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

Harper & Brothers, 1846 - 503 pàgines

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Continguts

 Square of Polynomials 81 Square Root by Approximation 87 Rationalizing binomial Surds 97 Higher Roots of Numbers 107 Degree of Approximation of Series 115 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 Negative indeterminate and infinite Solutions 173 Problem of the Couriers 181 Problems in indeterminate Analysis 191 QUADRATIC EQUATIONS 199 Examples in complete Quadratics 205 Quadratics containing two unknown Quantities 218 Problems producing pure Equations 224 Problem of the Lights 232 Decomposition of Trinomials of the second Degree into Factors of the first Degree 239 PERMUTATIONS AND COMBINATIONS 246 Calculus of Probabilities 253 General Theorem 255 LOGARIth 261
 Equation whose Roots separate those of the proposed 320 Examples 328 Conditions of Reality of Roots from Sturms Theorem 340 Examples 349 To transform an Equation into another whose Roots shall be any Multiple or Submul 355 Deguas Criterion 361 Newtons Method 369 When the Exponent is a composite Number 375 Multiple Value of Radicals 383 Theory of vanishing Fractions 390 Method of Labatie 397 Eulers Method 404 SERIES 410 Difference Series 416 Piling of Balls and Shells 422 To find the Sums of the like and entire Powers of the Roots of an Equation 428 Quadratic Factors of Equations 433 Method of Tschirnhausen for solving Equations 439 Resolution of the Equation of the third Degree by the Method of Cardan 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 Gausss Method of solving binomial Equations 501

Passatges populars

Pàgina 129 - ... two triangles are to each other as the products of their bases by their altitudes.
Pàgina 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.
Pàgina 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.
Pàgina 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.
Pàgina 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.
Pàgina 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.
Pàgina 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.
Pàgina 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".
Pàgina 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.
Pàgina 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.