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Side 23 - 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.
Side 154 - 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.
Side 234 - 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.
Side 81 - 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.
Side 171 - 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.
Side 69 - 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
Side 166 - 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...
Side 162 - ... if the terms of a ratio be multiplied or divided by the same quantity, it does not alter the value of the ratio.
Side 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.