Girard Desargues (1951-1662) was a key figure in the transformation of architectural geometry from its ancient and venerated status as transcendental knowledge and supreme reality to a mere technological instrument for the control of building construction practice. As a friend of Rene Descartes and Marin Mersenne, Desargues participated in the development of the mechanistic worldview which accompanied the emergence of experimental science and the renewed interest in mathematics and geometry as axiomatic, deductive systems. This dissertation examines in detail Desargues' methods of stereotomy (the geometrical basis of architectural stone cutting) and his system of perspective construction without vanishing points beyond the picturespace. Desargues' theorem and other key discoveries for which he is still known in the history of mathematics are discussed as they bear upon his methods of stereotomy and perspective. Desargues' stereotomy is almost certainly the first attempt at a universal descriptive geometry such as Gaspard Monge finally developed after the French revolution. Desargues' work in this area may thus be seen as a precocious foreshadowing of the engineering geometry in common use today. The writings of Desargues have been consulted in the original French. Extensive passages are quoted and translated, and a number of illustrations from the original texts are reproduced. Supplementary illustrations are also provided. Appendices list the known architectural works of Desargues, his writings and those of his friend and student Bosse which bear upon the exposition of Desargues' methods. / Ph. D.