Studies in a Geometry of Situation with a Letter to Christian Huygens

Abstract

Leibniz’s interest in the application of the general characteristic to geometry seems to have been stimulated by a rereading of the first book of Euclid’s Elements early in 1679. (His notes are given in GM., V, 183–211.) He proposed the new, nonquantitative approach in a letter to Huygens, which is also interesting for its report on the properties of phosphor us, and sent with the letter (I) an essay in which he developed fundamental geometrical definitions and relations on the basis of the relationship of congruence and the operations involved in it (II).1 In a later second paper he used the less determinate but more general relationship of similarity in his demonstrations (HI). Both relations are particular derivatives of the logical principle of identity or equivalence.2 Leibniz’s efforts to found such a geometry met with no response until Riemann and Grassmann, in the 19th century, undertook related studies. He returned to it several times, however, particularly in 1698–99 and near the close of his life (No. 69).