We begin in my room, in front of a blackboard. After a few evenings, prolonged into the peaceful watches of the night, I become aware, to my great surprise, that my teacher, the past master in these hieroglyphics, is really, more often than not, my pupil. He does not see the combinations of the abscissæ and ordinates very clearly. I make bold to take the chalk in hand myself, to seize the rudder of our algebraical boat. I comment on the book, interpret it in my own fashion, expound the text, sound the reefs, until daylight comes and leads us to the haven of the solution. Besides, the logic is so irresistible, it is all such easy going and so lucid that often one seems to be remembering rather than learning. And so we proceed, with our positions reversed. My comrade—I can now allow myself to speak of him on equal terms—my comrade listens, suggests objections, raises difficulties which we try to solve in unison. After fifteen months of this exercise, we went up together for our examination at Montpellier; and both of us received our degrees as bachelors of mathematical science. My companion was a wreck; I, on the other hand, had refreshed my mind with analytical geometry. [36] The quartermaster declared himself satisfied with this achievement. Analytic geometry did not precisely strike him as a recreation. He knew enough of it for what he had to do; he did not want to know any more. In vain I hold out the glittering prospect of a new degree, that of licentiate of mathematical science, which would lead us to the splendours of the higher mathematics and initiate us into the mechanics of the heavens: I cannot prevail upon him, cannot make him share my audacity. He calls it a mad scheme, which will exhaust us and come to nothing. I am free to go and break my neck in distant countries; he is more prudent and will not follow me. My partner, therefore, leaves me. Henceforth, I am alone, alone and wretched. There is no one left with whom I can sit up and thresh out the subject in exhilarating discussion. [37] And now let us note the words and the emotions with which he approaches for the last time, in his declining years, this town of Carpentras, where, from his earliest youth, he suffered so greatly and laboured so valiantly: