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that would preclude any reference to subsequent principles. Such a plan could, indeed, not be adopted, without destroying that classification of the Rules, which is so highly useful for the sake of reference, and it has therefore been left to the judgment of the intelligent teacher, to make those selections which he may find best adapted to the capacities, the previous knowledge, and the objects of his pupils.

It has been in deference to these precedents, that the doctrine of fractions and decimals, which should properly follow the theory of whole numbers, has here been placed after the course of those calculations which are required for the common purposes of Commerce; but this does not preclude their being used at any period of the pupil's practice, the earlier the better, because many of the previous exercises can be rendered more easy and concise by the employment of the decimal instead of the usual separations of the integer, and to clearly understand the principles of many operations that may almost be considered but as elementary, requires some knowledge of the nature and modes of using ordinary fractions.

In the arrangement of those branches of calculations which are dependent on mercantile usages, the principle here adopted, is, to place those first which are either the most useful or the most easy : consequently, those which particularly belong to the higher departments of the Counting-house, as well as those which are difficult to be surmounted, have been selected, and formed into an Appendix, that may be employed either in continuation of this work, or as a supplement to any other system of Arithmetic.

As it is more by the exercise of his own judgment, than by a rigid adherence to general rules, that any one can acquire great facility in calculations, advantage has been taken of every opportunity to show the learner the best means by which it can be directed; and as a powerful auxiliary, mental arithmetic has received great attention, as will be found from a variety of new rules and observations, which have been interspersed throughout this treatise.

In conclusion, it is incumbent on me to state, in support of my claims to public confidence, that in all subjects relating to Commerce, very valuable

assistance has been afforded me by several gentlemen of great experience in business, and no pains have been spared to procure whatever information might contribute to insure the work a favourable reception.

W. TATE, Junr. Commercial Academy, Well Court, Queen Street,

London.

P. S. In a Key, which will shortly be published, further explanations of the best methods of working the more difficult calculations will be given, as well as the routine of business which directs their application.

ALGEBRAIC CHARACTERS

USED IN

ARITHMETICAL OPERATIONS.

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The sign of Addition, and also of excess: thus, 5 + 2 denotes that 2 is added to 5; also, 5 + means that there is excess in the result beyond 5, or that the result is more than 5.

minus

The sign of Subtraction, and also of deficiency: thus, 5 — 2 denotes that 2 is taken from 5; also, 5 means, that the result is less than 5.

X into

The sign of Multiplication : as, 5 X 4 means that 5 is multiplied by 4.

• by

The sign of Division : as, 5 • 2 means that 5 is divided by 2.

= equal to The sign of Equality : as, 4 + 3 = 11 -4 = 7

means that the sum of 4 and 3 is equal to the difference of 11 and 4, or that each is equal to 7.

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