SECTION B GEOMETRY 



(Hall 9, September 24, 10 a. TO.) 



CHAIRMAN: PROFESSOR M. W. HASKELL, University of California. 



SPEAKERS: M. JEAN GASTON DARBOUX, Perpetual Secretary of the Academy of 



Sciences, Paris. 



DR. EDWARD KASNER, Columbia University. 

 SECRETARY: PROFESSOR THOMAS J. HOLGATE, Northwestern University. 



A STUDY OF THE DEVELOPMENT OF GEOMETRIC 



METHODS 



BY M. JEAN QASTON DARBOUX 



(Translated from the French by Professor George Bruce Hoisted, Kenyan College) 



[ Jean GastonDarboux, Perpetual Secretary Academy of Sciences, Paris; Doyen 

 Honorary, Professor of Higher Geometry of the Faculty of Sciences, Paris, 

 b. August 13, 1842, NImes, France. Dr.Sc., LL.D., University of Cambridge, 

 University of Christiania, University of Heidelberg, et al. Professor of 

 Special Mathematics, Lycee Louis le Grand, 1867-73; Master of Confer- 

 ences in Superior Normal Schools, Paris, 1873-81; Professor Suppliant of 

 Rational Mechanics and Higher Geometry, The Sorbonne, 1873-81; since 

 1881, Professor Titulaire of the Faculty of Sciences, and Doyen of the Fac- 

 ulty of Sciences since 1889; also Professor in Higher Normal School for 

 Schools of Science ; Member of Bureau des Longitudes; President of the 

 First General Assembly of the International Association of Academies; and 

 Honorary Vice-President for France of the Congress of Arts and Science; 

 Member of Institute of France, Royal Society of London; Academies of 

 Berlin, St. Petersburg, Rome, Amsterdam, Munich, Stockholm; American 

 Philosophical Society, et al. Author of many publications and addresses 

 on Mathematics, and editor of the Bulletin of Science of Mathematics} 



To appreciate the progress geometry has made during the cen- 

 tury just ended, it is of advantage to cast a rapid glance over the 

 state of mathematical science at the beginning of the nineteenth 

 century. 



We know that, in the last period of his life, Lagrange, fatigued by 

 the researches in analysis and mechanics, which assured him, however, 

 an immortal glory, neglected mathematics for chemistry (which, 

 according to him, was easy as algebra), for physics, for philosophic 

 speculations. 



This mood of Lagrange we almost always find at certain moments 

 of the life of the greatest savants. The new ideas which came to 

 them in the fecund period of youth and which they introduced into 

 the common domain have given them all they could have expected; 

 they have fulfilled their task and feel the need of turning their 



