College AlgebraD.C. Heath & Company, 1890 - 577 páginas |
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Página 1
... four kinds : 1. Symbols of Number . 2. Symbols of Operation . 3. Symbols of Relation . 4. Symbols of Abbreviation . SYMBOLS OF NUMBER . 3. The symbols of number usually employed are the Arabic numerals , and the letters of the alphabet ...
... four kinds : 1. Symbols of Number . 2. Symbols of Operation . 3. Symbols of Relation . 4. Symbols of Abbreviation . SYMBOLS OF NUMBER . 3. The symbols of number usually employed are the Arabic numerals , and the letters of the alphabet ...
Página 30
... four negative terms , positive ; and so on . And in general , the product of any number of terms is posi- tive or negative according as the number of negative terms is even or odd . - Example . Required the product of 2a2b3 , 6bc3 , and ...
... four negative terms , positive ; and so on . And in general , the product of any number of terms is posi- tive or negative according as the number of negative terms is even or odd . - Example . Required the product of 2a2b3 , 6bc3 , and ...
Página 100
... four principal methods of elimination . I. Elimination by Addition or Subtraction . The example in Art . 190 is an illustration of elimination by addition ; we will now give an example of elimination by subtraction . Example . Solve the ...
... four principal methods of elimination . I. Elimination by Addition or Subtraction . The example in Art . 190 is an illustration of elimination by addition ; we will now give an example of elimination by subtraction . Example . Solve the ...
Página 103
... the form ax + by = c , where a , b , and c are known quantities ; when the equations are thus reduced , they may be solved by any one of the four methods of elimination . 1. Solve the equations 3 = 0 . ( 1 SIMPLE EQUATIONS . 103.
... the form ax + by = c , where a , b , and c are known quantities ; when the equations are thus reduced , they may be solved by any one of the four methods of elimination . 1. Solve the equations 3 = 0 . ( 1 SIMPLE EQUATIONS . 103.
Página 111
... Four men , A , B , C , and D , play at cards , B having $ 2 more than C. After A has won half of B's money , B one - third of C's , and C one - fourth of D's , A , B , and C have each $ 36 . How much had each at first ? 11. A and B can ...
... Four men , A , B , C , and D , play at cards , B having $ 2 more than C. After A has won half of B's money , B one - third of C's , and C one - fourth of D's , A , B , and C have each $ 36 . How much had each at first ? 11. A and B can ...
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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.