## New Elementary Algebra: Containing the Rudiments of the Science for Schools and Academies |

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added addition algebraic analysis ANALYSIS.-We Assume binomial cents changed coefficient complete condition contain correction cost cube root denominator difference Divide dividend division divisor dollars entire equal equation EXAMPLES Expand exponent expressed extracting extremes factors figure find the values four fourth fraction geometrical Given gives greater greatest half Hence horse indicated inequality last term least common less letter means method miles minus Multiply negative NOTE number of terms obtain OPERATION paid period polynomial positive PRACTICE principles problem proportion quadratic quotient radical Raise ratio Reduce remainder represent Resolve result Rule RULE.-I second term simple SOLUTION Solving square root subtract taken term third three numbers tion Transposing twice unit unknown quantity whole write

### Popular passages

Page 228 - It is required to divide -the number 14 into two such parts that the quotient of the greater divided by the less, may be to the quotient of the less divided by the greater as 16 to 9.

Page 276 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.

Page 252 - To divide 100 into two such parts, that the sum of their square roots may be 14. Ans. 64 and 36 14.

Page 189 - 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 310 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive $ '75, and, for every day he was idle, he should forfeit $ '25 ; at the expiration of the time, he received $ 27'50 ; how many days did he work...

Page 59 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.

Page 277 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.

Page 260 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.

Page 99 - Reduce compound fractions to simple ones, and mixt numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for. a new denominator.

Page 186 - Subtract the square of the root thus found from the first term, and bring down the next two terms for a dividend. III. Divide the first term of the dividend by twice the root already found, and write the result both in the root and in the divisor. IV. Multiply the divisor, thus completed, by the, term of the root last found, and subtract the product from the dividend, and proceed with the remainder, if any, as before.