College AlgebraD.C. Heath & Company, 1890 - 577 páginas |
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... CONTAINING ONE UNKNOWN QUANTITY 85 XII . SIMPLE EQUATIONS CONTAINING TWO OR MORE UNKNOWN QUANTITIES 98 XIII . DISCUSSION OF SIMPLE EQUATIONS XIV . INEQUALITIES . 113 • 124 XV . INVOLUTION 130 · · • XVI . EVOLUTION . 136 • . XVII XVIII ...
... CONTAINING ONE UNKNOWN QUANTITY 85 XII . SIMPLE EQUATIONS CONTAINING TWO OR MORE UNKNOWN QUANTITIES 98 XIII . DISCUSSION OF SIMPLE EQUATIONS XIV . INEQUALITIES . 113 • 124 XV . INVOLUTION 130 · · • XVI . EVOLUTION . 136 • . XVII XVIII ...
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... contains as many units and fractional parts of units as the numbers 2 and 3 taken together ; that is , the sum of 21 and 33 is 51 . We shall then be free to attach any meaning we please to Addition or Subtraction involving other forms ...
... contains as many units and fractional parts of units as the numbers 2 and 3 taken together ; that is , the sum of 21 and 33 is 51 . We shall then be free to attach any meaning we please to Addition or Subtraction involving other forms ...
Página 23
... containing the highest power of that letter is placed first , that having the next lower immediately after , and so ... containing the lowest power of x in the above expression . A polynomial is said to be arranged according to the ...
... containing the highest power of that letter is placed first , that having the next lower immediately after , and so ... containing the lowest power of x in the above expression . A polynomial is said to be arranged according to the ...
Página 37
... containing the highest power of 2 in the product is the product of the terms containing the highest powers of x in the multiplicand and multiplier . Therefore 1023 is the product of 22 and the term DIVISION . 37.
... containing the highest power of 2 in the product is the product of the terms containing the highest powers of x in the multiplicand and multiplier . Therefore 1023 is the product of 22 and the term DIVISION . 37.
Página 38
... containing the highest power of a by the term containing the highest power of x in the divisor , we obtain 3 as the second term of the quotient . - ― Multiplying the divisor by 3 , we have the product −6x2 + 9x + 12 ; which , when ...
... containing the highest power of a by the term containing the highest power of x in the divisor , we obtain 3 as the second term of the quotient . - ― Multiplying the divisor by 3 , we have the product −6x2 + 9x + 12 ; which , when ...
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Términos y frases comunes
a₁ ab² absolute value Algebra arithmetical arithmetical means b₁ Binomial Binomial Theorem coefficient common factor Commutative Law Compare Art complex number continued fraction convergent cube root decimal denominator denote determinant Dividing divisible divisor equal EXAMPLES exponent Extracting the square figures Find the numbers follows from Art geometrical progression given equation Hence imaginary number infinite series last term letters logarithm mantissa Multiplying Note nth root number Art number of terms obtained P₁ partial fractions perfect power polynomial positive integer prove pure imaginary quadratic equation quotient radical sign rational and integral rational numbers real number remainder represented result rule of Art second term Solve the equation square root Sturm's Theorem Substituting Subtracting surd Theorem third unknown quantities Whence zero
Pasajes populares
Página 41 - The square of the sum of two numbers is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Página 270 - In any proportion the terms are in proportion by Composition; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Página 271 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Página 269 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = ос.
Página 268 - The terms of a ratio are the two numbers to be compared; thus, in the above ratio, 20 and 4 are the terms. When both terms are considered together, they are called a couplet ; when considered separately, the first term is called the antecedent, and the second term the consequent. Thus, in the ratio 20 : 4, 20 and 4 form a couplet, and 20 is the antecedent, and 4 the consequent.
Página 140 - ... from the given expression. Divide the first term of the remainder by twice the first term of the root, and add the quotient to the root and also to the divisor.
Página 137 - Arts. 200 and 201 we derive the following rule : Extract the required root of the numerical coefficient, and divide the exponent of each letter by the index of the root.
Página 38 - Divide the first term of the dividend by the first term of the divisor, giving the first term of the quotient. Multiply the whole divisor by this term, and subtract the product from the dividend, arranging the remainder in the same order of powers as the dividend and divisor.
Página 79 - Multiply the numerators together for the numerator of the product, and the denominators together for the denominator of the product.
Página 270 - In any proportion the terms are in proportion by Alternation ; that is, the first term is to the third as the second term is to the fourth.