The Elements of Algebra |
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... 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.
... 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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... equation : viz . 2x + 3 = 13 . Now as 2x increased by 3 , is equal to 13 , 2x must be equal to 13 diminished by 3 , or 2x must equal 10 ; and if twice a number equal 10 , the number itself must be the half of 10 or 5 , i . e . x = 5 ...
... equation : viz . 2x + 3 = 13 . Now as 2x increased by 3 , is equal to 13 , 2x must be equal to 13 diminished by 3 , or 2x must equal 10 ; and if twice a number equal 10 , the number itself must be the half of 10 or 5 , i . e . x = 5 ...
Page 74
... -X = 1/100 812 x3 5x1 - & c . 16 128 x2 ( 24 ) √a2x2 ენ 5x8 = a - & c . 2 a 8a3 16a5 128 a 5x8 ( 25 ) √a2 + x2 = a + 2 a + 8a3 16a5 128a7 + & c . CHAPTER III . EQUATIONS . 78. A PRINCIPAL object of 74 EVOLUTION .
... -X = 1/100 812 x3 5x1 - & c . 16 128 x2 ( 24 ) √a2x2 ენ 5x8 = a - & c . 2 a 8a3 16a5 128 a 5x8 ( 25 ) √a2 + x2 = a + 2 a + 8a3 16a5 128a7 + & c . CHAPTER III . EQUATIONS . 78. A PRINCIPAL object of 74 EVOLUTION .
Page 75
... equation . The two algebraical expressions are called mem- bers of the equation : Thus if 2x + 4 = x + 10 ; such an equality is an equation , and 2a + 4 and x + 10 are the members of the equation . To solve an equation is , to find the ...
... equation . The two algebraical expressions are called mem- bers of the equation : Thus if 2x + 4 = x + 10 ; such an equality is an equation , and 2a + 4 and x + 10 are the members of the equation . To solve an equation is , to find the ...
Page 76
... equation of this kind : and it is in fact to equalities of this description that the name equation is usually applied . Our attention will at present be directed solely to equations of this class . 80. Algebraic equations are also ...
... equation of this kind : and it is in fact to equalities of this description that the name equation is usually applied . Our attention will at present be directed solely to equations of this class . 80. Algebraic equations are also ...
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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.