EXAMINATION BY M. MONGE. 7 



conversation took place between M. Monge (the exami- 

 ner) and me. 



" If you are going to answer like your comrade, it is 

 useless for me to question you." 



" Sir, my comrade knows much more than he has 

 shown ; I hope I shall be more fortunate than he ; but 

 what you have just said to me might well intimidate me 

 and deprive me of all my powers." 



"Timidity is always the excuse of 'the ignorant; it is 

 to save you from the shame of a defeat that I make you 

 the proposal of not examining you." 



" I know of no greater shame than that which you now 

 inflict upon me. Will you be so good as to question me ? 

 it is your duty." 



" You carry yourself very high, sir ! "We shall see 

 presently whether this be a legitimate pride." 



" Proceed, sir ; I wait for you." 



M. Monge then put to me a geometrical question, 

 which I answered in such a way as to diminish his pre- 

 judices. From this he passed on to a question in algebra, 

 to the resolution of a numerical equation. I had the 

 work of Lagrange at my fingers' ends ; I analyzed all 

 the known methods, pointing out their advantages and 

 defects ; Newton's method, the method of recurring series, 

 the method of depression, the method of continued frac- 

 tions, all were passed in review ; the answer had lasted 

 an entire hour. Monge, brought over now to feelings of 

 great kindness, said to me, " I could, from this moment, 

 consider the examination at an end. I will, however, for 

 my own pleasure, ask you two more questions. What 

 are the relations of a curved line to the straight line 

 which is a tangent to it ? " I looked upon this question 

 as a particular case of the theory of osculations which I 



