MODERN SCIENCE. 195 



calculation two facts which Newton had already made plain. 

 We shall see what magnificent use Lagrange made of his own 

 mathematical conceptions. Lagrange also brought back the 

 attention of geometers to algebra, which was being neglected, 

 by his Resolution of Numerical Equations. 



17461818. Monge improved DESCRIPTIVE GEOMETRY, 

 and caused its universal adoption; founded the nucleus of 

 the Polytechnic School, which became, under and after 

 Napoleon, the highest scientific school in Europe. 



17491827. Laplace extended the limits of mathe- 

 matical analysis. His " CELESTIAL MECHANICS/' a work 

 of mathematics as much as astronomy, places him by the 

 side of Newton in some respects. His " THEORY OF 

 PROBABILITIES " was a practical revolution : this theory, 

 certainly one of the noblest creations of intellect, is, said 

 its author, " good sense reduced to calculation." This famous 

 work contains Laplace's theory of Generating Functions 

 (Fonctions Generatrices). 



17521832. Legendre continued Ruler's labours in his 

 famous THEORY OF NUMBERS. His Elliptical Functions, 

 his researches on alterations of Homogeneous Spheroids, 

 contain new important theorems, and his THEORY OF 

 PARALLELS contains the famous Method of the Least 

 SQUARES OF ERRORS. These creations of his have given 

 powerful assistance to mathematicians. 



1753 1823. Carnot formulated the THEOREM (on loss 

 of forces) which bears his name, and established the great 

 mechanical principle of REVERSIBILITY OF ENERGY the 

 conversion of heat into mechanical effect : " The amount 

 of mechanical energy obtained from a certain given amount 

 of heat energy -, is the same at all times at the same temperature" 

 This thermodynamic law is held to be strictly true of all 

 matter without exception ; but Carnot failed to grasp its 

 full significance. It was reserved to Joule and Hirn fully 

 to expound and develop it into modern Thermodynamics. 

 Carnot stands high in the sphere of mathematics by four 

 works : On Infinitesimal Calculus, Correlation of Geometrical 

 Figures, Geometry of Position, Relation between the Re- 

 spective Distances of Five Points in Space. 



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