What Geometry Will Do For A Boy

( Originally Published 1885 )

-HOW PRESIDENT LINCOLN BECAME AN EXPERT REASONER.

NOW, boys, let us have a little talk about geometry. You know it has been a famous study for boys for many ages. Euclid was an old Egyptian, who lived about three hundred years before Christ. His treatise on geometry has been the foundation for all modern works upon the subject. Plato, who lived a century earlier, founded a noted academy at Athens, and it is related that over its entrance he placed this celebrated inscription, Let no one ignorant of geometry enter here.

This branch has been considered an important part of a good education for two thou-sand years. Yet I. hear many boys in these days saying, "I don't like geometry. I wonder what good it will do me."

I once heard a very interesting story about Abraham Lincoln, which may help you to understand the " good." Before Mr. Lincoln was a candidate for President, he made a tour through New England, and lectured in many cities and towns. Among other places, he spoke in Norwich, Ct. A gentleman who heard him, and was struck with his remark-able logical power, rode the next day in the cars with Mr. Lincoln to New Haven. During the ride, the following conversation took place : —

" Mr. Lincoln, I was delighted with your lecture last evening."

" Oh, thank you ; but that was not much of a lecture ; I can do better than that."

" I have no doubt of it, Mr. Lincoln ; for whoever can do so well, must inevitably be able to do better."

Well, well, you are a good reasoner, are n't you? That is cute."

"But that reminds me," continued the gentleman, " to ask how you acquired your wonderful logical power. I have heard that you are entirely self-educated, and it is seldom that I find a self-educated man who has a good system of logic in his reasoning. How did you acquire such an acute power of analysis ? "

"Well, Mr. G., I will tell you. It was my terrible discouragement which did that for me."

" Your discouragement : what do you mean?"

"You see," said Mr. Lincoln in reply, "when I was a young man I went into an office to study law. Well, after a little while I saw that a lawyer's business was largely to prove things. And I said to myself, 'Lincoln, when is a thing proved?

That was a poser. I could not answer the question. What constitutes proof? Not evidence ; that was not the point. There may be evidence enough, but wherein consists the proof?

" You remember the old story of the German, who was tried for some crime, and they brought half a dozen respectable men who swore that they saw the prisoner commit the crime. Vell,' he replies, ' vat of dot ? Six men schwears dot dey saw me do it. I prings more nor two tozen goat men who schwears dey did not see me do it.'

" So, wherein is the proof? I groaned over the question, and finally said to myself, 'Ah, Lincoln, you can't tell.' Then I thought, ' What use is it for me to be in a law office if I can't tell when a thing is proved?' So I gave it up and left the office, and went back home, over in Kentucky."

" So you gave up the law ? "

Oh, Mr. G., don't jump at your conclusions ; that is n't logical. But really I did give up the law, and I thought I should never go back to it. This was in the fall of the year. Soon after I returned to the old log-cabin, I fell in with a copy of Euclid. I had not the slightest notion what Euclid was, and I thought I would find out. I found out ; but it was no easy job. I looked into the book and found it was all about lines, angles, surfaces, and solids ; but I could not understand it at all. I therefore began, very deliberately, at the beginning ; I learned the definitions and axioms ;; I demonstrated the first proposition; I said, that is simple enough; I went on to the next and the next ; and before spring I had gone through that old Euclid's geometry, and could demonstrate every proposition like a book.

"I knew it all from beginning to end. You could not stick me on the hardest of them. Then, in the spring, when I had got through with it, I said to myself one day, 'Ah, do you know now when a thing is proved?' And I answered right out loud, Yes, sir, I do.' ' Then you may go back to the law shop' ; and I went."

" Thank, you, Mr. Lincoln, for that story. You have answered my question. I see now where you found your logical acumen ; you dug it out of that geometry."

" Yes, I did ; often by the light of pitch-pine knots ; but I got it. Nothing but geometry will teach you the power of abstract reasoning. Only that will tell you when a thing is proved."

Said Mr. G., "I think this is a remarkable incident. How few men would have thought to ask themselves the question, When is a thing proved? What constitutes proof? And how few young men of today would be able to master the whole of Euclid in a single winter, without a teacher. And still fewer, after they had done so much, would have realized and acknowledged what geometry had done for them ; that it had told them what proof was."

So, my young friends, you may perhaps see by this incident what geometry will do for a boy.