A Theoretical and Practical Treatise on Algebra ...: Designed for Schools, Colleges and Private Students |
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2d divisor 3d power 3d term 4th power algebraic algebraic quantities apply arithmetical arithmetical progression assumed binomial square binomial theorem cent Clearing of fractions coefficients common measure Completing the square couriers cube root cubic equation denominator distance dividend division dollars equa equal roots equation becomes EXAMPLES Expand exponent factors find the values geometrical progression give greater Hence infinity last term least common multiple less letter logarithm lower terms method Multiply negative number of terms observe operation positive root primitive equation problem Prod proportion quadratic quadratic equations quotient radical real roots Reduce remainder represent resolved result second power second term solution specific gravity square root substitute subtract suppose surd theorem third three numbers tion Transform the equation transformed equation Transpose trial divisor unity unknown quantity values of x variations of signs whole numbers
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Page 26 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 36 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Page 204 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.
Page 199 - Three quantities are said to be 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.
Page 31 - 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 92 - It is required to divide the number 24 into two such parts, that the quotient of the greater part divided by the less, may be to the quotient of the less part divided by the greater, as 4 to 1.
Page 56 - Any term may be transposed from one member of an equation to the other by changing its sign; (1, 2).
Page 206 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 199 - 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 25 - Hence, for the multiplication of polynomials we have the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier, observing that like signs give plus in the product, and unlike signs minus.