"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,
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 that is a
tangent to it?" I looked upon this question as a particular case of the
theory of osculations which I had studied in Legrange's "Fonctions
Analytiques." "Finally," said the examiner to me, "how do you determine
the tension of the various cords of which a funicular machine is
composed?" I treated this problem according to the method expounded in
the "Mécanique Analytique." It was clear that Lagrange had supplied all
the resources of my examination.

I had been two hours and a quarter at the board. M. Monge, going from
one extreme to the other, got up, came and embraced me, and solemnly