An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 3
... dividend over the divisor with a line between them . a Thus , a ÷ b , or a : b , or denotes the quotient of a di- b vided by b . Signs of Equality and Inequality . Algebraic Quantity . 9. CH . I. I. ] DEFINITIONS AND NOTATION . 3.
... dividend over the divisor with a line between them . a Thus , a ÷ b , or a : b , or denotes the quotient of a di- b vided by b . Signs of Equality and Inequality . Algebraic Quantity . 9. CH . I. I. ] DEFINITIONS AND NOTATION . 3.
Page 14
... quotient , the quotient must be obtained by suppressing in the dividend all the factors of the divisor which are ex- plicitly contained in the dividend , and simply indicating the division with regard to the remaining factors of the ...
... quotient , the quotient must be obtained by suppressing in the dividend all the factors of the divisor which are ex- plicitly contained in the dividend , and simply indicating the division with regard to the remaining factors of the ...
Page 15
... quotient is positive ; but when they are affected by contrary signs , the quotient is negative . Thele for the signs in both division and multiplication may be expressed still more concisely as follows . Like signs give + ; unlike signs ...
... quotient is positive ; but when they are affected by contrary signs , the quotient is negative . Thele for the signs in both division and multiplication may be expressed still more concisely as follows . Like signs give + ; unlike signs ...
Page 16
... quotient becomes zero . But the quotient of a quantity di- vided by itself is unity . Whence any quantity with an exponent equal to zero is unity . Thus , amam ao = 1 . 36 38. Corollary . When , in example 6 of art . 30 , the ex- ponent ...
... quotient becomes zero . But the quotient of a quantity di- vided by itself is unity . Whence any quantity with an exponent equal to zero is unity . Thus , amam ao = 1 . 36 38. Corollary . When , in example 6 of art . 30 , the ex- ponent ...
Page 18
... quotient which contains the highest power of the same letter . , ༞ A term of the quotient is consequently obtained by dividing , as in art . 35 , the term of the dividend which contains the highest power of any letter by that term of ...
... quotient which contains the highest power of the same letter . , ༞ A term of the quotient is consequently obtained by dividing , as in art . 35 , the term of the dividend which contains the highest power of any letter by that term of ...
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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