Geometry

Abstract

Abandoning the domain of historical research to attempt an assessment of the geometrical results Leibniz achieved through his new and celebrated science, we cannot escape a feeling of embarrassment. Those today’s scholars who may want to read and reread and peruse the many theorems and the very many definitions that have been handed down to us in Leibniz’s yellowed and tattered manuscripts, are unlikely to find anything there but a somewhat ramshackle reasoning or a rather trivial geometrical truth. If therefore, at the end of such a tour de force, they wondered: cui, hodie, prodest?, they would dismally answer that the entire construction of the Analysis of Situation was, in itself, not worth the effort. The study of it would not be of any help to the historian of science who, in the absence of any bit of fortune of this discipline, could not even ascribe any maieutic virtue nor any fertile seed, however only later germinated in the crop of a better geometer, to those primitive, meager results. Nor would this Leibnizean discipline be of any help to the mathematician, who has long ago abandoned the problems of elementary geometry and who regards Euclid’s Elements as undoubtedly belonging to the prehistory of science. In these Leibnizean studies, in fact, there is hardly any result not already known to the Greeks, whose works are endowed with such a deep, vast, and articulated richness as to rise well above the dozen or so theorems, some of them disputably demonstrated too, with which Leibniz regales his reader.