Renato Fucini.
Renato Fucini.
Renato Fucini.
Renato Fucini.
THE THEOREM OF PYTHAGORAS.
“The forty-seventh proposition!” said Professor Roveni, in a tone of mild sarcasm, as he unfolded a paper which I had extracted, very gingerly, from an urn standing on his desk. Then he showed it to the Government Inspector who stood beside him, and whispered something into his ear. Finally, he handed me the document, so that I might read the question with my own eyes.
“Go up to the blackboard,” added the Professor, rubbing his hands.
The candidate who had preceded me in the arduous trial, and had got out of it as best he could, had left theschool-room on tiptoe, and, in opening the door, let in a long streak of sunshine, which flickered on wall and floor, and in which I had the satisfaction of seeing my shadow. The door closed again, and the room was once more plunged into twilight. It was a stifling day in August, and the great sun-blinds of blue canvas were a feeble defence against the glass, so that the Venetian shutters had been closed as well. The little light which remained was concentrated on the master’s desk and the blackboard, and was, at any rate, sufficient to illuminate my defeat.
“Go to the blackboard and draw the figure,” repeated Professor Roveni, perceiving my hesitation.
Tracing the figure was the only thing I knew how to do; so I took a piece of chalk and conscientiously went to work. I was in no hurry; the more time I took up in this graphic part, the less remained for oral explanation.
But the Professor was not the man to lend himself to my innocent artifice.
“Make haste,” he said. “You are not going to draw one of Raphael’s Madonnas.”
I had to come to an end.
“Put the letters now. Quick!—you are not giving specimens of handwriting. Why did you erase that G?”
“Because it is too much like the C I have made already. I was going to put an H instead of it.”
“What a subtle idea!” observed Roveni, with his usual irony. “Have you finished?”
“Yes, sir,” said I; adding under my breath, “More’s the pity!”
“Come,—why are you standing there moonstruck? Enunciate the theorem!”
Then began my sorrows. The terms of the question had escaped my memory.
“In a triangle ...” I stammered.
“Go on.”
I took courage and said all I knew.
“In a triangle ... the square of the hypothenuse is equal to the squares of the other two sides.”
“In any triangle?”
“No, no!” suggested a compassionate soul behind me.
“No, sir!” said I.
“Explain yourself. In what sort of a triangle?”
“A right-angled triangle,” whispered the prompting voice.
“A right-angled triangle,” I repeated, like a parrot.
“Silence there, behind!” shouted the Professor; and then continued, turning to me, “Then, according to you, the big square is equal to each of the smaller ones?”
Good gracious! the thing was absurd. But I had a happy inspiration.
“No, sir, to both of them added together.”
“To the sum then,—say to the sum. And you should sayequivalent, not equal. Now demonstrate.”
I was in a cold perspiration—icy cold—despite the tropical temperature. I looked stupidly at the right-angled triangle, the square of the hypothenuse, and its two subsidiary squares; I passed the chalk from one hand to the otherand back again, and said nothing, for the very good reason that I had nothing to say.
No one prompted me any more. It was so still you might have heard a pin drop. The Professor fixed his grey eyes on me, bright with a malignant joy; the Government Inspector was making notes on a piece of paper. Suddenly the latter respectable personage cleared his throat, and Professor Roveni said in his most insinuating manner, “Well?”
I did not reply.
Instead of at once sending me about my business, the Professor wished to imitate the cat which plays with the mouse before tearing it to pieces.
“How?” he added. “Perhaps you are seeking a new solution. I do not say that such may not be found, but we shall be quite satisfied with one of the old ones. Go on. Have you forgotten that you ought to produce the two sides, DE, MF, till they meet? Produce them—go on!”
I obeyed mechanically. The figure seemed to attain a gigantic size, and weighed on my chest like a block of stone.
“Put a letter at the point where they meet—an N. So. And now?”
I remained silent.
“Don’t you think it necessary to draw a line down from N through A to the base of the square, BHIC?”
I thought nothing of the kind; however, I obeyed.
“Now you will have to produce the two sides, BH and IC.”
Ouf! I could endure no more.
“Now,” the Professor went on, “a child of two could do the demonstration. Have you nothing to observe with reference to the two triangles, BAC and NAE?”
As silence only prolonged my torture, I replied laconically, “Nothing.”
“In other words, you know nothing at all?”
“I think you ought to have seen that some time ago,” I replied, with a calm worthy of Socrates.
“Very good, very good! Is that the tone you take? And don’t you even know that the theorem of Pythagoras is also called the Asses’ Bridge, because it is just the asses who cannot get past it? You can go. I hope you understand that you have not passed in this examination. That will teach you to readDon Quixoteand draw cats during my lessons!”
The Government Inspector took a pinch of snuff; I laid down the chalk and the duster, and walked majestically out of the hall, amid the stifled laughter of my school-fellows.
Three or four comrades who had already passed through the ordeal with no very brilliant result were waiting for me outside.
“Ploughed, then?”
“Ploughed!” I replied, throwing myself into an attitude of heroic defiance; adding presently, “I always said that mathematics were only made for dunces.”
“Of course!” exclaimed one of my rivals.
“What question did you have?” asked another.
