# New Elementary Algebra: Embracing the First Principles of the Science

A.S. Barnes & Company, 1859 - Algebra - 299 pages
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### Contents

 CHAPTER I 33 AlgebraDefinitionsExplanation of the Signs 41 AdditionRuleExamples 67 CHAPTER III 76 CHAPTER IV 87 To Reduce a Fraction to its Lowest Terms 90 Addition of Fractions 9698 97 CHAPTER V 105
 CHAPTER VII 173 Square Root of Fractions 179181 179 Addition of Radicals 187189 187 Multiplication of Radicals 190191 190 CHAPTER VIII 198 Four Forms 211227 211 Four Properties 227229 227 Problems 236240 236

### Popular passages

Page 71 - 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 295 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Page 72 - ... the first term of the quotient ; multiply the divisor by this term, and subtract the product from the dividend. II. Then divide the first term of the remainder by the first term of the divisor...
Page 77 - 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 118 - A fish was caught whose tail weighed 9Z6. ; his head weighed as much as his tail and half his body, and his body weighed as much as his head and tail together : what was the weight of the fish?
Page 173 - The Square Root of a number is one of its two equal factors. Thus, the square root of 25 is 5, since 5x5 are 25.
Page 145 - To divide the number 75 into two such parts, that three times the greater may exceed seven times the less by 15. Ans. 54 and 21.
Page 146 - A person has two horses, and a saddle worth £50. Now, if the saddle be put on the back of the first horse, it will make his value double that of the second ; but if it be put on the back of the second, it will make his value triple that of the first. What is the value of each horse ? Ans.
Page 179 - ... equal to the square root of the numerator divided by the square root of the denominator.
Page 146 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from home, it lasted the woman 30 days ; how many days would the man alone be in drinking it ? Ans.