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Updated: May 18, 2025
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. 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
It grew, as all his ideas grew, not out of a theorem, not from a constitutional interpretation, but from his overpowering commiseration for the mass of mankind. It was a practical matter. Here were poor people to be assisted, to be enriched in their estate, to be enlarged in spirit. The mode of reaching the result was not the thing. Any mode, all sorts of modes, might be used.
A fact, not a principle; for the old theorem of sovereignty remains undisputed as ever. Neither the nation, in mass, nor the citizens, in class, lay claim to human rights. All upper attributes legislative, judicial, administrative remain in the land-master's breast alone. It is an absurdity, therefore, to argue with Grotius concerning the unknown antiquity of the Batavian republic.
Not the wretchedest circulating-library novel, which foolish girls thumb and con in remote villages, but will help to regulate the actual practical weddings and households of those foolish girls. So "Celia" felt, so "Clifford" acted: the foolish Theorem of Life, stamped into those young brains, comes out as a solid Practice one day. What built St. Paul's Cathedral?
I immediately stepped down from the pontifical chair, and asked the little man to occupy it and tell us more about the matter, which he did. Whether the theorem to which I have alluded was included in his statement, I do not recall. If it was not, he told me about it subsequently, and spoke of a paper he had published, or was about to publish, in the "American Journal of Science."
But though each of these inventors proved the theorem that a heavier-than-air machine could be made to fly, all failed to get practical results because no motor had then been invented which combined the necessary lightness with the generation of the required power. In America we like to think of the brothers Wright as being the true inventors of the airplane.
If we represent by N the angular velocity of the earth, and by M the angular velocity of the moon in its orbit round the earth, the quantity we desire to express is N M; we shall call it the relative rotation. The mathematical theorem which tells us what we want can be enunciated in a concise manner as follows.
When Pythagoras discovered the theorem of the squares erected on the sides of a right-angled triangle, it had the effect on him of a most preposterous joke. The apple dropping on the head of Newton struck him like a very far-fetched pun. Show a child the picture of a wild Tartar, and his first motion will be to laugh at it.
The discovery of the binomial theorem was an effort of genius; but there was none shown in Jedediah Buxton's being able to multiply 9 figures by 9 in his head. If he could have multiplied 90 figures by 90 instead of 9, it would have been equally useless toil and trouble. He is a man of capacity who possesses considerable intellectual riches: he is a man of genius who finds out a vein of new ore.
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.
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