Perspective in Leibniz's invention of \textit{characteristica geometrica}: the problem of Desargues' influence
type: Item
instance of: scholarly article
title: Perspective in Leibniz's invention of \textit{characteristica geometrica}: the problem of Desargues' influence
zbMATH Open document ID: 1294.01012
author: Valérie Debuiche
published in: Historia Mathematica
publication date: 2014-01-10T00:00:00Z
reviewed by: Charlotte Wahl
Mathematics Subject Classification ID: 01A45
Mathematics Subject Classification ID: 51-03
zbMATH DE Number: 6244196
zbMATH Keywords: Leibniz
zbMATH Keywords: Desargues
zbMATH Keywords: analysis situs
zbMATH Keywords: projective geometry
zbMATH Keywords: characteristica geometrica
MaRDI profile type: Publication
full work available at URL: j.hm.2013.08.001
OpenAlex ID: W1972363152
cites work: The geometry of an art. The history of the mathematical theory of perspective from Alberti to Monge
cites work: Q4013713
cites work: Geometry and monadology. Leibniz's \textit{analysis situs} and philosophy of space
cites work: Q3745822
cites work: Q4773652
cites work: Q4767271
cites work: Q4770913
cites work: Q4846441
cites work: Q3863840
cites work: Q3986383
DOI: 10.1016/J.HM.2013.08.001
review text: From 1677 on and throughout his life Leibniz spent considerable effort on the design of a new symbolic calculus, which he called alternatively \textit{characteristica geometrica}, \textit{geometria situs} and \textit{analysis situs}. Its aim was to encode geometric arguments and thereby make the use of figures superfluous. Furthermore, in contrast to Cartesian analysis, it was designed to be coordinate-free. Instead of magnitude, its basic notion was the relative position of geometrical objects in space, the \textit{situs}.NEWLINENEWLINEDuring his stay in Paris (1672--1676), Leibniz got to know Desargues' work, but it is difficult to determine to what extent. Since he mentioned Desargues quite often without acknowledging any direct influence, the question studied in the present paper, how far his project of a \textit{characteristica geometrica} was inspired by Desargues, is natural. One difference is obvious (p. 376): The fundament of Leibniz's geometrical calculus is Euclidean plane geometry and not projective geometry.NEWLINENEWLINEAfter reviewing ideas of Desargues which may have interested and influenced Leibniz and confronting them with key concepts of Leibniz's \textit{geometria situs}, the author concludes: ``[I]t appears that what is common is what distinguishes these two kinds of geometrical methods: the role of quantity, the place of figures and the imagination, the relation between similarity and congruence, the use of the identification of parallel and secant lines, and the conception of space through perceptive considerations.'' (p. 382). In the end, the author points to the influence of other sources, in particular Pascal (p. 382 f.).
description: scientific article; zbMATH DE number 6244196