Later 16th century fortification theory was conceived to be a mathematical science. The mathematical approach was considered valuable for the quality of public demonstrability and certainty it gave; for the dignified\ud and worthy art that resulted, suitable to those of a certain (elevated) station of life. Epistemologically, the general Euclidian method used was supported by the Christian model of the relationships between God, man and the world. The prince on earth had need of such a tool to govern his domain. Concentration in design on the needs of defensive guns and 'the principle of no dead ground' established this pattern. The idea of the irresistability of attacking artillery legitimized the program.\ud Other disciplines of the renaissance: naval architecture, perspective, dialling, surveying, navigation and mapping, ballistics and general architecture, evidence a similar cluster of ideas. The preference of the period was for theoretical technologies as against the mere following of successful craft practices. Earlier fortification theory involved a method of design by reference to the resisting capacity of particular forms. The increasing use of artillery in siege warfare in attack, and defence, meant that the ability of defending guns to punish the attack could no longer be so neglected in design. The shift to the diametrically opposite mode of design based on the functioning of defending artillery was facilitated by a number of factors: An increasing concentration on the urban enceinte; the changing nature of warfare, technical and otherwise; changing conception of political and war related\ud needs; and the desirable quality of the science that arose. Many factors interacted in this process which was paralleled epistemologically in religious thought and political theory. The resultant attitudes and the emergent mathematical picture of the world of many areas of practical\ud knowledge formed the background for the work of such figures as Descartes and Galileo.\ud \u
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