New University Algebra: A Theoretical and Practical Treatise, Containing Many New and Original Methods and Applications. For Colleges and High SchoolsIvison, Phinney, Blakeman, & Company, 1864 - 420 σελίδες |
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Σελίδα 14
... hence , - 23. The Terms of an algebraic quantity are the parts or divis- ions made by the signs and Thus , in the quantity 5a + 262 - cx , there are three terms , of which 5a is the first , + 262 the second , and cx the third . 24. When ...
... hence , - 23. The Terms of an algebraic quantity are the parts or divis- ions made by the signs and Thus , in the quantity 5a + 262 - cx , there are three terms , of which 5a is the first , + 262 the second , and cx the third . 24. When ...
Σελίδα 20
... Hence , The algebraic sum of two or more similar terms having like signs , is the sum of their absolute values taken with their common sign . 3. Add 7a and -3a . From Ax . 11 we have 7a = 4a + 3a The sum of 7a and -3a is therefore the ...
... Hence , The algebraic sum of two or more similar terms having like signs , is the sum of their absolute values taken with their common sign . 3. Add 7a and -3a . From Ax . 11 we have 7a = 4a + 3a The sum of 7a and -3a is therefore the ...
Σελίδα 25
... Hence , in Algebra , Subtracting any quantity consists in adding the same quantity with its sign changed . 54. This principle may be established in a more general manner as follows : Let it be required to subtract the quantity b - c ...
... Hence , in Algebra , Subtracting any quantity consists in adding the same quantity with its sign changed . 54. This principle may be established in a more general manner as follows : Let it be required to subtract the quantity b - c ...
Σελίδα 31
... Hence , The coefficient of the product is equal to the product of the coeffi- cients of the multiplicand and multiplier . 2d . The law of exponents . Let it be required to multiply ab3 by ab3 . Since a * b * = aaaa bbb , and a3l2 = aaa ...
... Hence , The coefficient of the product is equal to the product of the coeffi- cients of the multiplicand and multiplier . 2d . The law of exponents . Let it be required to multiply ab3 by ab3 . Since a * b * = aaaa bbb , and a3l2 = aaa ...
Σελίδα 32
... Hence we conclude that the signs , and when prefixed to a multiplier , must be interpreted as follows : The plus sign before a multiplier shows that the multiplicand is to be successively added ; and the minus sign before a multiplier ...
... Hence we conclude that the signs , and when prefixed to a multiplier , must be interpreted as follows : The plus sign before a multiplier shows that the multiplicand is to be successively added ; and the minus sign before a multiplier ...
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added algebraic quantity arithmetical progression binomial factors clearing of fractions coefficients cube root degree denote derived polynomial division dollars EXAMPLES FOR PRACTICE exponent expression figure Find the cube Find the logarithm Find the sum find the values following RULE formula geometrical progression given equation given number given quantities greater greatest common divisor identical equation imaginary indicated inequality irreducible fraction last term least common multiple less letters minus sign monomial Multiply nth root number of terms obtain OPERATION partial fractions permutations positive roots problem proportion quadratic quadratic equation quotient radical sign rational Reduce remainder represent required root result second member second term square root Sturm's Theorem subtracted suppose surd taken third three numbers tion transformed equation transposing trial divisor Tx+U University Algebra unknown quantity whence whole number X₁ zero
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Σελίδα 204 - ... 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.
Σελίδα 36 - 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.
Σελίδα 61 - To reduce a fraction to its lowest terms. A fraction is in its lowest terms, when the numerator and denominator are prime to each other.
Σελίδα 396 - VARIATIONS of sign, nor the number of negative roots greater than the number of PERMANENCES. 325. Consequence. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots is equal to the number of permanences. For, let m denote the degree of the equation, n the number of variations of the signs, p the number of permanences ; we shall have m=n+p. Moreover, let n' denote the number of positive roots, and p' the number...
Σελίδα 173 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Σελίδα 359 - From this we might conclude that every equation involving but one unknown quantity, has as many roots as there are units in the exponent of its degree, and can have no more.
Σελίδα 72 - 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.
Σελίδα vii - Fractional exponents are used to denote both involution and evolution in the same expression, the numerator indicating the power to which the quantity is to be raised, and the denominator the required root of this power. Thus, the expression a* signifies the 4th root of the 3d power of a, and is equivalent to Va'.
Σελίδα 31 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first and second, plus the square of the second.
Σελίδα 93 - Divide 48 into two such parts, that if the less be divided by 4, and the greater by 6, the sum of the quotients will be 9. Ans. 12 and 36. 11. An estate is to be divided among 4 children, in the following manner : The first is to have $200 more than 1 of the whole.