“The forty-seventh proposition. What can it matter to me whether the square of the hypothenuse is or is not equal to the sum of the squares of the two sides?”
“Of course it can’t matter to you—nor to me—nor to any one in the world,” chimed in a third with all the petulant ignorance of fourteen. “If it is equal, why do they want to have it repeated so often? and if it is not, why do they bother us with it?”
“Believe me, you fellows,” said I, resuming the discussion with the air of a person of long experience, “you may be quite certain of it, the whole system of instruction is wrong; and as long as the Germans are in the country, it will be so!”
So, being fully persuaded that our failure was a protest against the Austrian dominion, and a proof of vivid and original genius, we went home, where, for my part, I confess I found that the first enthusiasm soon evaporated.
My ignominious failure in this examination had a great influence on my future. Since it was absolutely impossible for me to understand mathematics, it was decided that very day that I was to leave school, especially as the family finances made it necessary for me to begin earning something as soon as might be.
It was the most sensible resolution that could have been come to, and I had no right to oppose it; yet, I confess, I was deeply saddened by it. My aversion to mathematics did not extend to other branches of learning, in which I had made quite a respectable show; and besides, I loved the school. I loved those sacred cloisters which we boys filled with life and noise,—I loved the benches carved with our names,—even the blackboard which had been the witness of my irreparable defeat.
I blamed Pythagoras’ theorem for it all. With some other question—who knows?—I might just have scraped through, by the skin of my teeth, as I had done in past years. But, as Fate would have it, it was just that one!
I dreamt about it all night. I saw it before me—the fatal square with its triangle atop, and the two smaller squares, one sloping to the right, and the other to the left, and a tangle of lines, and a great confusion of letters; and heard beating through my head like the strokes of a hammer—BAC = NAF; RNAB = DEAB.
It was some time before I was free from that nightmare and could forget Pythagoras and his three squares. In the long run, however, Time, who with his sponge wipes out so many things from the book of memory, had nearly effaced this; when, a few weeks ago, the ill-omened figure appeared to me in one of my son’s exercise-books.
“Has this curse been transmitted to my descendants?” I exclaimed. “Poor boy! What if the theorem of Pythagoras should be as fatal to him as it has been to me?”
I thought I would question him about it on his return from school.
“So,” I began gravely, “you have already reached the forty-seventh proposition of Euclid in your geometry?”
“Yes, father,” he replied simply.
“A difficult theorem,” I added, shaking my head.
“Do you think so?” he asked with a smile.
“Oh! you want to boast and make me think you find it easy?”
“But I do find it easy.”
“I should like to see you try it”—the words slipped out almost involuntarily. “It’s no use—I can’t bear vanity and boasting.”
“At once,” replied the dauntless youth. And action succeeded words. He took a piece of paper and a pencil, and quickly traced the cabalistic figure.
“As for demonstrations,” he began, “there are plenty to choose from. Is it all the same to you which I take?”
“Yes,” I replied mechanically. In fact ithadto be all the same to me. If there had been a hundred demonstrations I should not have known one from the other.
“Then we’ll take the most usual one,” my mathematician went on; and proceeded to produce the lines which Professor Roveni, of respected memory, had made me produce twenty-seven years before, and, with the accents of the sincerest conviction, prepared to prove to me that the triangle BAC was equal to the triangle NAF, and so on.
“And now,” said my son, when he had finished, “we can, if you wish, arrive at the same conclusion in another way.”
“For pity’s sake!” I exclaimed in terror, “since we have reached the journey’s end, let us rest.”
“But I am not tired.”
Not even tired! Was the boy an embryo Newton? And yet people talk about the principle of heredity!
“I suppose you are at the top of your class in mathematics,” I said, not untouched by a certain reverential awe.
“No, no,” he replied. “There are two better than I. Besides, you know very well that everybody—except downright asses—understands the forty-seventh proposition.”
“Except downright asses!” After twenty-seven years I heard, from the lips of my own son, almost the very identical words which Professor Roveni had used on the memorable day of the examination. And this time they were heightened by the savage irony of the added “You know very well!”
I wished to save appearances, and added in haste—
“Of course I know that. I was only in fun. I hope you would not be such a fool as to be proud of a small thing like that.”
Meanwhile, however, my Newton had repented of his too sweeping assertion.
“After all,” he went on, with some embarrassment, “there are some who never attend to their lesson, and then ... even if they are not asses....”
It seemed to me that he was offering me a loophole of escape, and with a sudden impulse of candour—
“That must be the way of it,” I said. “I suppose I never paid attention.”
“How! You?” exclaimed my boy, reddening to the roots of his hair. Yet ... I would bet something that, at the bottom of his heart, he was longing to laugh.
I put my hand over his mouth.
“Hush,” I said; “we will not pursue our inquiries into detail.”
Well, the Theorem of Pythagoras has, as you see, cost me a new and very serious humiliation. In spite of this, I no longer keep up the old grudge. There will never be any confidence between us, but I consider it as a family friend whom we must not treat with rudeness, though he may not be personally congenial to ourselves.
Enrico Castelnuovo.
Enrico Castelnuovo.
Enrico Castelnuovo.
Enrico Castelnuovo.