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Updated: May 18, 2025
Every induction, therefore, which suffices to prove one fact, proves an indefinite multitude of facts: the experience which justifies a single prediction must be such as will suffice to bear out a general theorem.
His discovery of the Binomial Theorem and its most important applications, as well as his still greater discovery of the Law of Gravitation, were not published for years after they were made; and when he communicated to Collins his solution of the theory of the moon's rotation round the earth, he forbade him to insert his name in connection with it in the 'Philosophical Transactions, saying: "It would, perhaps, increase my acquaintance the thing which I chiefly study to decline."
So long as men can be induced to THINK there is hope for the race. Although his Single Tax theorem will perish, it has served a good purpose. A Denver party wants to know if I would KNEEL if given an audience by the Pope of Rome. I would be pretty apt to do so if such action on my part was expected.
There are many things in the "eternal womanly" which men understand about as well as a kitten does the binomial theorem, but some mysteries become simple enough when the leading fact is grasped that woman's song of life is written in a minor key and that she actually enjoys the semblance of sorrow. Still, the average woman wishes to be idealised and strongly objects to being understood.
What is proved true from one geometrical theorem, what would be true if no other geometrical principles existed, can not be altered and made no longer true by reason of some other geometrical principle. What is once proved true is true in all cases, whatever supposition may be made in regard to any other matter.
Painful recollections of my boyhood and the binomial theorem rose in my mind as I let the leaves turn under my fingers. "What do you make of it?" I asked. His tone became even more confidential. "Part of it, monsieur, is in English; that is plain. I have found an English word in it that I know the word 'O. But much of the printing is also in Arabic." "Arabic!" I exclaimed.
According to Sir W. Thomson's theory of Vortex Atoms, the substance of which the molecule consists is a uniformly dense plenum, the properties of which are those of a perfect fluid, the molecule itself being nothing but a certain motion impressed on a portion of this fluid, and this motion is shewn, by a theorem due to Helmholtz, to be as indestructible as we believe a portion of matter to be.
The ideas of a man who has taken his boots and his suspenders off, are no longer those of a man who is still sporting these two tyrants of the mind. Take notice that this is only an axiom in wedded life. In morals, it is what we call a relative theorem. Caroline watches, like a jockey on the race course, the moment when she can distance her adversary.
By this time he had reached the banks of the Serpentine and was approaching the grey stone bridge that crosses just where Hyde Park ends and Kensington Gardens begins. Following upon his doubts of his religious faith had come another still more extraordinary question: "Although there is a God, does he indeed matter more in our ordinary lives than that same demonstrable Binomial Theorem?
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.
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