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### Contents

 CHAPTER 4 ADDITION AND SUBTRACTION 12 MULTIPLICATION 26 DIVISION 39 SIMPLE EQUATIONS 48 MULTIPLICATION AND DIVISION 61 FACTORS 70 COMMON FACTORS AND MULTIPLES 93
 SIMULTANEOUS QUADRATIC EQUATIONS 260 PROPERTIES OF QUADRATICS 271 RATIO PROPORTION AND VARIATION 277 CHAPTER PAGE XXIII PROGRESSIONS 295 INDETERMINATE COEFFICIENTS 312 BINOMIAL THEOREM 319 COMMON LOGARITHMS 331 INTEREST AND ANNUITIES 346

 FRACTIONS 109 FRACTIONAL EQUATIONS 134 SIMULTANEOUS EQUATIONS OF THE FIRST DEGREE 154 PROBLEMS INVOLVING TWO UNKNOWN NUMBERS 169 SIMPLE INDETERMINATE EQUATIONS 186 INEQUALITIES 192 INVOLUTION AND EVOLUTION 194 THEORY OF EXPONENTS 207 RADICAL EXPRESSIONS 214 IMAGINARY EXPRESSIONS 231 QUADRATIC EQUATIONS 236
 CHOICE 356 CHANCE 377 CONTINUED FRACTIONS 381 SCALES OF NOTATION 392 THEORY OF NUMBERS 397 VARIABLES AND LIMITS 403 SERIES 412 GENERAL PROPERTIES OF EQUATIONS 441 NUMERICAL EQUATIONS 473 DETERMINANTS 499 COMPLEX NUMBERS 515

### Popular passages

Page 299 - If the number is less than 1, make the characteristic of the logarithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number.
Page 125 - A man leaves the half of his property to his wife, a sixth to each of his two children, a twelfth to his brother, and the remainder, amounting to \$600, to his sister. What was the amount of his property ? 17.
Page 135 - A cask contains 12 gallons of wine and 18 gallons of water ; another cask contains 9 gallons of wine and 3 gallons of water. How many gallons must be drawn from each cask to produce a mixture containing 7 gallons of wine and 7 gallons of water?
Page 249 - If the product of two numbers is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. For, if ad = bc, then, dividing by bd, or / (л- с'- v / 316.
Page 155 - The sum of the two digits of a number is 6, and if the number is divided by the sum of the digits the quotient is 4. What is the number ? 19.
Page 455 - Form all the possible products of n elements each that can be formed by taking one, and only one, element from each row, and one, and only one, element from each column ; prefix to each of the products thus formed either...
Page 270 - The sum of the squares of the extremes of four numbers in arithmetical progression is 200, and the sum of the squares of the means is 136. What are the numbers ? 24.
Page 274 - Of three numbers in geometrical progression, the sum of the first and second exceeds the third by 3, and the sum of the first and third exceeds the second by 21. What are the numbers ? 15.
Page 412 - The coefficient pt of the fourth term with its sign changed is equal to the sum of the products of the roots taken three...
Page 249 - The equation ad = be gives be ad a = -у, b — — ; a с so that an extreme may be found by dividing the product of the means by the other extreme ; and a mean may be found by dividing the product of the extremes by the other mean.