## Elements of Algebra: For Colleges, Schools, and Private Students |

### Contents

24 | |

28 | |

37 | |

43 | |

51 | |

57 | |

62 | |

68 | |

198 | |

213 | |

220 | |

265 | |

274 | |

280 | |

298 | |

309 | |

74 | |

83 | |

89 | |

103 | |

111 | |

127 | |

142 | |

158 | |

167 | |

169 | |

176 | |

186 | |

315 | |

352 | |

357 | |

358 | |

364 | |

370 | |

372 | |

377 | |

384 | |

395 | |

404 | |

### Other editions - View all

### Common terms and phrases

2d Bk algebraic ALGEBRAIC QUANTITIES arithmetical arithmetical progression binomial Binomial Theorem coefficients Completing the square Corollary cube root decimal degree denotes difference dividend divisible equa equation whose roots EQUATIONS CONTAINING evident example exponent Extract the square Find the cube find the G.C.D. find the number Find the square Find the sum find the value fraction given equation given number gives greater greatest common divisor Hence inequality LEAST COMMON MULTIPLE less letters logarithms method miles minus monomial Multiply nth root number of balls number of terms operation perfect square positive root preceding Proposition quadratic equation quotient ratio real roots Reduce remainder Required the numbers required to find result second term solution solved square root substituted subtracted taken Theorem third tion transposing trinomial unity unknown quantity variation Whence whole number

### Popular passages

Page 289 - Take the first term from the second, the second from the third, the third from the fourth, &c. and the remainders will form a new series, called the first order of

Page 33 - Obtain the exponent of each literal factor in the quotient by subtracting the exponent of each letter in the divisor from the exponent of the same letter in the dividend; Determine the sign of the result by the rule that like signs give plus, and unlike signs give minus.

Page 37 - 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 105 - Two persons, A and B, can perform a piece of work in 16 days. They work together for 4 days, when A being called off, B is left to finish it, which he does in 36 days more. In what time would each do it separately ? Ans. A in 24 and B in 48 days.

Page 136 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.

Page 66 - Reduce the fractions to a common denominator ; then subtract the numerator of the subtrahend from the numerator of the minuend, and write the result over the common denominator. EXAMPLES. H ,_, Zx . ^ 3x 1. From -^- subtract — . oo . Eeducing to a common denominator, the fractions become Wx 9x "15...

Page 253 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.

Page 242 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.

Page 236 - In any proportion the product of the means is equal to the product of the extremes.

Page 41 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.