THE FORMAL INTRODUCTIONS HAD PLAYED against the backdrop of a fireplace large enough to burn a small village. For half an hour or so, Nicolas Fatio de Duillier and Gottfried Wilhelm Leibniz had inched towards each other as if conjoined by an invisible spring stretched through the middle of the muttering swarm of Freiherren and Freifrauen. When finally they drew within hailing distance of each other they switched over to French and launched into an easy chat about involutes, evolutes, and radial curves. Leibniz moved on into a tutorial about a new notion he had been toying with in his spare time, called parallel curves, which he illustrated by drawing invisible lines on the hearth with the toe of his boot. Petty nobles of Lower Saxony who trespassed on these were politely asked to move, so that Fatio could draw several invisible lines and curves of his own. Then he managed, in a single grammatically correct sentence, to make reference to Apollonius of Perga, the Folium of Descartes, and the Limaçon of Pascal.