There I listened for a moment to the solicitations of my family, who pressed me to renounce the prospects which the Polytechnic School opened.  But my taste for mathematical studies soon carried the day; I increased my library with Euler’s “Introduction a l’Analyse Infinitesimale,” with the “Resolution des Equations Numeriques,” with Lagrange’s “Theorie des Fonctions Analytiques,” and “Mecanique Analytique,” and finally with Laplace’s “Mecanique Celeste.”  I gave myself up with great ardour to the study of these books.  From the journal of the Polytechnic School containing such investigations as those of M. Poisson on Elimination, I imagined that all the pupils were as much advanced as this geometer, and that it would be necessary to rise to this height to succeed.

From this moment, I prepared myself for the artillery service,—­the aim of my ambition; and as I had heard that an officer ought to understand music, fencing, and dancing, I devoted the first hours of each day to the cultivation of these accomplishments.

The rest of the time I was seen walking in the moats of the citadel of Perpignan, seeking by more or less forced transitions to pass from one question to another, so as to be sure of being able to show the examiner how far my studies had been carried.[2]

At last the moment of examination arrived, and I went to Toulouse in company with a candidate who had studied at the public college.  It was the first time that pupils from Perpignan had appeared at the competition.  My intimidated comrade was completely discomfited.  When I repaired after him to the board, a very singular conversation took place between M. Monge (the examiner) 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 prejudices.  From this he passed on to a question in algebra, then 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 effects; Newton’s method, the method of recurring series, the method of depression, the method of continued fractions,—­all were passed in review; the answer had lasted an entire hour.  Monge, brought over now to feelings of great kindness,