# The University Algebra ...

Sheldon & Company, 1859 - 528 σελίδες

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### Περιεχόμενα

 Symbols of Quantity 15 Axioms 21 Propositions Multiplication of Signs 32 33 34 and 35 Propositions Division of Signs c 40 4142 4344 and 45 and II 80 PROBLEMTofind the Greatest Common Divisor of Two or more Polynomials 86 PROBLEM To Reduce a Fraction to One Entire or Mixed Quantity 93 PROBLEMTo Convert a Fraction into an Equivalent One having a Given 98
 Examples 275 Examples 281 Examples 287 Miscellaneous Examples 293 Questions Producing Affected Quadratics 299 Pure Biquadratics 322 Biquadratics Containing Two Unknown Quantities 339 Miscellaneous Questions 346

 DIVISION OF FRACTIONS 106 PROBLEM To Raise a Monomial to the nth power 113 PROBLEM To Square a Polynomial 119 PROBLEM To Extract the Square Root ofa 125 PROBLEM To Extract the Cube Root of a Polynomial 134 PROBLEM To Reduce a Rational Quantity to the Form of a Proposed Surd 140 PROBLEM To Reduce Two or more Radicals having Different Indices 142 MULTIPLICATION OF RADICALS 148 PROBLEM To Extract the Square Root of a Binomial Surd One of whose 154 PROBLEM To Find such a Multiplier or such Multipliers as will make 160 SUBTRACTION OF IMAGINARY QUANTITIES 166 Evolution of IMAGINARY QUANTITIES 172 Theorems 179 180 181 and 182 Simple Equations Containing One Unknown Quantity 189 Questions Involving Simple Equations Containing One Unknown Quantity 197 Elimination by Substitution 211 Elimination by Addition and Subtraction 217 Simultaneous Equations of the First Degree Containing Three or More 224 Questions involving Simultaneous Equations of the First Degree 235 INTERPRETATION OF NEGATIVE RESULTs 242 Examples 255 Pure Quadratics 261 Affected Quadratics 268
 Examples 352 Problems 358 Problems 365 Introductory Definitions and Explanations 375 HARMONICAL PROPORTION 382 Expansion of Series 392 Decomposition of Rational Fractions 399 Examples 407 SUMMATION or SERIES Examples 415 THE DIFFERENTIAL METHODExamples 426 SPECIAL SERIES 432 Promiscuous Questions 439 Questions 447 IN T E R 456 Ratio of the Circumference of a Circle to its Diameter 470 Definitions Problems and Solutions 478 Miscellaneous Examples 486 Examples 493 TRANSFORMATION OF EQUATIONS 500 LIMIts of Roots of EQUATIONS 508 REAL Roots 516 HoRNERs METHOD of RESOLVING NUMERICAL EQUATIONS 522

### Δημοφιλή αποσπάσματα

Σελίδα 56 - ... the square of the second. _ Again, (a — by = (a — 5) (a — 5) = a2 — 2a6 + 52. (2) That is, The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Σελίδα 373 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.
Σελίδα 48 - 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.
Σελίδα 363 - A and B 165 miles distant from each other set out with a design to meet; A travels 1 mile the first day, 2 the second, 3 the third, and so on. B travels 20 miles the first day; 18 the second, 16 the third, and so on.
Σελίδα 382 - Three quantities are said to be in harmonical proportion, when the first is to the third, as the difference between the first and second is to the difference between the second and third.
Σελίδα 306 - ... which was moving at the rate of 9 miles in 4 hours. B overtook the same drove of geese at the 45th...
Σελίδα 301 - 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.
Σελίδα 382 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Σελίδα 203 - A farmer has a stack of hay, from which he sells a quantity, which is to the quantity remaining in the proportion of 4 to 5. He then uses 15 loads, and finds that he has a quantity left, which is to the quantity sold as 1 to 2. How many loads did the stack at first contain ? 10. There are 3 pieces of cloth, whose lengths are in the proportion of 3, 5, and 7 ; and 8 yards being cut off" from each, the whole quantity is diminished in the proportion of 15 to 11.
Σελίδα 239 - Some smugglers discovered a cave which would exactly hold the cargo of their boat, viz., 13 bales of cotton and 33 casks of wine.