The renowned notebook of the twelfth-century architect Villard de Honnecourt contains some deleted diagrams, which have been studied by Roland Bechmann. An infra-red photograph of a page revealing an erased drawing of a pointed arch is reproduced as Fig. 25, a redrawn diagram is given as Fig. 26 and an enhanced version (with supplementary constructions) is given as Fig. 27. That enhanced version includes a simple geometrical construction of a line AE, with the radius of each of the semi-circles labelled as R.

In his Telluris Theoria Sacra and its English translation The Theory of the Earth (1681–90), the English clergyman and schoolmaster Thomas Burnet (c.1635–1715) constructed a geological history from the Creation to the Final Consummation, positing predominantly natural causes to explain biblical events and their effects on the Earth and life on it. Burnet's insistence on appealing primarily to natural rather than miraculous causes has been interpreted both by his contemporaries and by some historians as an essentially Cartesian principle. On this reading, Burnet adhered to a Cartesian style of explanation in which there was no place for miracles. In this paper, I propose a different interpretation. Burnet's commitment to natural over miraculous causes, I argue, was grounded in an anti-voluntarist theology which he inherited from the Cambridge Platonists and Latitudinarians. This anti-voluntarism, moreover, also dictated the kind of miracles to which he did appeal. This reading of Burnet contrasts with the view that he was simply following Cartesian principles. First, Descartes had espoused a radical form of theological voluntarism. Second, Burnet's and Descartes's views of providence were based on distinct attributes of God, and these attributes had quite different implications regarding the place of miracles in the providential order.