The radical nature of Cordemoy’s proposals was not to the fore in the first edition of his book. Though he preferred the three Greek orders, more than half his book is taken up with a description of all five orders and their parts, and they are the subject of most of his illustrations. He indicated, in discussing pediments and roof design, that he preferred a four-square silhouette, though it was only when he took up the design of churches that he made clear his preference for an orthogonal architecture – freestanding columns and lintels rather than piers and arches. He roundly condemned the piers and arches of Saint Peter’s in Rome, suggesting that columnar supports, as in the piazza outside, would have been preferable by far. He made the same critique of the Val-de-Grâce in Paris. Following Perrault and Fremin, he also recognized something of the clear-cut structural expression he aimed at in Gothic architecture – he named the churches of Longpoint, Royaumont and Sainte-Croix at Orléans. The terms he used to describe the effect, once again deriving from Perrault, were "dégagement "(disengagement) and "apreté "(sharpness). He condemned the bas-relief effect of contemporary architecture. He disliked the numerous motifs and mouldings scattered over the surfaces of buildings. He suggested that even pedestals, applied orders and pilasters might be dispensed with. He preferred plain masonry surfaces He wanted the freestanding column to resume its structural role.