## A Complete Course in AlgebraLeach, Shewell, and Sanborn, 1885 |

### From inside the book

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**less**than " respectively , when placed between two quantities , indicates that the quantity toward which the opening of the sign turns is the greater . Thus , x > y is read " is greater than y " ; x 6 < y is read " minus 6 is**less**... Page 10

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**less**than the recipro- sal of a cube . AXIOMS . 42. An Axiom is a truth assumed as self - evident . Algebraic operations are based upon definitions , and the following axioms : 1. If equal quantities be added to equal quantities , the ... Page 11

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**less**number , plus 4 times the**less**number , equals 30 ( b ) Therefore 5 times the**less**number equals 30 . ( c ) Hence the**less**number is one - fifth of 30 , or 6 . ( d ) Then the greater number is 4 times 6 , or 24 . Let Then ... Page 12

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**less**, and their sum is 42. What are the numbers ? 6 5. The sum of the ages of A and B is 68 years , and B is years older than A. What are their ages ? 6. Divide $ 1200 between A and B , so that A may receive $ 128**less**than B. 7. A man ... Page 17

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**less**coefficient from the greater , affix to the result the common sym- bols , and prefix the sign of the greater coefficient . Note . A clear understanding of the nature of the processes in Arts . 52 and 53 may be obtained by comparing ...### Other editions - View all

### Common terms and phrases

a²+2ab+b² a²b² a³b ab+b² ab² ab³ Adding Algebra arithmetical means arithmetical progression ax² ax³ binomial cents change the sign coefficient cologarithm Completing the square cube root decimal derive the formulæ digits dividend divisor EXAMPLES exponent expression Extracting the square Find the H.C.F. Find the value Find two numbers following equations following rule formula fraction geometrical progression Hence highest common factor last term less logarithm lowest common multiple mantissa monomial Multiplying Note number of terms parenthesis perfect square polynomial positive proportion QUADRATIC EQUATIONS quotient radical sign Reduce the following remainder Required the number result rods rule of Art second term simplest form Solve the equation Solve the following square root subtract third Transposing trial-divisor twice unknown quantity Whence

### Popular passages

Page 166 - Arts. 200 and 201 we derive the following rule : Extract the required root of the numerical coefficient, and divide the exponent of each letter by the index of the root.

Page 213 - In any trinomial square (Art. 108), the middle term is twice the product of the square roots of the first and third terms...

Page 44 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.

Page 49 - The exponent of b in the second term is 1, and increases by 1 in each succeeding term.

Page 255 - The first and fourth terms of a proportion are called the extremes; and the second and third terms the means. Thus, in the proportion a : b = с : d, a and d are the extremes, and b and с the means.

Page 258 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: b = c: d = e:f.

Page 5 - If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be changed.

Page 44 - The square of the sum of two quantities is equal to the SQuare of the first, plus twice the product of the first by the second, plus the square of the second.

Page 107 - Any term may be transposed from one side of an equation to the other by changing its sign. For, consider the equation x + a = b.

Page 227 - A' courier proceeds from P to Q in 14 hours. A second courier starts at the same time from a place 10 miles behind P, and arrives at Q at the same time as the first courier. The second courier finds that he takes half an hour less than the first to accomplish 20 miles. Find the distance from P to Q.