# An Elementary Treatise on Algebra: Designed to Facilitate the Comprehension, Demonstration and Application of the Leading Principles of that Science

E. Morgan & Company, 1845 - 294 pages

### Contents

 INTRODUCTION EXPLANATIONS AND DEFINITIONS 13 The Square Root 101 Binomial Theorem 143 SUBJECT XI 159 Surd Quantities 173 Decomposition of a General Equation of the mth Degree 181 SUBJECT XIV 196
 SUBJECT XV 202 Unequal Roots of an Equation 212 SUBJECT XVII 238 SUBJECT XVIII 260 SUBJECT XIX 272 SUBJECT XX 279 SUBJECT XXI 294

### Popular passages

Page 38 - 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.
Page 142 - B's journey in 15\$ days, but B would have been 28 days in performing A's journey. What was the distance between C and D ? Ans.
Page 32 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first and second, plus the square of the second. Thus, (a — 6)* = (a — b) (a — 6)=a2— 2a6 + 6'.
Page 96 - Two persons, A and B, lay out equal sums of money in trade ; A gains \$126, and B loses \$87, and A's money is now double of B's : what did each lay out ? Ans. \$300.
Page 58 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 142 - What number is that, which, being divided by the product of its digits, the quotient is 3 ; and if 18 be added to it, the digits will be inverted ? Ans.
Page 99 - A person bought a chaise, horse, and harness for 60?.; the horse came to twice the price of the harness, and the chaise to twice the price of the horse and harness ; what did he give for each ? Ans. 13/.
Page 99 - Divide the number 90 into 4 such parts, that the . first increased by 2, the second diminished by 2, the third multiplied by 2, and the fourth divided by 2, shall all be equal.
Page 163 - Multiply the complete divisor by the second term of the root, and subtract the product from the remainder.
Page 163 - Divide the first term of the remainder by three times the square of the first term of the root as a trial divisor, and the quotient will be the next term of the root.