added addition algebraic arithmetical binomial cents changed coefficient complete consequently consisting containing cube root Define denote difference Divide dividend division equal equation EXAMPLES Explain the operation exponent expression factors figures find the values formulas four fourth fraction geometrical Given gives greatest common divisor Hence indicated known last term less letter means method miles Multiply negative NOTE number of terms obtain perfect person polynomial positive pounds problem progression proportion quadratic equation quotient radical Raise ratio Reduce remainder Repeat the Rule represent Required Resolve result second power simple solution solved square root Substituting subtraction taken Theorem third tion transposing twice units unknown quantity values of x Whence whole write
Page 53 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 181 - Find the greatest square in the first- period on the left, and place its root on the right after the manner of a quotient in division. Subtract the square of the root from the first period, and to the remainder bring down the second period for a dividend.
Page 279 - ... if the circumference of each wheel be increased one yard, it will make only 4 revolutions more than the hind wheel, in the same distance ; required the circumference of each wheel.
Page 44 - The exponent of a letter in the quotient is equal to its exponent in the dividend, minus its exponent in the divisor. 439. Let it be required to divide a* by a1.
Page 16 - If equal quantities be multiplied into the same, or equal quantities, the products will be equal. 4. If equal quantities be divided by the same or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be altered.
Page 279 - Divide the number 24 into two such parts, that their product shall be to the sum of their squares, as 3 to 10.
Page 303 - ... that is, Any term of a geometric series is equal to the product of the first term, by the ratio raised to a power, whose exponent is one less than the number of terms. EXAMPLES. 1.
Page 180 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 51 - 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.