SIMSON. 485 



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 ' Mecanique Celeste,' and La Grange's ' Meca- 

 nique Analytique,' have treated of the whole science of 

 dynamics and of physical astronomy, comprehending 

 all the doctrine of trajectories, dealing with geome- 

 trical 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, 



f ds 3 * 



11 / 



we may ask if V v dx z +dy z , , , , / dy \ can pos- 



9 X ~ \dx) 



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 curvature 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 reference to geometrical con- 



* Or (dx*+dy*)* 



TTTMA 



dx-d { -f } 

 \dxj 



