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added algebraic antecedent arithmetical mean arithmetical series binomial cent Clearing of fractions coefficient common difference Completing the square compound continued fraction cube root cubic equation decimal dividend Dividing divisible equal Evolving EXAMPLES exponent expression Extract the square figure Find the values following general RULE formula fourth power geometrical mean geometrical series given number greater greatest common divisor Hence inequality infin infinite series involved jlns last term least common multiple less letters logarithm monomial Multiply negative number of terms obtain order of difference perfect square polynomial preceding problem proportion quotient radical sign Reduce the equation Reduce the fraction remainder represent Required the fourth Required the second Required the simplest Required the third result rithms second power second term square root Substituting subtract Theorem third power third root tion Transposing units unknown quantity Vb+Vc vulgar fraction Whence whole number yards
Page 165 - 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 209 - Several gentlemen made an excursion, each taking the same sum of money. Each had as many servants attending him as there were gentlemen ; the number of dollars which each had was double the number of all the servants, and the whole sum of money taken out was 3456 dollars.
Page 172 - Subtract this square number from the first period, and to the remainder bring down the next period for a dividend.
Page 42 - 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 68 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 235 - If the numerator and denominator of each fraction is multiplied (or divided) by the same number, the value of the fraction will not change.
Page 234 - 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.
Page 60 - The least common multiple of two or more numbers, is the least number which can be divided by each of them without a remainder.