278 LIMITS AND FLUXIONS 



thetical twilight zone between finite quantity and 

 no quantity. Their abandonment added to the 

 clearness and logicai rigour of mathematics. From 

 the standpoint of rigour, the British treatment of 

 the calculus was far in advance of the Continental. 

 It is certainly remarkable that in Great Britain 

 there was achieved in the eighteenth century, in the 

 geometrical treatment of fluxions, that which was 

 not achieved in the algebraical treatment until the 

 nineteenth century ; it was not until after the time 

 of Weierstrass that infinitesimals were cast aside 

 by many mathematical writers on the Continent. 



235. There is a perversity in historic events 

 exhibited in the fact that after infinitesimals had 

 been largely expelled in the eighteenth century 

 from Great Britain as undesirable, unreal, and 

 mischief-making, they should in the nineteenth 

 century be permitted to return again and to flourish 

 for a time as never before. About 18 16 the 

 Leibnizian notation of the calculus and the vast 

 treasures of mathematical analysis due to the 

 Bernoullis, Euler, D'Alembert, Clairaut, Lagrange, 

 Laplace, Legendre, and others, which were ali ex- 

 pressed in that notation, found their way into 

 England. This influx led to enrichment and advance- 

 ment of mathematics in England, but also to a 

 recrudescence — this return of the infinitely small. 

 How thoroughly the infinitesimal invaded certain 

 parts of British territory is seen in Frice's large 

 work on the Infinitesiinal Calculus^ a work which in 

 many ways is most admirablc and useful. 



