# An Introduction to the Elements of Algebra; Designed for the Use of Those Who Are Acquainted Only with the First Principles of Arithmetic

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1821 edition. Excerpt: ...denominator has been increased to infinity. M. It is the more necessary to pay attention to this idea of infinity, as it is derived from the first foundations of our knowledge, and as it will be of the greatest importance in the following part of this treatise. We may here deduce from it a few consequences, that are extremely curious and worthy of attention. The fraction F, represents the quotient resulting from the division of the dividend 1 by the divisor oc. Now we know that if we divide the dividend 1 by the quotient, which is equal to 0, we obtain again the divisor Qd: hence we acquire a new idea of infinity; we learn that it arises from the division of 1 by 0; and we are therefore entitled to say, that 1 divided by 0 expresses a number infinitely great, or oo. 84. It may be necessary also in this place to correct the mistake of those who assert, that a number infinitely great is not susceptible of increase. This opinion is inconsistent with the just principles which we have laid down; for signifying a number infinitely great, and being incontestably the double of, it is evident that a number, though infinitely great, may still become twe or more times greater. CHAPTER VIII. Of the properties of Fractions. 85. We have already seen, that each of the fractions, makes an integer, and that consequently they are all equal to one another. The same equality exists in the following fractions, 1 4 t - 10 If T, T, 7' 1, T, y' occ-, each of them making two integers; for the numerator of each, divided by its denominator, gives 2. So all the fractions 3 6 9 13 15 It.W T', 7' T, T, ff Kc-, are equal to one another, since 3 is their common value. M. We may likewise represent the value of any fraction, in an infinite variety of ways. For...