 Among the French philosophes, the dominant position in the 1740s was the Cartesian one, which, as exemplified by Clairaut’s Élémens de géométrie (1741) was perhaps unduly naïve in its insistence on clear and immediate ideas. The position of d’Alembert, in his articles in the Encylopédie Méthodique (1784), was more sophisticated. The objects of geometry are to be understood by abstracting from bodies every quality except that of being divisible and figured extents. Among these objects are lines, that lack breadth, and surfaces, that lack depth. Truths established about the objects of geometry are purely abstract and hypothetical, because there is no such thing, for example, as a perfect circle. The demonstrated properties can hold of actual circles only insofar as the actual object approaches the state of being a perfect circle,