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

Harper & Brothers, 1846 - Algebra - 503 pages
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### Contents

 Problems producing pure Equations 224 Problem of the Lights 240 PERMUTATIONS AND COMBINATIONS 246 Arithmetical Complement 255 218 258 Definitions and Calculation of Tables 261 Exponential Theorem 272 Examples 278 Examples 284 Present Value and Discount at Compound Interest 291 NATURE AND COMPOSITION OF EQUATIONS 302 246 312 Theorem of Sturm 322 Hernes Method of resolving numerical Equations of all Orders 332 Conditions of Reality of Roots from Sturms Theorem 341 Examples 349 Budans Criterion 359 285 362 Newtons Method of finding the Limits 365
 328 411 Summation of Series 415 332 417 345 425 SYMMETRICAL FUNCTIONS 427 365 433 372 439 Irreducible Case 447 Resolution of the Equation of the fourth Degree 455 Questions for Exercise 467 To decompose a Number into prime Factors and to find afterward all its Divisors 473 397 475 No Algebraic Formula can contain prime Numbers only 479 417 481 CONTINUED FRACTIONS 486 427 488 To develop any Quantity in a continued Fraction 493 Gausss Method of solving binomial Equations 501 294

### Popular passages

Page 129 - ... two triangles are to each other as the products of their bases by their altitudes.
Page 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.
Page 278 - 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 237 - B set out from two towns, which were distant 247 miles, and travelled the direct road till they met. A went 9 miles a day ; and the number of days, at the end of which they met, was greater by 3 than the number of miles which B went in a day. How many miles did each go ? 17.
Page 184 - It is required to divide the number 99 into five such parts, that the first may exceed the second by 3, be less than the third by 10, greater than the fourth by 9, and less than the fifth by 16.
Page 239 - ... digit ; but if the digits be inverted, and the resulting number be divided by a number greater by unity than the sum of the digits, the quotient is greater by 2 than the preceding quotient : find the number.
Page 236 - A's journey. How far did each travel ? A 72 miles. B 54 miles. 9. A company at a tavern had £8 15s. to pay for their reckoning ; but before the bill was settled, two of them left the room, and then those who remained had 10s. apiece more to pay than before : how many were there in the company ? Ans. 7.
Page 314 - Every equation of an odd degree has at least one real root ; and if there be but one, that root must necessarily have a contrary sign to that of the last term. - 4".
Page 145 - Elimination by Substitution consists in finding the value of one of the unknown quantities in one of the equations, in terms of the other unknown quantity and known terms, and substituting this, instead of the quantity, in the other equation.
Page 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.