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Updated: June 22, 2025
There are nevertheless, in mathematics, some examples of so-called induction, in which the conclusion does bear the appearance of a generalization grounded on some of the particular cases included in it. A mathematician, when he has calculated a sufficient number of the terms of an algebraical or arithmetical series to have ascertained what is called the law of the series, does not hesitate to fill up any number of the succeeding terms without repeating the calculations. But I apprehend he only does so when it is apparent from
In that superstitious age, when emperors and princes daily investigated the future, by alchemy, by astrology, and by books of fate, filled with formula; as gravely and precisely set forth as algebraical equations; when men of every class, from monarch to peasant, implicitly believed in supernatural portents and prophecies, it was not singular that a somewhat striking appearance, observed in the sky some weeks previously to the battle of Mookerheyde, should have inspired many persons with a shuddering sense of impending evil.
Next Juan Antonio handed to Tartaglia eight algebraical questions which had been confided to him by Cardan, and asked for answers to them; but Tartaglia, having glanced at them, declared that they were not framed by Cardan at all, but by Giovanni Colla. Colla, he declared, had sent him one of these questions for solution some two years ago.
To the eyes of the economist, the revolutions of empires seem now like the reduction of algebraical quantities, which are inter-deducible; now like the discovery of unknown quantities, induced by the inevitable influence of time.
Earthquakes startle, but the firmness of the solid earth attracts no observation. God is thought to speak in the extraordinary, but most men do not hear His voice in the normal. Scientific godlessness formularises this tendency into a system, and proclaims that laws are everything and God a mere algebraical x. III. The lesson which they are meant to teach. God's works are a revelation of God.
This hieroglyphical or algebraical method of 'taking off' the occurrences of human life is applied with almost unvarying uniformity. Such was high art among the Egyptians; whom it is now the fashion to cry up at the expense of those impertinent Grecians, who presumed to arrive at excellence, almost at perfection, in so many departments.
Shutting their eyes to the visible world around them, they had busied themselves with burrowing in the mysterious depths of Absolute Being, grappling with the ego and the non-ego, constructing the great world, visible and invisible, out of their own puny internal self-consciousness, endeavouring to appropriate all departments of human thought, and imparting to every subject they touched the dryness and rigidity of an algebraical formula.
They opened the bundle, and found it to be composed of three slips of cotton, upon which were written, in red ink, curious things which they could not make much of. Upon one of these pieces of cotton were certain cabalistic signs, such as figures, algebraical marks, and geometrical figures. Upon another was traced a plan of some building.
I was just going to say, when I was interrupted, that one of the many ways of classifying minds is under the heads of arithmetical and algebraical intellects. All economical and practical wisdom is an extension or variation of the following arithmetical formula: 2+2=4. Every philosophical proposition has the more general character of the expression a+b=c.
The system of general language called algebraical notation does this. The expressions a and a2+3a denote, the one any number, the other the number formed from it in a particular manner. The following may be stated as the general problem of the algebraical calculus: F being a certain function of a given number, to find what function F will be of any function of that number.
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