leave him the merit of the
discovery, I shed a little light on the path. The solution is found. My
pupil triumphs; so do I, but silently, in my inner consciousness, which
says:

'You understand, because you succeed in making another understand.'

The hour passed quickly and very pleasantly for both of us. My young man
was contented when he left me; and I no less so, for I perceived a new
and original way of learning things.

The ingenious and easy arrangement of the binomial gave me time to
tackle my algebra book from the proper commencement. In three or four
days, I had rubbed up my weapons. There was nothing to be said about
addition and subtraction: they were so simple as to force themselves
upon one at first sight. Multiplication spoilt things. There was a
certain rule of signs which declared that minus multiplied by minus made
plus. How I toiled over that wretched paradox! It would seem that
the book did not explain this subject clearly, or rather employed too
abstract a method. I read, reread and meditated in vain: the obscure
text retained all its obscurity. That is the drawback of books in
general: they tell you what is printed in them and nothing more. If
you fail to understand, they never advise you, never suggest an attempt
along another road which might lead you to the light. The merest word
would sometimes be enough to put you on the right track; and that word
the books, hidebound in a regulation phraseology, never give you.

How greatly preferable is the oral lesson! It goes forward, goes back,
starts afresh, walks around the obstacle and varies the methods of
attack until, at long last, light is shed upon the darkness. This
incomparable beacon of the master's word was what I lacked; and I went
under, without hope of succor, in that treacherous pool of the rule of
signs.

My pupil was bound to suffer the effects. After an attempt at an
explanation in which I made the most of the few gleams that reached me I
asked him:

'Do you understand?'

It was a futile question, but useful for gaining time. Myself not
understanding, I was convinced beforehand that he did not understand
either.

'No,' he replied, accusing himself, perhaps, in his simple mind, of
possessing a brain incapable of taking in those transcendental verities.

'Let us try another method.'

And I start again this way and that way and yet another way. My pupil's
eyes serve as my thermometer and tell me of the progress of my efforts.