DEVELOPMENT OF MATHEMATICAL THOUGHT. 659 



had foretold 1 the possibility and necessity of such an 

 independent development of pure geometry, in which the 

 relations of position in space, as opposed to those of 

 measure, magnitude, or quantity, would be placed in the 

 foreground. Projection, as practised in the drawing of 

 maps, and perspective, as practised in the fine and 

 descriptive arts, had already revealed a number of 

 remarkable properties of figures in the plane and in 

 space. By continuous motion of points or lines, by 

 artifices like throwing of shadows, by sections of solids 

 with lines and surfaces, a vast number of problems had 

 been solved and isolated theorems established. The 

 method here practised was that of construction, as in 

 analysis the method was that of calculation with sub- 

 sequent interpretation. All this purely constructive 

 work was to be brought together and systematically 

 combined in a whole. It was evidently a distinct line 

 of research, based upon intellectual processes other 

 than the purely analytical method a line which, 

 as it seemed to its followers, had been unduly neglected 

 and pushed into the background. Although Monge 

 became the founder of this purely descriptive or con- 

 structive branch of geometry, he was himself equally 

 great as an analyst ; in fact, the fusion in his mind 

 of the two methods was the origin of much of his 

 greatest work. In attempting to carry out more 

 thoroughly the separation or independent development 

 of the constructive or descriptive method, his great pupil, 

 J. V. Poncelet whilst deprived of all literary resources Ponceiet. 



1 See the quotations from his letters to Huygens and others given 

 above, vol. i. p. 103 note. 



