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Excerpt from An Elementary Treatise on Algebra: Theoretical and Practical
In the following Treatise it has been the aim of the Author to render the various investigations and processes as simple natural, and easy as possible, and to establish and illustrate the principles in a plain and familiar manner. He trusts, in particular, that the modes in which he has established the rule for subtraction (not new, he admits, in principle), and the rule for the signs in multiplication and division, and also the methods which he has employed in explaining the theory of fractions and radicals, will divest those subjects of much of the mystery and difficulty which have unnecessarily been thrown around them. In a similar manner, using freely, but not servilely, what has been done by previous writers, he has endeavoured to simplify the elementary principles and processes in the resolution of equations; and he hopes that the views and explanations which he has given regarding infinite quantities and the sums of infinite series, will remove much of the difficulty which is very generally and very naturally felt in reference to those subjects. Of the binomial theorem, he has given a proof which he considers simple and easy; and the experienced algebraist will recognise various other improvements in the course of the work, which it is unnecessary here to particularise.
Much absolute novelty, unless in the mode of exposition, cannot now be expected in a work on algebra. Some things, however, the Author believes are new altogether, while others are now for the first time fully developed, and extensively and advantageously applied. Of this kind is the method of detached co-efficients, which is explained and exemplified in pages 26.35, 84, &c; a method which is at once greatly shorter and easier than the common one, and which, throughout the operation, relieves the mind from the trouble and fatigue of considering what powers of the quantities are to be written in the several terms.
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