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When we demonstrate the forty-seventh proposition of Euclid, it is not necessary that the words should raise in us an image of all right-angled triangles, but only of some one right-angled triangle: so in algebra we need not, under the symbol a, picture to ourselves all things whatever, but only some one thing; why not, then, the letter itself?
Yet, during his father's long illness, and after his death, when Elihu was but a lad in his teens, with the family partially dependent upon the work of his hands, he found time, if only a few moments, at the end of a fourteen-hour day of labor, for his books. While working at his trade as a blacksmith, he solved problems in arithmetic and algebra while his irons were heating.
I'm working like a nigger at algebra and Euclid this half, just because I think it would almost kill me to be beaten again by a low cad. This was perhaps the first time that Godwin found expression for the prejudice which affected all his thoughts and feelings. It relieved him to have spoken thus; henceforth he had become clear as to his point of view.
So the algebra was of some use in the world after all; Algernon Kirkendall was a scout without knowing it. "S.N. thinks more of that new car than he does of the troop," said Fido. "Sure, the car don't give him as much trouble," said Nick. "We're a Hunkajunk troop and Safety First's troop is a Ford troop; it's small but it makes a lot of noise. If I ever start a troop it will be air-cooled.
And there had always been, as far back as she could remember, only little Miss Masten to teach multiplication and geography and algebra alike; she and the other children who made up the "advanced grade" of the school at Miller's Notch always called her "Miss Sarah." Would there be anyone like Miss Sarah at Lincoln?
Accordingly, while Jean struggled with French, algebra, drawing, history, and literature at the new school in which Uncle Tom had entered her and while she and Fräulein Decker had many a combat with German, Giusippe began wrestling with the problems of plate glass making.
"Can he make a hundred and thirty-five ringside without being weak?" asked Sally. The effect of this simple question on Mr. Burrowes was stupendous. He dropped away from Fillmore's coat-button like an exhausted bivalve, and his small mouth opened feebly. It was as if a child had suddenly propounded to an eminent mathematician some abstruse problem in the higher algebra.
But lower, much lower in the shopkeeper's estimate than even such commodities thrown into a bin because they were rubbish, and yet not quite valueless was a mass of odd volumes. The First Principles of Algebra, Acts Relating to Pawnbrokers, and Jessica's First Prayer, were discovered in that order. The next was Superstitions of the Sea. I am not superstitious. I have never met a man who was.
Else, important departments will be overlaid, as in Oxford and in Harvard, natural history was until now. Now, it looks as if natural history would obtain in time to come the like predominance as mathematics have here, or Greek at Oxford. It will not grieve me if it should, for we are all curious of nature, but not of algebra.
I never saw an algebra, or other mathematical work higher than the arithmetic, in Georgetown, until after I was appointed to West Point. I then bought a work on algebra in Cincinnati; but having no teacher it was Greek to me. My life in Georgetown was uneventful.
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