Appendix 37 1 



practises higher geometry without knowing 

 or caring. The thing works of itself and takes 

 its impetus from an instinct imposed upon 

 creation from the start. 



The stone thrown by the hand returns to 

 earth describing a certain curve ; the dead leaf 

 torn and wafted away by a breath of wind 

 makes its journey from the tree to the ground 

 with a similar curve. On neither the one side 

 nor the other is there any action by the moving 

 body to regulate the fall ; nevertheless, the 

 descent takes place according to a scientific 

 trajectory, the * parabola,' of which the section 

 of a cone by a plane furnished the prototype 

 to the geometer's speculations. A figure, which 

 was at first but a tentative glimpse, becomes a 

 reality by the fall of a pebble out of the vertical. 



The same speculations take up the parabola 

 once more, imagine it rolling on an indefinite 

 straight line and ask what course does the 

 focus of this curve follow. The answer comes : 

 The focus of the parabola describes a * catenary,' 

 a line very simple in shape, but endowed with 

 an algebraic symbol that has to resort to a kind 

 of cabalistic number at variance with any sort 



