# Higher Algebra: A Sequel to Elementary Algebra for Schools

Macmillan, 1891 - 557 páginas

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### Contenido

 Powers of w 80 Formation of equations when the roots are given 86 Examples IX b 92 Equations involving one unknown quantity 100 CHAPTER XI 114 Number of ways in which m+n+p+ things can be divided into 120 Number of permutations of n things r at a time when each may 126 PAGE 136 BINOMIAL THEOREM ANY INDEX 149 Cubic equations Cardans Solution 154 a 155 Comparison of Eun with an auxiliary series 162 Number of homogeneous products of r dimensions formed out of 164 MULTINOMIAL THEOREM 170 CHAPTER XVI 175 Advantages of logarithms to base 10 181 CHAPTER XVII 187 Commensurable and incommensurable quantities 188 Product of an infinite number of factors 189 CONTINUED FRACTIONS 192 CHAPTER XVIII 198 Annuities Definitions 205 6 215
 or x according 281 354 290 RECURRING CONTINUED FRACTIONS 292 Solution of x2 Nya 1 306 SUMMATION OF SERIES 312 Method of Subtraction 318 392 320 1+P1M p where p is a prime 324 Method succeeds when Un is a rational integral function of n 326 b 332 C 338 Sum of the divisors of a given integer 344 Examples XXX 354 anan+10 362 Definition of congruent 350 373 C 389 Concurrent testimony 398 Examples XXXII 405 CHAPTER XXXV 409 CHAPTER III 429 434 550 Derechos de autor

### Pasajes populares

Página 55 - ... any number divided by 9 will leave the same remainder as the sum of its digits divided by 9.
Página 169 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Página 111 - The number of combinations of n things г at a time is equal to the number of combinations of n things n—r at a time.
Página 488 - At the 50th mile stone from London, A overtook a drove of geese which were proceeding at the rate of three miles in two hours ; and two hours afterwards met a stage waggon, which was moving at the rate of 9 miles in 4 hours.
Página 450 - If then we suppose the factors corresponding to the negative and imaginary roots to be already multiplied together, each factor x— a corresponding to a positive root introduces at least one change of sign ; therefore no equation can have more positive roots than it has changes of sign. To prove the second part of Descartes...
Página 109 - Pr always denotes the number of factors in the formula we are using. Ex. 1. Four persons enter a carriage in which there are six seats : in how many ways can they take their places ? The first person may seat himself in 6 ways ; and then the second person in 5 ; the third in 4 ; and the fourth in 3 ; and since each of these ways may be associated with each of the others, the required answer is б x 5 x 4 x 3, or 360.
Página 13 - Hence if any three terms of a proportion are given, the fourth may be found. Thus if...
Página 172 - The integral part of a logarithm is called the characteristic, and the decimal part is called the mantissa.
Página 482 - A railway train after travelling for one hour meets with an accident which delays it one hour, after which it proceeds at three-fifths of its former rate, and arrives at the terminus...
Página 455 - Every equation of an odd degree has at least one real root whose sign is opposite to that of its last term.