Vitruvius named three qualities required of architecture in his "De architectura", c. 15 B.C.: firmness, usefulness (or "Commodity" in Henry Wotton's 16th century English), and delight. These can be used as categories for classifying the ways in which mathematics is used in architecture. Firmness encompasses the use of mathematics to ensure a building stands up, hence the mathematical tools used in design and to support construction, for instance to ensure stability and to model performance. Usefulness derives in part from the effective application of mathematics, reasoning about and analysing the spatial and other relationships in a design. Delight is an attribute of the resulting building, resulting from the embodying of mathematical relationships in the building; it includes aesthetic, sensual and intellectual qualities.