## A New and Complete System of Arithmetick: Composed for the Use of the Citizens of the United States |

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### Common terms and phrases

added amount annuity annum answer Balance base body Book bushels called cent circle common difference compound contained continued cost cube debt decimal denominator diameter difference discount distance Divide dividend divisor dollars double equal evident EXAMPLES expressed extract extremes fall feet figure foot four fourth fraction gain gallons give given gold greater greatest half hand Hence hundred inches interest last term least length less livres loss manner mean measure method miles months Multiply Note number of terms operation paid payment pence pounds present worth principal Prob PROBLEM Proof proportion quantity question quotient ratio received Reduce remainder root Rule shillings side simple solid square square root subtract Suppose Table taken things third true unit weight whole yard

### Popular passages

Page 199 - 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 239 - Write down a few of the leading terms of the series, and begin the indices with a cypher : Thus, 0, 1, 2, 3, &c. 2. Add together the most convenient indices to make an index less by 1 than the number expressing the place of the term sought.

Page 197 - RULE. 1. Separate the given number into periods of three figures each, by putting a point over the unit figure and every third figure beyond the place of units. 2. Find the greatest cube in the left hand period, and put its root in the quotient. 3.

Page 275 - The present worth of any sum, due some time hence, is such a sum, as, if put to interest, would in that time, and at the rate per cent. for which the discount is to be made, amount to the sum or debt then due.

Page 221 - PROBLEM II. The first term, the last term, and the number of terms given, to find the common difference. RULE. — Divide the difference of the extremes by the number of terms less 1 , and the quotient will be the common diffcrenct.

Page 78 - Multiply all the numerators together for a new numerator, and all the denominators for a new denominator; and they will form the fraction required.

Page 372 - A hare starts 12 rods before a hound ; but is not perceived by him till she has been up 45 seconds ; she scuds away at the rate of 10 miles an hour ; and the dog, on view, makes after her at the rate of 16 miles an hour ; how long will the course hold, and what space will be run over, from the spot where the dog started ? Ans.

Page 383 - As the distance between the body to be raised, or balanced, and the fulcrum, or prop, is to the distance between the prop and the point where the power is applied, so is the power to the weight which it will balance.

Page 84 - To reduce any given quantity to the fraction of any greater denomination of the same kind. RULE. — Reduce the given quantity to the lowest term mentioned for a.

Page 77 - To reduce a whole number to an equivalent fraction, having a given denominator. RULE. Multiply the whole number by the given denominator v place the product over the said denominator, and it will