## A New and Concise System of Arithmetick: Containing Vulgar, Decimal, and Logarithmical Arithmetick; Calculated for the Use of the Inhabitants of the United States; Wherein is Shown a Universal Mode of Cancelling ... |

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### Common terms and phrases

added amount annex ansr answer base breadth called carry cent circle column common compound consequently contained continue cost cube currency cyphers decimal denominator diameter difference direct divide dividend division divisor dollars double equal EXAMPLE extract extremes farthings feet figure foot four fourth fraction gain given given number gives greater greatest half hundred inches integer interest left hand length less logarithm manner mean measure method middle mixed months multiply Note observe OPERATION payment pence perpendicular pounds present principal PROBLEM PROOF proportion quantity question quotient ratio reason reduce remainder repeating right hand root RULE shillings side simple solid sought square square root stand subtract superficial Suppose taken term things third unit unity weight whole worth yards

### Popular passages

Page 276 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...

Page 267 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.

Page 13 - Alligation alternate is the method of finding what quantity of any number of simples, whose rates are given, will compose a mixture of a given rate ; so that it is the reverse of Alligation medial, and may be proved by it. RULE 1.* 1. Write the rates of the simples in a column under each other.

Page 3 - If the errors are alike, divide the difference of tire products by the difference of the errors, and the quotient will be the answer. 5. If the errors are unlike, divide the sum of the products by the sum of the errors, and the quotient will be the answer.

Page 36 - Division : 1. The Dividend, or number given to be divided. 2. The Divisor, or number given to divide by. 3. The Quotient, or answer to the question, which shows how many times the divisor is contained in the dividend. 4. The Remainder, which is always less than the divisor, and of the same name with the Dividend.

Page 267 - RULE. 1 . Separate the given number into periods of three figures each, by putting a point over the unit figure and every third figure bejond the place of units.

Page 79 - Multiply each numerator into all the denominators except its own, for a new numerator : and all the denominators into each other continually for a common denominator; this written under the several new numerators will give the fractions required.

Page 2 - RULE. 1 . Take any number and perform the same operations with it as are described to be performed in the question. 2. Then say as the sum of the errors is to the given sum, so is the supposed number to the true one required.* , PROOF. Add the several parts of the sum together, and if it agree with the sum, it is right.

Page 75 - Divide by any number that will divide two or more of the given numbers without a remainder, and set the quotients, together with the undivided numbers, in a line beneath.

Page 208 - Multiply the first and second terms together, and divide the product by the third ; the quotient will be the answer in the same denomination as the middle term was reduced into.