EXAMINATION BY M. MONGE. _ 
conversation took place between M. Monge (the exami- 
ner) and me. 
“Tf 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.” | 
“T 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 
