This is an explanatory digression, just to let you know what sort of stage our characters are acting upon.
It was Saturday afternoon, and a half-holiday, and there was only one boy left in Dr Jolliffe's house. His name was Buller, and he was neither sick nor under punishment. His window was wide open, for it was very hot and stuffy in his little room, into which the sun poured, and on the other side of a lane which ran underneath was the cricket-field, from which the thud of balls struck by the bat, voices, and laughter resounded in a way to tempt any fellow out of his hole. But there he stuck with his elbows on the table and his head in his hands, forcing himself to concentrate his attention upon a book which lay open before him.
"Because _a divided by b_ equals _c divided by d_," he murmured, "the first quotients _m m_ are equal. Yes, I see that; again, since _a divided by b_ equals _m_ plus _x divided by b_, and _c divided by d_ equals _m_ plus _r divided by d_, hum, hum, why, in the name of all that's blue--oh, yes! I see. But then--oh, a thousand blisters on the idiot who invented this rot! But I won't be licked."
And he began again and again, sticking to it for another half-hour, when he suddenly cried out, "I have it! What a double-distilled ass I am! Of course it is simple enough. If _a divided by b_ equals _c divided by d_, and _a_ and _b_ be prime to each other, _c_ and _d_ are equimultiples of _a_ and _b_. Of course they are; how could they be anything else? The other fellows saw it at once, no doubt. What a lot of trouble it gives one to be a fool! Now, I'll go and practise bowling."
Buller was no fool; indeed he would not have thought himself one if he had been; but he was slow at everything--learning, games, accomplishments--though he had this compensation, no slight one either, that when he had once mastered a thing he had got it for ever. His school-fellows called him a duffer, but it did not vex him in the least, for he considered it a mere statement of a patent fact, and was no more offended than if they had said that he had two legs. But he had a strong belief that perseverance, _sticking_, he called it, could make up in a great measure for want of natural ability. The fable of the hare and tortoise had given him great encouragement, and, finding in practice that he passed boys who had far more brilliant parts than himself, he never gave way to despair, however hopeless the task before him might seem.