An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 2
... exponent of the power . The power is expressed by writing the quantity Coefficient . Power . Root . once with the exponent 2 [ CH . I. § I. ALGEBRA .
... exponent of the power . The power is expressed by writing the quantity Coefficient . Power . Root . once with the exponent 2 [ CH . I. § I. ALGEBRA .
Page 3
... exponent to the right of the quantity , and a little above it . When no exponent is written , the exponent may be considered to be unity . Thus the fifth power of a is written a3 ; but when a stands by itself , it may be regarded as a1 ...
... exponent to the right of the quantity , and a little above it . When no exponent is written , the exponent may be considered to be unity . Thus the fifth power of a is written a3 ; but when a stands by itself , it may be regarded as a1 ...
Page 5
... exponents of its literal factors . Thus , 7x is of one dimension , or of the first degree ; 5a2 b c is of four dimensions , or of the fourth degree , & c . 16. A polynomial is homogeneous , when all its terms are of the same degree ...
... exponents of its literal factors . Thus , 7x is of one dimension , or of the first degree ; 5a2 b c is of four dimensions , or of the fourth degree , & c . 16. A polynomial is homogeneous , when all its terms are of the same degree ...
Page 10
... exponent equal to the sum of all its exponents in the different factors . 29. EXAMPLES . 1. Multiply a b by c d e . Ans . abcde . 2. Find the continued product of 3 a b , 2 cd , and e f g . 3. Multiply am by a " . Ans . 6 abcdefg . Ans ...
... exponent equal to the sum of all its exponents in the different factors . 29. EXAMPLES . 1. Multiply a b by c d e . Ans . abcde . 2. Find the continued product of 3 a b , 2 cd , and e f g . 3. Multiply am by a " . Ans . 6 abcdefg . Ans ...
Page 14
... exponent , and re- tain it in the other term , giving it an exponent equal to the difference of its exponents in the two terms . But when a letter occurs in only one term , it is to be retained in that term , with its exponent unchanged ...
... exponent , and re- tain it in the other term , giving it an exponent equal to the difference of its exponents in the two terms . But when a letter occurs in only one term , it is to be retained in that term , with its exponent unchanged ...
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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