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Updated: June 22, 2025
It is to this method of subjecting everywhere infinity to algebraical calculations, that the name is given of differential calculations or of fluxions and integral calculation. It is the art of numbering and measuring exactly a thing whose existence cannot be conceived.
"Nothing easier." replied the worthy secretary of the committee; and, rapidly tracing a few algebraical formulae upon paper, among which n^2 and x^2 frequently appeared, he presently said: "The sides will require a thickness of less than two inches." "Will that be enough?" asked the major doubtfully. "Clearly not!" replied the president.
Let us place the first move in a game of chess, in juxta-position with the data of an algebraical question, and their great difference will be immediately perceived. From the latter from the data the second step of the question, dependent thereupon, inevitably follows. It is modelled by the data. It must be thus and not otherwise.
An heroic method of learning to swim is to leap boldly into the sea. Let us hurl ourselves head first into the algebraical gulf; and perhaps the imminent danger of drowning will call forth efforts capable of bringing me to land. I know nothing of what he wants. It makes no difference: let's go ahead and plunge into the mystery. I shall learn by teaching.
As soon as we conceive a thing divided into equal parts, without knowing into what number of parts, we may call it a or x, and apply to it, without danger of error, every algebraical formula in the books.
For the lines of beauty there are no abscissae and ordinates; circles and ellipses are not described by means of their algebraical formulae. As one of these simplified characteristic points as a mental appliance, we look upon the principle of watching continually over the co-operation of all forces, or in other words, of keeping constantly in view that no part of them should ever be idle.
Then you could see about the next: sufficient for the day is the evil thereof. But you haven't the book. And it's no use running out to the bookshop. Algebraical treatises are not current wares. You'll have to send for one, which will take a fortnight at least. And I've promised for tomorrow, for tomorrow certain!
Arriving there, he plunged fiercely into solving algebraical equations and working out geometry exercises, determined to put out of his head forthwith all vain imaginings of an enchanted orchard, white in the moonshine, with lilts of elfin music echoing down its long arcades. The next day was Sunday and Eric went to church twice.
As time went on, this image was no longer reproduced, and the bare indication remained, until the word gradually lost all material representation, and became an algebraical sign, which merely recalled the object in question to the mind.
Here Thorndyke smiled mischievously I understood the meaning of that smile later in the evening and asked: "What do you think of the affair yourself?" "I have given it up," I answered. "To my paralysed brain, the Blackmore case is like an endless algebraical problem propounded by an insane mathematician." Thorndyke laughed at my comparison, which I flatter myself was a rather apt one.
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