Elementary AlgebraRivingtons, 1870 - Algebra |
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Page 33
... Divisor with a line drawn between them , thus a In this Chapter we shall treat only of cases in which the Dividend contains the Divisor an exact number of times . S. A. 3 CASE I. 74. When the Dividend and Divisor are each .DIVISION . 33 ...
... Divisor with a line drawn between them , thus a In this Chapter we shall treat only of cases in which the Dividend contains the Divisor an exact number of times . S. A. 3 CASE I. 74. When the Dividend and Divisor are each .DIVISION . 33 ...
Page 34
... Divisor are equal . Thus a x2y ? = 1 ; = 1 ; a xy2 and this will hold true when the Dividend and the Divisor are compound quantities . Thus a + b a + b = 1 ; x2 - y2 x2 - y2 = 1 . Divide 1. x6 by x3 . EXAMPLES . - XI . x10 by x2 . 3 ...
... Divisor are equal . Thus a x2y ? = 1 ; = 1 ; a xy2 and this will hold true when the Dividend and the Divisor are compound quantities . Thus a + b a + b = 1 ; x2 - y2 x2 - y2 = 1 . Divide 1. x6 by x3 . EXAMPLES . - XI . x10 by x2 . 3 ...
Page 35
James Hamblin Smith. CASE II . 76. If the Divisor be a single term , while the Dividend contains two or more terms , the quotient will be found by dividing each term of the Dividend separately by the Divisor and connecting the results ...
James Hamblin Smith. CASE II . 76. If the Divisor be a single term , while the Dividend contains two or more terms , the quotient will be found by dividing each term of the Dividend separately by the Divisor and connecting the results ...
Page 36
... Divisor and the Dividend contain more terms than one . The operation is conducted in the following way : Arrange the Divisor and Dividend according to the powers of some one symbol , and place them in the same line as in the process of ...
... Divisor and the Dividend contain more terms than one . The operation is conducted in the following way : Arrange the Divisor and Dividend according to the powers of some one symbol , and place them in the same line as in the process of ...
Page 37
... Divisor and Dividend by descending powers of x , x + y - 1 ) x + 3xy + y3 — 1 ( x2 - xy + x + y2 + y + 1 x3 + x2y - x2 - x2y + x2 + 3xy + y3 — 1 — x2y — xy2 + xy - x2 + xy2 + 2xy + y3 — 1 x2 + xy - x xy2 + xy + x + y3 − 1 - xy2 + y3 ...
... Divisor and Dividend by descending powers of x , x + y - 1 ) x + 3xy + y3 — 1 ( x2 - xy + x + y2 + y + 1 x3 + x2y - x2 - x2y + x2 + 3xy + y3 — 1 — x2y — xy2 + xy - x2 + xy2 + 2xy + y3 — 1 x2 + xy - x xy2 + xy + x + y3 − 1 - xy2 + y3 ...
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Common terms and phrases
2ab+b² a+b-c a²+2ab+b² a²+b² Algebra arithmetic means Arithmetical Progression Cambridge coefficient College List Crown 8vo denominator denote difference Divide Dividend division divisor Edition equal Find the number Find the value following expressions gallons Geometrical Progression given greater Greek Hence Highest Common Factor integer less logarithms miles an hour Multiply negative Nonary number of permutations number of terms obtain positive proceed proper fraction q factors quadratic equation quantity quotient radix ratio remainder represent the number result Rivington's School rules scale whose radix School and College second term Senary shew shillings sides Simplify solve the equations square root Subtracting surds take the square things taken third Thomas Kerchever Arnold tion unknown symbol whole number
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Page 253 - ... if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth ; or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth ; or, if the multiple of Book V.
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Page 328 - A number is divisible by 11 if the difference between the sum of the digits in the even places and the sum of the digits in the odd places is either 0 or a multiple of 11.
Page 292 - Recall the general formula for the number of combinations of n different things taken r at a time, C(n,r) n\ r!(nr)!
Page 328 - Suppose that a*=n, then x is called the logarithm of n to the base a : thus the logarithm of a number to a given base is the index of the power to which the base must be raised to be equal to the number. The logarithm of n to the base a is written log.