DEVELOPMENT OF GEOMETRIC METHOD*. 415 



propositions in juxtaposition ; and he had the idea of substituting 

 for Poncelet's demonstrations, which required an intermediary curve 

 or surface of the second degree, the famous ' principle of duality,' of 

 which the signification, a little vague at first, was sufficiently cleared 

 up by the discussions which took place on this subject between Ger- 

 gonne, Poncelet and Pluecker. 



Bobillier, Chasles, Steiner, Lame, Sturm, and many others whose 

 names escape me, were, at the same time as Pluecker and Poncelet, as- 

 siduous collaborators of the Annales de Mathematiques. Gergonne hav- 

 ing beconle rector of the Acadamv of Montpellier, was forced to suspend 

 in 1831 the publication of his journal. But the success it had obtained, 

 the taste for research it had contributed to develop, had commenced to 

 bear their fruit. Quetelet had established in Belgium the Corre- 

 spondance mathematique et physique. Crelle, from 1826, brought out 

 at Berlin the first sheets of his celebrated journal, where he published 

 the memoirs of Abel, of Jacobi, of Steiner. 



A great number of separate works began also to appear, wherein 

 the principles of modern geometry were powerfully expounded and 

 developed. 



First came in 1827 the c barycentrische Calcul ' of Moebius, a 

 work truly original, remarkable for the profundity of its conceptions, 

 the elegance and the rigor of its exposition; then in 1828 the ' Analy- 

 tisch-geometrische Entwickelungen ' of Pluecker, of which the second 

 part appeared in 1831 and which was soon followed by the 'System 

 der analytischen Geometrie ' of the same author published at Berlin 

 in 1835. 



In 1832 Steiner brought out at Berlin his great work: ' System- 

 atische Entwickelung der Abhaengigkeit der geometrischen Gestalten 

 von einander,' and, the following year, ' Die geometrischen Konstruk- 

 tionen ausgefuehrt mittels der geraden Linie und eines festen Kreises,' 

 where was confirmed by the most elegant examples a proposition of 

 Poncelet's relative to the employment of a single circle for the geome- 

 tric constructions. 



Finally, in 1830, Chasles sent to the Academy of Brussels, which 

 happily inspired had offered a prize for a study of the principles of 

 modern geometry, his celebrated ' Apercu historique sur l'origine et le 

 developpement des methodes en geometrie,' followed by ' Memoire sur 

 deux principes generaux de la science: la dualite et 1'homographie/ 

 which was published only in 1837. 



Time would fail us to give a worthy appreciation of these beautiful 

 works and to apportion the share of each. Moreover, to what would 

 such a study conduct lis, but to a new verification of the general laws 

 of the development of science. "When the times are ripe, when the 

 fundamental principb s have been recognized and enunciated, nothing 



