## 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 ... |

### Common terms and phrases

aliquot amount annexing cyphers annuity annum ansr answer arithmetical avoirdupois breadth carry cent circle common difference common ratio compound interest cube root currency decimal places diagonal diameter discount divide the product dividend divisor dollars equal EXAMPLE extract the square extremes farthings feet find the solid frustum gallons given number given sum gives greater improper fraction inches integer Irish money left hand length less livres Livres Tournois logarithm measure middle term mixed number moidore multiplicand New-Jersey New-York number of terms numbers given OPERATION payment pence perpendicular pounds present worth principal PROBLEM proportion quantity quotient reduce remainder right hand figure rule of three shew shillings side sliding rule solid content sought South-Carolina Spanish milled dollars square root subtract superficial content Suppose tare THEOREM thereof third unit unity vulgar fraction whole numbers yards cost

### Popular passages

Page 274 - 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 265 - 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 355 - 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 359 - 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 265 - 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 358 - 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.