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Treatise, is to present a full and regular course of whatever is useful in A rithmetic. With this view, rules are given for performing all the requisite operations, and are illustrated by many examples; and numerous exercises are prescribed, to afford the pupil that practice which alone can produce expertness and accuracy in the management of numbers. The Definitions andR ules, which it may perhaps be proper for the learner to commit to memory, are in the largest type employed in the work; theE xamples andE xercises, and the principal illustrations, are in a character somewhat smaller; the less important illustrations and remarks are in a type still smaller, and may perhaps be omitted by the younger pupil ;and the notes contain miscellaneous information, which may often be interesting to the reader. The reasons of the rules and operations are explained, not in strict, formal demonstrations, but generally by simple and easy illustrations of particular cases and examples; and it is hoped, that the subject will thus be rendered as intelligible and attractive as possible. This part of Arithmetic is too generally neglected, both in treatises on the subject, and in teaching: and thus one of the principal divisions of Mathematical Science is converted into a mere practical art; and what is calculated to call forth and improve the reasoning powers of the pupil, is degraded into a dry exercise of memory. Of theE xamples andE xercises, some are proposed in purely abstract terras, being intended merely to afford practice to the learner in the rules and modes of calculation. To these are subjoined, in those parts of the work in which it conid be conveniently done, other questions, which will not only afford the pupil farther exercise on the rules which precede them, but will also furnish him with many important facts inC ommerce, Geography, A stronomy, Chronology, Chemi
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