Algebra for Beginners |
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Page 8
... taken as indicating a reversal of direction . ( iii ) The freezing point of the Centigrade thermometer is marked zero , and a temperature of 15 ° C. means 15 ° above the freezing point , while a temperature 15 ° below the freezing point ...
... taken as indicating a reversal of direction . ( iii ) The freezing point of the Centigrade thermometer is marked zero , and a temperature of 15 ° C. means 15 ° above the freezing point , while a temperature 15 ° below the freezing point ...
Page 11
... taken . This also holds in the case of algebraical quantities . Thus ab + c is equivalent to a + c - b , for in the first of the two expressions b is taken from a , and c added to the result ; in the second c is added to a , and b taken ...
... taken . This also holds in the case of algebraical quantities . Thus ab + c is equivalent to a + c - b , for in the first of the two expressions b is taken from a , and c added to the result ; in the second c is added to a , and b taken ...
Page 12
... taken away c too much , and must therefore add c to a - b . Thus In like manner , a- ( b − c ) = a - b + c . a − b − ( c - d − e ) = a − b - c + d + e . - - Accordingly the following rule may be enunciated : Rule . When an ...
... taken away c too much , and must therefore add c to a - b . Thus In like manner , a- ( b − c ) = a - b + c . a − b − ( c - d − e ) = a − b - c + d + e . - - Accordingly the following rule may be enunciated : Rule . When an ...
Page 13
... taken to mean the sum of the two quantities a and b without any regard to the relative magnitudes of a and b . Example 1. Find the sum of 3a - 5b + 2c , 2a + 3b - d , - - - 4a + 2b ) The sum = ( 3a - 5b + 2c ) + ( 2a + 3b − d ) + ...
... taken to mean the sum of the two quantities a and b without any regard to the relative magnitudes of a and b . Example 1. Find the sum of 3a - 5b + 2c , 2a + 3b - d , - - - 4a + 2b ) The sum = ( 3a - 5b + 2c ) + ( 2a + 3b − d ) + ...
Page 19
... + ax ) , when a 0 , b = 1 , c = 2 , x = S , y = 3 , z = 4 . = 15. Subtract the sum of 23 - 3x2 , 2x2 - 7x , 8x - 2 , 5-3x3 , 2x3 - 7 from x3 + x2 + x + 1 . 16. What expression must be taken from the sum of IV . ] 19 SUBTRACTION .
... + ax ) , when a 0 , b = 1 , c = 2 , x = S , y = 3 , z = 4 . = 15. Subtract the sum of 23 - 3x2 , 2x2 - 7x , 8x - 2 , 5-3x3 , 2x3 - 7 from x3 + x2 + x + 1 . 16. What expression must be taken from the sum of IV . ] 19 SUBTRACTION .
Common terms and phrases
aČ+bČ acres algebraical sum Arithmetic arranged beginner cents CHAPTER coefficient Completing the square compound expressions convenient cube root descending powers difference digits dimes Divide division divisor Elementary Algebra equal examples see Elementary EXAMPLES XVII exceeds Find the highest Find the lowest find the number Find the product Find the square Find the sum find the value following expressions given expressions half-dollars Hence highest common factor lowest common denominator lowest common multiple lowest terms miles an hour miles per hour minute-hand Multiply negative numerator and denominator obtain quadratic equation quotient Reduce to lowest remainder removing brackets Resolve into factors result rule of signs side simple equation simultaneous equations Solve the equations square root Subtract Transposing trinomial unknown quantities walk whence write yards α α
Popular passages
Page 91 - The product is a2+2a6-}-62; from which it appears, that 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 - Conversely, the difference of the squares of any two quantities is equal to the product of the sum and the difference of the two quantities.
Page 89 - It is evident from the Rule of Signs that (1) no even power of any quantity can be negative; (2) any odd power of a quantity will have the same sign as the quantity itself. NOTE. It is especially worthy of notice that the square of every expression, whether positive or negative, is positive.
Page 54 - Transpose all the terms containing the unknown quantity to one side of the equation, and the "known quantities to the other.