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

Harper & Brothers, 1846 - 503 sider

Hva folk mener -Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

Innhold

 RAtios AND PROPORTION Page 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
 Examples 328 Conditions of Reality of Roots from Sturms Theorem 340 Examples 349 To transform an Equation into another whose Roots shall be the Square of those of 355 Deguas Criterion 361 Newtons Method 369 When the Exponent is a composite Number 375 Multiple Value of Radicals 383

 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 Definitions 246 Calculus of Probabilities 252 General Theorem 255 General Properties of Logarithms 261 Examples 268 Series for computing Logarithm 275 Account of the Origin of Logarithms from Progressions 282 Compound Interest 288 Method of first Differences 295 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 31 4 314 Equation whose Roots separate those of the proposed 320
 Theory of vanishing Fractions 391 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 Lagrange 439 Irreducible Case 446 Irrational Expressions analogous to those obtained in the Resolution of Equations 452 Examples 458 Questions for Exercis 467 To decompose a Number into prime Factors and to find afterward all its Divisors 473 No Algebraic Formula can contain prime Numbers only 479 CONTINUED FRACTIONs 486 To develop any Quantity in a continued Fraction 493 Gausss Method of solving binomial Equations 501

Populære avsnitt

Side 129 - ... two triangles are to each other as the products of their bases by their altitudes.
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 107 - There will be as many figures in the root as there are periods in the given number.
Side 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.
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 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 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.
Side 128 - When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c.
Side 48 - Multiply all the numerators together for a new numerator, and all the denominators together for a new denominator.
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.