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added algebraical amount annuity appears balls base becomes Binomial called cent changed CHAPTER coefficient combinations common complete consists contains continued cube root denominator denote difference Divide division divisor equal equation Examples expansion expression Extract factors figure find the number Find the sum Find the value former formula four fraction gallons given gives greater half Hence hour indices length less letters log.a logarithm means measure method miles multiplied negative Note number of terms obtained places positive present prove quadratic quantity quotient ratio reduced relation remainder resolved respectively result Rule seen sides Similarly simple solved square root Subtract taken things third true varies walking write written
Page 19 - 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 150 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 233 - The logarithm of a number to a given base is the index of the power to which the base must be raised to be equal to the number; thus, in the equation a* = N, x is called the logarithm of N to the base a.
Page 77 - A bill of 25 guineas was paid with crowns and halfguineas, and twice the number of half-guineas exceeded three times the number of crowns by 17. How many were there of each ? Ans.
Page 167 - CF as EB is to FD. [V. 16. And as one of the antecedents is to its consequent, so is the sum of the antecedents to the sum of the consequents; [V.
Page 65 - A railroad runs from A to C. A goods' train starts from A at 12 o'clock, and a passenger train at 1 o'clock. After going two-thirds of the distance the goods' train breaks down, and can only travel at three-fourths of its former rate. At 40 minutes past 2 o'clock a collision occurs, 10 miles from C. The rate of the passenger train is double the diminished rate of the goods
Page 162 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple of the first be less than that of the second, the multiple of the third is also...
Page 159 - ... if the terms of a ratio be multiplied or divided by the same quantity, it does not alter the value of the ratio.
Page 53 - 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.