube as a fundamental shape expressing stability and strength might not be familiar today but was a common idea in historical art and anatomy studies.