A 1938 French treatise by Brandon-Guiguet presenting a mathematical approach to shaft (harness) loom weaving, centered on the concept of the "Initiale" (the underlying periodic grid governing threading and weave possibilities). The first part studies forms as curves defined by parametric equations of threading (remettage) and tie-up/treadling (armure, marchure), covering normal and tied (embrevage) setups, symmetry, harmonics, and point transposition. The second part, on textures (contextures), applies the Initiale to linear and interfering threadings, reduced shaft counts, and cell-based designs, with many drawdown figures. It closes with supplementary notes, a table of contents, and plates of fabrics woven on dobby looms by this method on threadings of up to twenty shafts.