ARITHMETIC. 321 



proportions ; by means of which it may always be resolved ; with- 

 out requiring any special rules. 



.5. Of the strictly Mercantile Rules of Arithmetic, most of which 

 depend upon the principles of proportion, we have only room to speak 

 very briefly. Tare and Trett, is a rule for making allowances in 

 selling goods by weight. Tare, is an allowance for the weight of 

 the box, bag, or other recipient ; and trett, or draft, is a per centage 

 deduction for refuse, waste, or loss. These being taken from the 

 gross weight, leave the net weight for the remainder. Interest, is 

 an allowance made for the use of money ; and is generally reckoned 

 at a certain rate per cent., per annum: that is a certain number of 

 dollars paid for the use of one hundred dollars for one year. Insu- 

 rance, paid for risks ; Brokerage or Commissions, paid for exchanges 

 or sales ; and Discount, allowed for the payment of money before it 

 becomes due ; are also usually reckoned at a certain rate per cent. 

 Loss and Gain, is the rule by which merchants discover their 

 total profit or loss, in buying or selling certain quantities at fixed 

 rates : and Fellowship relates to the division of profit or loss among 

 partners. Alligation, is the rule for finding the price of mixtures, 

 or for making mixtures of a given value. 



6. The Powers, of any number, are the successive products of 

 that number by itself, and of this product by the same number again : 

 the exponent of the power denoting how many times the same num- 

 ber is taken as a factor. One multiplication produces the square, or 

 second power, of which two is the exponent ; and a second multipli- 

 cation produces the cube, or third power, the exponent of which is 

 three. Thus 25 is the square, and 125 is the cube, of the number 5 ; 

 and its fourth power, or biquadrate, is 725. The Root, of any 

 number, is another number, which, multiplied by itself a certain 

 number of times, will produce the given number. Thus 5 is the 

 square root of 25 ; and it is the cube root of 125. Involution is the 

 process of finding powers ; and the name Evolution is given to that 

 of finding roots. 



A Progression, is a series of numbers in continued proportion. 

 In an Arithmetical series or progression, each term is found by add- 

 ing or subtracting the common difference to or from the preceding ; 

 according as the series is increasing or decreasing. In either case, 

 the sum of the series is equal to the sum of the two extreme terms 

 multiplied by half the number of terms. A series is in Geometrical 

 progression, when each term is either the product or the quotient of 

 the preceding term by a common ratio. In such a series, any four 

 consecutive terms form a geometrical proportion. The Rules of 

 Position, for which those of Algebra are a far preferable substitute, 

 we have no room to describe. 



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