Let me make this clearer. The more one examines the typical points in the Saxon, Norman, and Gothic styles of Architecture, the more clearly one sees that the Architects of the two former used circles and squares on their tracing-boards, as units for their proportions, in drawing up both ground plans and elevations, with here and there suggestions only of the Equilateral Triangle having been made use of in some of the smaller details; whereas the Gothic Architects seem to have used the Vesica Piscis almost entirely. This explains the reason why true Gothic buildings have always been said to be built mainly on the basis of the Equilateral Triangle; this naturally follows, because the use of the Vesica creates, and therefore necessitates, the appearance of the Equilateral Triangle in every conceivable situation. The following quotation is typical of the leading essay writers on this subject: "The Equilateral Triangle enters largely into, if it does not entirely control, all mediaeval proportions, particularly in the ground plans. In Chartres Cathedral the apices of two Equilateral Triangles (_vide_ frontispiece to these Views), whose common base is the internal length of the transept, measured through the two western piers of the intersection, will give the interior length, one apex extending to the east end of the chevet within the aisles, the other to the original termination of the Nave westward, and the present extent of the side aisles in that direction. With slight deviation, most, if not all, the ground plans of the French Cathedrals are measurable in this manner, and their choirs may be so measured almost without exception. Troyes Cathedral is in exact proportion with that of Chartres, and the choirs of Rheims, Beauvais, St. Ouen at Rouen, and others are equally so. Bourges Cathedral, which has no transept, is exactly three Equilateral Triangles in length inside, from the East end of the outer aisle to the Eastern columns supporting the West Towers. Most English Cathedrals appear to have been constructed in their original plans upon similar rules." White's Classical Essay on Architecture compares the Norman with the Gothic, where he says: "In what is usually called the Norman period, the general proportions and outlines of the Churches are reducible to certain rules of setting out by the plain Square. As Architecture progressed the Square gradually disappeared, and the proportion of general outline, as well as of detail, fell in more and more with applications of the Equilateral Triangle, till the art, having arrived at its culminating point, or that which is generally acknowledged to be its period of greatest beauty and perfection in the thirteenth and the beginning of the fourteenth centuries, again began to decline. With this decline the Equilateral Triangle was almost lost sight of, and then a mode of setting out work by diagonal squares was taken up, for such is the