An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 1
... letters of the alphabet , and the operations to be performed upon them are indicated by signs . In this sense it would embrace almost the whole science of mathematics , elementary geometry alone being excepted . It is , consequently ...
... letters of the alphabet , and the operations to be performed upon them are indicated by signs . In this sense it would embrace almost the whole science of mathematics , elementary geometry alone being excepted . It is , consequently ...
Page 2
... letters , the sign may be altogether omitted . Thus 3 x 5 x 7 , or 3.5.7 is the continued product of 3 , 5 , and 7. Likewise 12 × a × b , or 12. a . b , or 12 ab , is the continued product of 12 , a , and b . 5. The factor of a product ...
... letters , the sign may be altogether omitted . Thus 3 x 5 x 7 , or 3.5.7 is the continued product of 3 , 5 , and 7. Likewise 12 × a × b , or 12. a . b , or 12 ab , is the continued product of 12 , a , and b . 5. The factor of a product ...
Page 4
... letters are not separated by the signs and , is called a monomial , or a quantity composed of a single term , or simply a term . Thus , 3 a2 , - 10 a3 x are monomials . 13. An algebraic expression composed of several terms , connected ...
... letters are not separated by the signs and , is called a monomial , or a quantity composed of a single term , or simply a term . Thus , 3 a2 , - 10 a3 x are monomials . 13. An algebraic expression composed of several terms , connected ...
Page 10
... letter may also be brought together , and since , by art . 6 , each exponent de- notes the number of times which the letter occurs as a factor in the corresponding term , the number of times which it occurs as a factor in the product ...
... letter may also be brought together , and since , by art . 6 , each exponent de- notes the number of times which the letter occurs as a factor in the corresponding term , the number of times which it occurs as a factor in the product ...
Page 14
... letter of the divisor or dividend in the term in which it has the least 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 ...
... letter of the divisor or dividend in the term in which it has the least 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 ...
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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