# A Treatise on Algebra: Containing the Latest Improvements. Adapted to the Use of Schools and Colleges

Harper & Brothers, 1847 - 503 sider

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 INTRodoction 1 ALGEBRAIC CALCULUS 7 Multiplication 13 Multiplication by detached Coefficients 19 Division by detached Coefficients 31 Least common Multiple 40 Addition 47 Addition and Subtraction of Radicals 59
 Ten Formulas in Arithmetical Progression 278 Ten Formulas in Geometric Progression 284 Present Value and Discount at Compound Interest 291 Example of Application to Tables 298 Definitions 302 An Equation containing one unknown Quantity has as many Roots as there are Units 308 All the Roots of an Equation must be of the Form a+b V1 314 Equation whose Roots separate those of the proposed 321

 Fractional and negative Exponents 65 Square of Polynomials 77 Property of prime Numbers 83 Square Root of decimal Fractions 89 Fourth Root of Numbers 95 Higher Roots of Numbers 107 Degree of Approximation of Series 117 Definitions and general Properties 119 Propositions in Proportion 128 Examples in simple Equations 134 Cases of Impossibility and Indetermination in simple Equations containing one unknown 142 General Formulas of Elimination 155 Problems producing simple Equations 138 173 Problem of the Couriers 183 Problems in indeterminate Analysis 191 QUADRATIC EQUATIONS 199 Examples in complete Quadratics 205 Quadratics containing two unknown Quantities 218 Problems producing pure Equations 224 28 232 General Theorem 235 Decomposition of Trinomials of the second Degree into Factors of the first Degree 239 PERMUTATIONS AND COMBINATIONS 246 Decomposition of Fractions 256 Definitions and Calculation of Tables 264 Effect of different Values of the Base 272
 Examples 328 Conditions of Reality of Roots from Sturms Theorem 340 Examples 3 49 351 Budans Criterion 359 Newtons Method of finding the Limits 365 When the Exponent is a composite Number 375 Multiple Value of Radicals 383 Theory of vanishing Fractions 390 Method of Labatie 399 Degree of the final Equation 406 To determine whether a Series be recurring 412 The differential Method of summing Series 419 Variation 425 Every rational and symmetric Function of the Root of an Equation can be expressed 431 Quadratic Factors of Equations 433 Method of Lagrange 439 Irreducible Case 446 Irrational Expressions analogous to those obtained in the Resolution of Equations 452 Examples 458 Questions for Exercise 467 To decompose a Number into prime Factors and to find afterward all its Divisors 473 Theorems with regard to congruous Numbers 483 Periodic continued Fractions 491 Method of resolving in rational Numbers indeterminate Equations of the second Degree 497 Variations of the general Formulas

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Side 172 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Side 23 - 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.
Side xii - ALPHA BETA GAMMA DELTA EPSILON ZETA ETA THETA IOTA KAPPA LAMBDA MU NU XI OMICRON PI RHO SIGMA TAU UPSILON PHI CHI PSI OMEGA...
Side 122 - Proportion is an equality of ratios. Thus, if a, b, c, d are four quantities, such that a, when divided by b, gives the same quotient as c when divided by d, then a, b, c, d are called proportionals, and we say that a is to b as c is to d...
Side 261 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Side 170 - His head weighed as much as his tail and half his body, and his body weighed as much as his head and tail together.
Side 310 - ... the sum of the products of every two roots with their signs changed ; the coefficient of the fourth term...
Side 172 - A work is to be printed, so that each page may contain a certain number of lines, and each line a certain number of letters. If we wished each page to contain 3 lines more, and each line 4 letters more, then there would be 224 letters more...
Side 183 - A company of 90 persons consists of men, women, and children ; the men are 4 in number more than the women, and the children are 10 more in number than both men and women ; what is the number of each 1 Ans.
Side 237 - There are two square buildings, that are paved with stones, a foot square each. The side of one building exceeds that of the other by 12 feet, and both their pavements taken together contain 2120 stones. What are the lengths of them separately ? Ans.