The early history of dimensional analysis: II. Legendre and the postulate of parallels

Abstract: In an attempt to prove Euclid’s fifth postulate, Legendre applied the principle of homogeneity. This was apparently the second historical use of dimensional analysis. This paper describes and analyses Legendre’s work. It is shown that he assumed as a basis of his argument the inexistence of an absolute length standard – as Lambert did before him. Some reactions against and for Legendre’s ideas are presented. It is shown that Legendre’s work was premature: his method did not have a solid foundation, and the mathematicians of his time had good reasons to dismiss his arguments as invalid. Keywords: dimensional analysis; postulate of parallels; foundations of geometry; non-Euclidian geometry; a priori proof; Legendre, Adrien-Mari