An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 2
... expression 15 a b , 15 is the numerical co- efficient of a b ; and , in the expression xy , 1 may be re- garded as the coefficient of x y . 6. The continued product of a quantity multiplied repeatedly by itself , is called the power of ...
... expression 15 a b , 15 is the numerical co- efficient of a b ; and , in the expression xy , 1 may be re- garded as the coefficient of x y . 6. The continued product of a quantity multiplied repeatedly by itself , is called the power of ...
Page 4
... expression in which this sign occurs is called an equation . Thus , the equation ab denotes that a is equal to b . 10. The sign is called greater than , and the sign < is called less than ; and the expression in which either of these ...
... expression in which this sign occurs is called an equation . Thus , the equation ab denotes that a is equal to b . 10. The sign is called greater than , and the sign < is called less than ; and the expression in which either of these ...
Page 36
... expression having any required denominator , by regarding it as a fraction , the denominator of which is unity . 70. EXAMPLES . 1. Reduce 325 8 ' 3 ' 6 ' to the common denominator 24 . 1 9 16 20 Ans . 24 ' 24 ' 24 ' 2. Reduce nator 4 c2 ...
... expression having any required denominator , by regarding it as a fraction , the denominator of which is unity . 70. EXAMPLES . 1. Reduce 325 8 ' 3 ' 6 ' to the common denominator 24 . 1 9 16 20 Ans . 24 ' 24 ' 24 ' 2. Reduce nator 4 c2 ...
Page 39
... expression + c . a + bc Ans . b 6. Reduce to one fraction 2 a 3bc 5df beg + 862 c 6 b2 c2 ° 16 abc15cdf - 4beg Ans . 24 62 c2 α b 7. Reduce to one fraction + x 1 x3 * ax2 bx + 1 Ans . x3 a 8. Reduce to one fraction a + z + azz a2 + z2 ...
... expression + c . a + bc Ans . b 6. Reduce to one fraction 2 a 3bc 5df beg + 862 c 6 b2 c2 ° 16 abc15cdf - 4beg Ans . 24 62 c2 α b 7. Reduce to one fraction + x 1 x3 * ax2 bx + 1 Ans . x3 a 8. Reduce to one fraction a + z + azz a2 + z2 ...
Page 50
... expressing of its conditions in alge- braic language ; this is called putting the problem into equations . 102. No rule can be given for putting questions into equations , which is universally applicable . The following rule , can ...
... expressing of its conditions in alge- braic language ; this is called putting the problem into equations . 102. No rule can be given for putting questions into equations , which is universally applicable . The following rule , can ...
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Common terms and phrases
126 become zero 3d root arithmetical progression coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots equal to zero equation x² factor Find the 3d Find the 4th Find the continued Find the greatest Find the number Find the square Find the sum Free the equation Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots last term least common multiple letter logarithm monomials multiplied number of real number of terms polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Second Degree Solution Solve the equation square root Sturm's Theorem subtracted Theorem unity unknown quan unknown quantity variable whence