138 SIMSON. 



of the Greek analysis, or at most, as a feat of geome- 

 trical force, and by no means as an indication of any 

 wish to substitute so imperfect, however beautiful, an 

 instrument, for the more powerful, though more or- 

 dinary one of the calculus which " alone can work 

 great marvels." At the same time, and with all the 

 necessary confession of the merits of the modern 

 method, it is certain that those geometricians would 

 have regarded the course taken by some of its votaries 

 in more recent times as exceptionable, whether with a 

 view to clearness or to good taste : a course to the full 

 as objectionable as would be the banishing of alge- 

 braical and substituting of geometrical symbols in the 

 investigations of the higher geometry. La Place's great 

 work, the i Mecanique Celeste,' and La Grange's * Me- 

 canique Analytique,' have treated of the whole science 

 of dynamics and of physical astronomy, comprehending 

 all the doctrine of trajectories, dealing with geometri- 

 cal ideas throughout, and ideas so purely geometrical 

 that the algebraic symbols, as far as their works are 

 concerned, have no possible meaning apart from lines, 

 angles, surfaces ; and yet in their whole compass they 

 have not one single diagram of any kind. Surely, 



_ ds 3 * 



we may ask if jLy dx*+dy*, jj/dN can 



y 



sibly bear any other meaning than the tangent and 

 the radius of curvature of a curve line : that is, a 

 straight line touching a curve, and a circle whose cur- 

 vature is that of another curve where they meet; any 

 meaning, at least, which can make it material that they 

 should ever be seen on the page of the analyst. These 

 expressions are utterly without sense, except in refer- 

 ence to geometrical considerations ; for although x and 



* Or (<fa4-<fy a )ft 



(I) 



