The Elements of Algebra |
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... Simple Equations 79 Quadratic Equations 98 Problems 131 CHAPTER IV . Surds 154 Binomial Quadratic Surds 160 CHAPTER V. Ratio 167 Proportion 172 Variation 178 Arithmetic Series CHAPTER VI . Geometric Series Harmonic Progression PAGE.
... Simple Equations 79 Quadratic Equations 98 Problems 131 CHAPTER IV . Surds 154 Binomial Quadratic Surds 160 CHAPTER V. Ratio 167 Proportion 172 Variation 178 Arithmetic Series CHAPTER VI . Geometric Series Harmonic Progression PAGE.
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Thomas Grainger Hall. and since . Also is to ; thus ab expresses the ratio : used between the terms of a pro- b c d which is read a is to bas c of a to b . And : , :: , portion , thus a is to d . 7. The use of some of these signs may now ...
Thomas Grainger Hall. and since . Also is to ; thus ab expresses the ratio : used between the terms of a pro- b c d which is read a is to bas c of a to b . And : , :: , portion , thus a is to d . 7. The use of some of these signs may now ...
Page 152
... ratio to unity , are called irrational quantities or surds . And terms such as √ - a2 and a + √ - b2 , already men- tioned ( Art . 73. ) are called imaginary or impossible quan- tities . But although these surds cannot be exactly ...
... ratio to unity , are called irrational quantities or surds . And terms such as √ - a2 and a + √ - b2 , already men- tioned ( Art . 73. ) are called imaginary or impossible quan- tities . But although these surds cannot be exactly ...
Page 165
... √13 +2 √10 + 4 √3 + 2 √30 = √2 + √5 + √6 . ( 18 ) √16 + 6 √2 + 4 √3 + 2 √6 +2 10 + 2 / 15 + 2√30 N = √2 + √3 + √5 + √ồ . CHAPTER V. RATIO , PROPORTION , AND VARIATION . RATIO SURDS AND IMAGINARY QUANTITIES . 165.
... √13 +2 √10 + 4 √3 + 2 √30 = √2 + √5 + √6 . ( 18 ) √16 + 6 √2 + 4 √3 + 2 √6 +2 10 + 2 / 15 + 2√30 N = √2 + √3 + √5 + √ồ . CHAPTER V. RATIO , PROPORTION , AND VARIATION . RATIO SURDS AND IMAGINARY QUANTITIES . 165.
Page 166
Thomas Grainger Hall. CHAPTER V. RATIO , PROPORTION , AND VARIATION . RATIO . 116. RATIO is the relation which quantities bear to each other with regard to magnitude . Thus if one magnitude be two - thirds of another magni- tude , they ...
Thomas Grainger Hall. CHAPTER V. RATIO , PROPORTION , AND VARIATION . RATIO . 116. RATIO is the relation which quantities bear to each other with regard to magnitude . Thus if one magnitude be two - thirds of another magni- tude , they ...
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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.