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Updated: May 3, 2025
The atomic notation was as serviceable to chemistry as the binomial nomenclature and the classificatory schematism of Linnæus were to zoölogy and botany. Side by side with these advances arose in another, which also has a close parallel in the history of biological science.
I have known him explain, and re-explain, for a quarter of an hour, and invariably without success. It might be a mere pun; Mrs. Poppleton no more understood the nature of a pun than of the binomial theorem. But worse was when the jest involved some allusion. When I heard Poppleton begin to elucidate, to expound, the perspiration already on his forehead, I looked at him with imploring anguish.
Within the individual limits of fatigue and exhaustion, it obeys the law which Quetelet expressed by his binomial curve, and which I believe to be one of the fundamental laws of living and inorganic nature. At the start the force or the speed is very slight afterward a maximum of force or speed is attained and at last the force or speed again becomes very slight.
Aleck knew as much about handcuffs and fetters as he did about the binomial theorem, but he was one of those lads who are always ready to "have a try" at anything, and, after examining the square deeply-set holes which secured the anklets, he placed the two pen-blades of the knives together, forced them in as far as they would go, and tried to turn them.
"Oh, thank you; I see," said Margaret, with the kind readiness of woman, who would profess to "see" the Secret of Hegel, or the inmost heart of the Binomial Theorem, or the nature of the duties of cover-point, or the latest hypothesis about the frieze of the Parthenon, rather than be troubled with prolonged explanations, which the expositor, after all, might find it inconvenient to give.
He has represented the results of his experiments by the binomial formula, au + bu squared, and gives values for the coefficients a and b, which diminish with an increase in diameter, but would indicate greater losses of pressure than D'Aubuisson's formula.
The answer to this question is the binomial theorem. And of this nature are all the theorems of the science of number. They assert the identity of the result of different modes of formation. They affirm that some mode of formation from x, and some mode of formation from a certain function of x, produce the same number. Such, as above described, is the aim and end of the calculus.
"It seems to me that we are wasting a lot of time." Elmer nodded. "Will you go on, Mr. Steven?" he said. Challis was ashamed for his compeers. "What children we are," he thought. Steven got to work again with various arithmetical questions, which were answered instantly, and then he made a sudden leap and asked: "What is the binomial theorem?"
I was in the game morning, noon, and night; it beat marching to class to recite Horace and fiddle with the binomial theorem, as it must for every man who counts for something in the world." Throughout, Prather's tone, except for the one moment of anger, had been that of an even recital of facts by one who does not allow himself to consider anything but facts in the judgment of his position.
Now I never was capable of committing such an unheard-of enormity as being the cause of flagellation to any man by simple or quadratic equations; and it must have been the binomial theorem which had tickled his catastrophe, for it was my father's treatise which had penetrated into the new world of Buffalonian education. It is a pity, is it not, gentle reader, that such feelings do not now exist?
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