An Elementary Treatise on Algebra: For the Use of Students in High Schools and Colleges |
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Page 133
... root , and finding the first power when the second is given , is called extracting the second root . The second root of a quantity then , is such as being multiplied by ... SECOND ROOTS OF NUMBERS . Extraction of the second roots of numbers,
... root , and finding the first power when the second is given , is called extracting the second root . The second root of a quantity then , is such as being multiplied by ... SECOND ROOTS OF NUMBERS . Extraction of the second roots of numbers,
Page 134
... second power will contain the second power of the tens , plus twice the product of the tens by the units , plus the second power of the units . Now let us reverse the process , and see by what means the root could be found from the ...
... second power will contain the second power of the tens , plus twice the product of the tens by the units , plus the second power of the units . Now let us reverse the process , and see by what means the root could be found from the ...
Page 135
... root , we have 25 , which raised to the second power gives 625 , Hence 25 is the the root sought . We shall now explain how the correctness of any figure in the root may be ascertained , without raising the ... SECOND ROOTS OF NUMBERS .
... root , we have 25 , which raised to the second power gives 625 , Hence 25 is the the root sought . We shall now explain how the correctness of any figure in the root may be ascertained , without raising the ... SECOND ROOTS OF NUMBERS .
Page 136
... second power of a number consisting of three figures , will contain five or six figures . We can , therefore , as- certain the number of figures in the root ... root , as there are periods in the power . Separating 127449 into periods , we ...
... second power of a number consisting of three figures , will contain five or six figures . We can , therefore , as- certain the number of figures in the root ... root , as there are periods in the power . Separating 127449 into periods , we ...
Page 137
... root , and subtracting its second power from 12 , we bring down the next period at the right of the remainder . We now consider 374 as a dividend . This dividend contains 2 a b + b2 , or twice the product of the hundreds by the tens ...
... root , and subtracting its second power from 12 , we bring down the next period at the right of the remainder . We now consider 374 as a dividend . This dividend contains 2 a b + b2 , or twice the product of the hundreds by the tens ...
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Common terms and phrases
3d power a b c a² b² a² b³ abc2 added algebra ALGEBRAIC QUANTITIES arithmetical bought bushels cents change the signs coefficient contain cows decimal difference Divide dividend division equal example exponent expressed Extract Find the 3d Find the 4th Find the third following RULE formula fraction gallons given gives greater greatest common divisor Hence integral quantity last term least common multiple less Let the learner letter logarithm manner monomial mth power Multiply number of terms numerator and denominator obtain Operation polynomials preceding prime factors progression by quotient proportion quan question ratio remainder Required the number result rods second power second root SECTION separated shillings square Substitute subtracted Suppose tens third power third root tities twice unknown quantity whole number yards
Popular passages
Page 50 - 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 46 - ANOTHER. 1. Divide the coefficient of the dividend by the coefficient of the divisor. 2.
Page 23 - A shepherd in time of war was plundered by a party of soldiers, who took \ of his flock and \ of a sheep ; another party took from him \ of what he had left and \ of a sheep ; then a third party took \ of what now remained and J of a sheep.
Page 226 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 258 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Page 260 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
Page 1 - Algebraic operations are based upon definitions and the following axioms : — 1. If the same quantity, or equal quantities, be added to equal quantities, the sums will be equal. 2. If the same quantity, or equal quantities, be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same quantity, or equal quantities, the products will be equal.
Page 223 - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Page 1 - If equal quantities be divided by the same or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be altered.
Page 137 - 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.