The Elements of Algebra |
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Page 4
... twice a number equal 10 , the number itself must be the half of 10 or 5 , i . e . x = 5 ; and therefore the smaller number being 5 , the larger must equal 8 . In fact 8+ 5 = 13 ; and 8- 5 = 3 . The process written algebraically would ...
... twice a number equal 10 , the number itself must be the half of 10 or 5 , i . e . x = 5 ; and therefore the smaller number being 5 , the larger must equal 8 . In fact 8+ 5 = 13 ; and 8- 5 = 3 . The process written algebraically would ...
Page 59
... twice the product of the two terms . Thus if a 7 and b = 6 or a + b = 13 . Then = ( a + b ) 2 or ( 13 ) 2 = 7o + 2 × 7 × 6 + 6o = 49 +84 + 36 = 169 . And by this formula may the squares of numbers often be found in a very convenient ...
... twice the product of the two terms . Thus if a 7 and b = 6 or a + b = 13 . Then = ( a + b ) 2 or ( 13 ) 2 = 7o + 2 × 7 × 6 + 6o = 49 +84 + 36 = 169 . And by this formula may the squares of numbers often be found in a very convenient ...
Page 60
... twice their product ; .. ( 2a5b ) 2 = 4a2 - 20 ab + 256 * ; ... ( 6x - 7y ) 2 = 36x2 — 24xy + 49y3 , 2 - ( x - 2 ) = x2 - px + 2 . 4 61. Hence also may we find the square of a binomial a + b + c , for considering b + c as one quantity ...
... twice their product ; .. ( 2a5b ) 2 = 4a2 - 20 ab + 256 * ; ... ( 6x - 7y ) 2 = 36x2 — 24xy + 49y3 , 2 - ( x - 2 ) = x2 - px + 2 . 4 61. Hence also may we find the square of a binomial a + b + c , for considering b + c as one quantity ...
Page 61
... twice . ( a + b ) 3 = ( a + b ) . ( a + b ) . ( a + b ) = ( a2 + 2 ab + b2 ) ( a + b ) = a3 + 3a2b + 3ab2 + b3 . And ( a - b ) 3 a3 − 3 a2 b + 3ab2 — b3 . - - - The student should render himself familiar with these equivalent ...
... twice . ( a + b ) 3 = ( a + b ) . ( a + b ) . ( a + b ) = ( a2 + 2 ab + b2 ) ( a + b ) = a3 + 3a2b + 3ab2 + b3 . And ( a - b ) 3 a3 − 3 a2 b + 3ab2 — b3 . - - - The student should render himself familiar with these equivalent ...
Page 118
... twice the second to the first ; • . x2 + 2xy + y2 = 169 ; .. x + y = ± 13 . ( 2 ) Subtract twice the second from the first ; .. x2 - 2xy + y2 = 1 ; ..x - y = 1 ; .. 2x = 14 ; x = 7 , and 2y = 12 ; y = ± 6 . .. ( Ex . 5. ) Given x + y ...
... twice the second to the first ; • . x2 + 2xy + y2 = 169 ; .. x + y = ± 13 . ( 2 ) Subtract twice the second from the first ; .. x2 - 2xy + y2 = 1 ; ..x - y = 1 ; .. 2x = 14 ; x = 7 , and 2y = 12 ; y = ± 6 . .. ( Ex . 5. ) Given x + y ...
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Common terms and phrases
2ab+b² a²+2ab+b² a²x² a³b ab² ab³ algebraical quantities arithmetic mean arithmetic series arithmetical progression ax² binomial coefficient common difference compound cube root decimal denominator digits divided dividend division divisor equal examples expressed Extract the square factor Find the greatest find the numbers Find the sum fraction geometrical progression greatest common divisor greatest common measure Hence last term least common multiple less letters logarithm multiplied negative number of terms numbers in arithmetical P₁ permutations QUADRATIC EQUATIONS quotient ratio remainder result rule shew square root subtract surd third unity unknown quantity whence write written xy³
Popular passages
Page 38 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
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 22 - 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 173 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.