Images from Jean Errard's Fortification réduicte art and démonstrée (Paris, 1600), a seminal work in fortification theory. Errard (1554-1610) was a mathematician by training, and used his love of geometry (he made several translation of Euclid's Elements) to develop a comprehensive theory of military fortifications. He developed a series of geometric designs, based on polygons of various kinds, which were optimised for defence. The most important of his rules stressed the reliance on infantry for defence of a fortress, who, with their potential rapid rate of fire, were better suited than the artillery, which at this period, given its enormous consumption of gunpowder, was only suitable for providing enfilade fire, not engaging in frontal action.