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The fact is not improbable: but a mathematician like Newton, who seemed to arrive per saltum at principles and conclusions that ordinary mathematicians only reached by a succession of steps, certainly could not have performed the comparison in question without being led by it to the a priori ground of the law; since any one who understands sufficiently the nature of multiplication to venture upon multiplying several lines of symbols at one operation, can not but perceive that in raising a binomial to a power, the co-efficients must depend on the laws of permutation and combination: and as soon as this is recognized, the theorem is demonstrated.
A chapter catches my attention in the middle of the volume; it is headed, Newton's Binomial Theorem. The title allures me. What can a binomial theorem be, especially one whose author is Newton, the great English mathematician who weighed the worlds? What has the mechanism of the sky to do with this? Let us read and seek for enlightenment.
One may not find it necessary to remember the binomial theorem or the algebraic formula for the contents of a circle, but he should at least have a formal acquaintance with Julius Caesar, Hannibal, Charlemagne, Martin Luther, Francis I, Queen Elizabeth, Louis XIV, Napoleon I and a dozen or so others. An educated man must speak the language of educated men.
If I remember rightly, they were the Theory of Combinations and Newton's Binomial. I seated myself on one of the back benches and pored over the two questions, but, inasmuch as I was not accustomed to working in a noisy room, and had even less time for preparation than I had anticipated, I soon found it difficult to take in all that I was reading. "Here he is.
This species has been particularly fortunate in escaping the numerous redescriptions to which almost all widely distributed forms have been subjected. By the writers of antiquity it was spoken of under its Aristotelian name, and in the tenth edition of his Systema Naturæ, at the very inception of binomial nomenclative, Linnaeus called it Xiphias gladius.
The courtships are varied between abrupt embraces soon after introduction, and discussions on Hebrew, Babel, "Christian-deism," and the binomial theorem.
He was still altogether convinced that he had to confess and proclaim God in his life. He was as sure that God was the necessary king and saviour of mankind and of a man's life, as he was of the truth of the Binomial Theorem. But what began first to fade was the idea that he had been specially called to proclaim the True God to all the world.
I'd want him to explain, too, what the binomial theorem has to do with complete living, and also the dative of reference. I got the notion, when I was struggling with that binomial theorem, that it would ultimately lead on to fame or fortune; but it hasn't done either, so far as I can make out.
I have known since Childhood that Education is more desirable than Paltry Gold. Although the Newspapers and the General Public do not seem to be with me to any Extent, it is better to hob-nob with the Binomial Theorem than to dally with the Champagne Supper." In due time the Faculty gave the Degree of M.A. to what was left of Otis and still his Ambition was not satisfied.
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.
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