Excerpt from Arithmetic, in Which the Principles of Operating by Numbers Are Analytically Explained, and Synthetically Applied: Illustrated by Copious Examples; Designed for the Use of Schools and Academies

Care has been taken to avoid an arbitrary arrangement, whereby the processes will be purely mechanical to the learner. If, for instance, all the reductions in common fractions precede the other operations, the pupil will have occasion to divide one raction by another long before he shall have learned the method of doing it, and must proceed by a rule, to himself perfectly unintelligible. The studied aim has been through out the entire work to enable the ordinary pupil to understand every thing as he advances. The author is yet to be convinced that mental discipline will be promoted, or any desirable end be subserved, by con ducting the pupil through blind, mechanical processes. Just so far as he can understand, and no farther, is there prospect of benefit. No good results from presenting things, however excellent in themselves, if they are beyond the comprehension Of the learner.

Those teachers who prefer to examine their classes by questions, will find that little will escape the pupil's attention, who shall correctly an swer all those in the present work, while teachers who practise the far superior method Of recitation by analysis, will find the work admirably adapted to their purpose.

The examples, it is hoped, will require very full applications of the principles.

Many antiquated things, which it has been fashionable to copy in arithmetics, from time immemorial, have been omitted or improved, while new and practical matter has been introduced. A Key to this revision is in progress.

With these remarks, the work is submitted to the candid examination of the public, by the author.

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