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Updated: May 18, 2025
Among the original things in Pappus's Collection is an enunciation which amounts to an anticipation of what is known as Guldin's Theorem. For calculating arcs in astronomy from other arcs given by means of tables he used propositions in spherical trigonometry.
The courtships are varied between abrupt embraces soon after introduction, and discussions on Hebrew, Babel, "Christian-deism," and the binomial theorem.
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.
Irving returned to his platform. His hands were trembling, and he felt weak. When he spoke, he hardly knew his own voice. But he struggled to control it, and said,— “Scarborough, please go to the board and demonstrate your theorem.” There was no more disorder in class that day; in fact, after Westby’s disappearance the boys were exceptionally well behaved.
In this example there is no induction, because there is no inference: the conclusion is a mere summing up of what was asserted in the various propositions from which it is drawn. A case somewhat, though not altogether, similar, is the proof of a geometrical theorem by means of a diagram.
He has written three lines of a simple nudity that reveals much, in which he says: "A man is responsible for the crimes which he commits; if, in committing a crime, his will is half free, he is responsible to the extent of one-half; if one-third, he is responsible one-third." There you have the uncompromising and absolute classic theorem.
See here! what I've got to do," said Tom, drawing Maggie toward him and showing her his theorem, while she pushed her hair behind her ears, and prepared herself to prove her capability of helping him in Euclid. She began to read with full confidence in her own powers, but presently, becoming quite bewildered, her face flushed with irritation.
Every theorem in geometry is a law of external nature, and might have been ascertained by generalizing from observation and experiment, which in this case resolve themselves into comparison and measurement.
It never seems to occur to the teacher that the pupil of the third grade might give the words of the binomial theorem without the slightest apprehension of its meaning. We grade for the repetition of words, not for intelligence.
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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