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added affected algebraic applied arithmetical arrangements becomes binomial called cent Clearing coefficients common complete compound consequently consisting contain continued corresponding cube root decimal denominator difference dividend Dividing divisible equal evidently Evolving EXAMPLES Expand exponent expression Extract the square factors fifth figure Find the values formula four fraction gain geometrical give given greater Hence increase indicated inequality infin infinite interest involved last term least length less letters logarithm manner mean method Multiply negative Note number of terms obtain operations period polynomial positive preceding principles problem proportion proposed quotient ratio Reduce the equation remainder represent Required result RULE second power second term share square root Substituting subtract taken tens Theorem third third power tion Transform Transposing units unknown quantity value of x Whence yards
Página 163 - Bring down the first figure of the next period to the remainder for a new dividend, to which find a new divisor as before, and in like manner proceed till the whole be finished.
Página 38 - 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.
Página 64 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Página 57 - To reduce fractions of different denominators to equivalent fractions, having a common denominator. RULE. — Multiply each numerator into all the denominators except its own for the new numerators ; and multiply all the denominators together for a common denominator.
Página 151 - 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. V. Double the whole root already found, for a new divisor, and continue the operation as before, until all the periods are brought down.
Página 227 - If the numerator and denominator of each fraction is multiplied (or divided) by the same number, the value of the fraction will not change.
Página 226 - BY RATIO is meant the relation which one quantity bears to another, with respect to magnitude. It is evident that this relation can exist only between quantities of a similar kind ; thus, a number must be compared with a number; a line with a line; &c. &c. ; and it would be absurd to compare a certain number of feet with a certain number of pomds; &c.
Página 68 - The part of the equation which is on the left of the sign of equality is called the first member ; the part on the right of the sign of equality, the second member.