The Elements of Algebra |
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... Series Harmonic Progression PAGE 182 190 199 CHAPTER VII . Permutations 205 Combinations 208 CHAPTER VIII . The Binomial Theorem 211 APPENDIX 231 INTRODUCTION . 1. IN Algebra , numbers and magnitudes are vi CONTENTS .
... Series Harmonic Progression PAGE 182 190 199 CHAPTER VII . Permutations 205 Combinations 208 CHAPTER VIII . The Binomial Theorem 211 APPENDIX 231 INTRODUCTION . 1. IN Algebra , numbers and magnitudes are vi CONTENTS .
Page 204
... 3 , 9 , 27 . ( 10 ) Find 3 numbers in geometrical progression whose sum is 7 and the sum of their cubes is 73. Ans . 1 , 2 , 4 . CHAPTER VII . PERMUTATIONS AND COMBINATIONS . 150. THE different 204 ARITHMETICAL AND GEOMETRICAL SERIES .
... 3 , 9 , 27 . ( 10 ) Find 3 numbers in geometrical progression whose sum is 7 and the sum of their cubes is 73. Ans . 1 , 2 , 4 . CHAPTER VII . PERMUTATIONS AND COMBINATIONS . 150. THE different 204 ARITHMETICAL AND GEOMETRICAL SERIES .
Page 205
Thomas Grainger Hall. CHAPTER VII . PERMUTATIONS AND COMBINATIONS . 150. THE different arrangements that can be made of any number of quantities are called their Permutations . Thus ab , and ba are the Permutations of a and b , and abc ...
Thomas Grainger Hall. CHAPTER VII . PERMUTATIONS AND COMBINATIONS . 150. THE different arrangements that can be made of any number of quantities are called their Permutations . Thus ab , and ba are the Permutations of a and b , and abc ...
Page 206
... permutations of n things ; for these are but the variations of n things taken , all , i . e . n and n together ; - making r = n , the last factor is n − ( n − 1 ) = 1 , and Vn ( n - 1 ) ( n - 2 ) ... 3.2.1 ; or the number of permutations ...
... permutations of n things ; for these are but the variations of n things taken , all , i . e . n and n together ; - making r = n , the last factor is n − ( n − 1 ) = 1 , and Vn ( n - 1 ) ( n - 2 ) ... 3.2.1 ; or the number of permutations ...
Page 207
... permutations would have been -- n ( n − 1 ) ( n − 2 ) ... ( 3.2.1 ) ; and because the r letters , if different , would have formed 1.2.3 ... permutations , and therefore combined with P , would have formed 1.2.3 ... rx P permutations ...
... permutations would have been -- n ( n − 1 ) ( n − 2 ) ... ( 3.2.1 ) ; and because the r letters , if different , would have formed 1.2.3 ... permutations , and therefore combined with P , would have formed 1.2.3 ... rx P permutations ...
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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.