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Updated: May 1, 2025
"Well," said Cub, bringing his feet down from the table with enough noise to rivet a conclusion; "you may call it addition, or subtraction, or multiplication, or division, or algebra, or geometry, or trigonometry, or calculus does that complete the list? I'm going to make my imagination leap across the spark gap; so here goes."
"Well, perhaps the Selenites have carried the integral calculus farther than you have; and, by the bye, what is this `integral calculus?" "It is a calculation the converse of the differential," replied Barbicane seriously. "Much obliged; it is all very clear, no doubt."
But the differential calculus shows in spite of all the protests of common sense that under certain conditions straight and crooked are identical, and reaches thereby a conclusion which is not in harmony with the common sense view of the absurdity of there being any identity between straight and crooked.
And here precisely is that which constitutes the inflexible rigour of the calculus, the luminous certainty before which every cultivated mind is forced to bow. Algebra is the oracle of the absolute truth, because it reveals nothing but what the mind had hidden in it under an amalgam of symbols. We put 2 and 2 into the machine; the rollers work and show us 4. That is all.
The kind of thing wanted is such a description of that divine work as will both explain to the unlearned the sort of thing it is the plan, the vast merit, the wonderful truths unfolded or methodized and the calculus by which all this is accomplished, and will also give a somewhat deeper insight to the uninitiated. Two treatises would do this.
Under chloroform the calculus and its nucleus were disengaged, and proved to be the handle of a tooth-brush, the exact size of which is represented in the accompanying illustration. The handle was covered with calcareous deposits, and was tightly fixed in the bladder.
"Got what?" demanded her seat-mate, who was a mathematical prodigy and had been working out problems in calculus all the way from Buffalo. "Not one of those examples of yours," laughed Betty, "only an idea, or at least about half an idea." "I don't find fractions of ideas very useful," said the seat-mate. "I never said they were," returned Betty irritably.
The following are the particulars of the instruction in the architectural branch, which commences in the student's second year, with Greek, Roman, and Mediæval architectural history, the Orders and their applications, drawing, sketching, and tracing, analytic geometry, differential calculus, physics, descriptive geometry, botany, and physical geography.
And if we consider this science in its whole extent, from common arithmetic up to the calculus of variations, the truths already ascertained seem all but infinite, and admit of indefinite extension. These truths, though affirmable of all things whatever, of course apply to them only in respect of their quantity.
I have a good mind to learn the Differential Calculus myself, only on purpose to bore you with it when you come home." "By the bye, Corrella has got a foal. Such a dear little duck of a thing, with a soft brown nose, and sweet long ears, like leaves! Do come back and see it; I am so very, very lonely!" "I hope Mr. Halbert is pretty well, and that his wound is getting quite right again.
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