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, hide-bound in a regulation phraseology, never give you. 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. A blink of satisfaction announces my success. I have struck home, I have found the joint in the armour. The product of minus multiplied by minus surrenders its mysteries to us. [35] The study of algebra was pursued in this fashion without any undue impediments as far as the pupil was concerned, but at the cost of a prodigious exertion of patience and penetration on the part of the primary schoolmaster who was so venturesome as to act as a professor of the higher mathematics. Audaces fortuna juvat. The young schoolmaster had not too greatly presumed on his powers. His pupil was accepted upon examination, and he himself was able to return the book to its place, having completely assimilated its contents.