A Treatise on Algebra: In which the Principles of the Science are Familiarly Explained ...

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E. C. & J. Biddle, 1848 - Algebra - 318 pages
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Page 63 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 34 - Then divide the first term of the remainder by the first term of the divisor...
Page 148 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons ; and then filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left. How much wine did he draw each time ? 50.
Page 57 - ... to the sum of the extremes multiplied by half the number of terms. Rule. — Add the extremes together, and multiply their sum by half the number of terms ; the product will be the sum of the series.
Page 177 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel, in going 120 yards ; but if the circumference of each wheel be increased...
Page 56 - ... a, a + d, a + 2 d, a + 3 d, a + 4 d...
Page 132 - There is a certain number, consisting of two places of figures, which is equal to four times the sum of its digits ; and if 18 be added to it, the digits will be inverted; what is the number? Ans. 24.
Page 192 - We then find the equation whose roots are the reciprocals of the roots of the transformed.
Page 146 - Divide the number 14 into two such parts, that the quotient of the greater divided by the less, shall be to the quotient of the less divided by the greater as 16 to 9.
Page 53 - Permutando, or alternando, by permutation or alternately; when there are four proportionals, and it is inferred that the first is to the third, as the second is to the fourth.

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