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Updated: May 3, 2025
Darling's beautiful, slender, graceful, blue-eyed girl with long, golden curls and rosy cheeks." The binomial system revolutionized the science. What the lines of longitude and latitude did for geography Linnæus' genius did for botany. And he did not let pride of achievement persuade him that he had said the last word.
It is said that Newton discovered the binomial theorem by induction; by raising a binomial successively to a certain number of powers, and comparing those powers with one another until he detected the relation in which the algebraic formula of each power stands to the exponent of that power, and to the two terms of the binomial.
I am sure that if the dove on the woman's finger had opened its painted bill and spoken, say about the binomial theorem, or the Effect of Too Much Culture upon Women's Clubs, I should have listened with equal gravity and the same abysmal absence of surprise. I pattered platitudinously: "The greatest of the Greeks considered the body divine in itself, my son, and so their noblest art was nude.
By means of the Arithmetical Triangle, an invention equally ingenious and original, he succeeded in solving a number of theorems which it would have been difficult to demonstrate in any other way, and in finding the coefficients of different terms of a binomial raised to an even and positive power.
Doubtless it is true that some native or intuitive gifts must be conjoined with much mental discipline and perseverance, in order to reach the highest result, in this method of reading, as in any other study. "Non omnia possumus omnes," Virgil says; and there are intellects who could no more master such a method, than they could understand the binomial theorem, or calculate the orbit of Uranus.
Linnaeus himself made several unsatisfactory attempts before he finally hit upon his system of "trivial names," which was developed in his Species plantarum, and which, with some, minor alterations, remains in use to this day. The essence of the system is the introduction of binomial nomenclature that is to say, the use of two names and no more to designate any single species of animal or plant.
"Except the binomial theorem," said Hamish, laughing. His sister shook her head at him too. Charmed with the "new kind of arithmetic" which Mr Rugg had brought, yet not enjoying any pleasure to the full unless his sister enjoyed it with him, Hamish had tried to beguile her into giving her spare hours to the study.
To him the world is indebted for the binomial theorem, discovered at the age of twenty-two; for the invention of fluxions; for the demonstration of the law of gravitation; and for the discovery of the different refrangibility of rays of light.
At the age of twenty-one he wrote a treatise upon the Binomial Theorem, which has had a European vogue. On the strength of it he won the Mathematical Chair at one of our smaller universities, and had, to all appearances, a most brilliant career before him. But the man had hereditary tendencies of the most diabolical kind.
With no knowledge of algebra except what was derived from the meagre text-books I could pick up, not having heard even the name of Abel, or knowing what view of the subject was taken by professional mathematicians, I made my first attempt at a scientific article, "A New Demonstration of the Binomial Theorem."
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