This paper applies CAD-based geometrical analysis to laser survey data from several major Gothic churches to provide a fresh perspective on a fundamental claim made by Otto von Simson in The Gothic Cathedral; namely, that French Gothic designers in the twelfth and thirteenth centuries used ideal figures such as the equilateral triangle, square, pentagon, and the Golden Rectangle to set the proportions of their buildings. Brief case studies of Saint-Denis Abbey and the cathedrals of Sens, Bourges, Chartres, and Reims demonstrate that this claim is essentially correct, while also demonstrating that Gothic builders modified their plans in the course of construction, often in response to advances made by their colleagues working on other projects. Taken together, therefore, these analyses help to clarify not only the geometrical methods used by Gothic designers, but also the way competition between them helped to drive architectural innovation in the decades around 1200.