Algebra for Beginners |
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Page 2
... difference between the notation of Arithmetic and Algebra should be here remarked . In Arithmetic the product of 2 and 3 is written 2 × 3 , whereas in Algebra the product of a and b may be written in any of the forms axb , a . b , or ab ...
... difference between the notation of Arithmetic and Algebra should be here remarked . In Arithmetic the product of 2 and 3 is written 2 × 3 , whereas in Algebra the product of a and b may be written in any of the forms axb , a . b , or ab ...
Page 3
... difference in meaning between 3a and a3 ? By 3a we mean the product of the quantities 3 and a . By a3 we mean the third power of a ; that is , the product of the quantities a , a , a . Thus , if a = = 4 , 3a = 3x a = 3 x 4 = 12 ; a3 = a ...
... difference in meaning between 3a and a3 ? By 3a we mean the product of the quantities 3 and a . By a3 we mean the third power of a ; that is , the product of the quantities a , a , a . Thus , if a = = 4 , 3a = 3x a = 3 x 4 = 12 ; a3 = a ...
Page 9
... difference of these two results , preceded by the sign of the greater , will give the coefficient of the sum required . Example 1. The sum of 17x and 8x is 9x , for the difference of 17 and 8 is 9 , and the greater is positive . Example ...
... difference of these two results , preceded by the sign of the greater , will give the coefficient of the sum required . Example 1. The sum of 17x and 8x is 9x , for the difference of 17 and 8 is 9 , and the greater is positive . Example ...
Page 16
... difference = 4a - 3b + 5c- ( 3a - 2b - c ) = 4a - 3b + 5c - 3a + 2b + c = 4a - 3a - 3b + 2b + 5c + c = a - b + 6c . The expression to be subtracted is first enclosed in brackets with a minus sign prefixed , then on removal of the ...
... difference = 4a - 3b + 5c- ( 3a - 2b - c ) = 4a - 3b + 5c - 3a + 2b + c = 4a - 3a - 3b + 2b + 5c + c = a - b + 6c . The expression to be subtracted is first enclosed in brackets with a minus sign prefixed , then on removal of the ...
Page 31
... In each of these cases it should be noticed that the index of any letter in the quotient is the difference of the indices of that letter in the dividend and divisor . 50. It is easy to prove that the rule of DIVISION.
... In each of these cases it should be noticed that the index of any letter in the quotient is the difference of the indices of that letter in the dividend and divisor . 50. It is easy to prove that the rule of DIVISION.
Common terms and phrases
a²+b² 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.