A Treatise on Algebra: By Charles SmithMacmillan and Company, 1888 - 571 σελίδες |
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Σελίδα viii
... Divisibility of x2 ± an by x ± a Remainder Theorem . An expression of the nth degree cannot vanish for more than n values of x , unless it vanishes for all values of a Cyclical order Symmetrical expressions . Factors found by use of ...
... Divisibility of x2 ± an by x ± a Remainder Theorem . An expression of the nth degree cannot vanish for more than n values of x , unless it vanishes for all values of a Cyclical order Symmetrical expressions . Factors found by use of ...
Σελίδα xii
... divisible by r - 1 . Rule for casting out the nines . Examples XXII . CHAPTER XIX . PERMUTATIONS AND COMBINATIONS . Permutations of different things Permutations all together of things which are not all different Combinations Cr = nCn ...
... divisible by r - 1 . Rule for casting out the nines . Examples XXII . CHAPTER XIX . PERMUTATIONS AND COMBINATIONS . Permutations of different things Permutations all together of things which are not all different Combinations Cr = nCn ...
Σελίδα xvi
... divisible by n Number of divisors of a given number PAGE 474 475-477 478 478 480 • 481 482 . 484 " 485 487 488 491 492 Number of positive integers less than a given number and prime to it [ see also p . 490 ] Forms of square numbers ...
... divisible by n Number of divisors of a given number PAGE 474 475-477 478 478 480 • 481 482 . 484 " 485 487 488 491 492 Number of positive integers less than a given number and prime to it [ see also p . 490 ] Forms of square numbers ...
Σελίδα 53
... divisible by that letter . Thus and 2ax + x2 = x ( 2a + x ) , ax + a2x2 = ax ( 1 + ax ) , 2a3b2x + 3a2b3y = a2b2 ( 2ax + 3by ) . Such monomial factors , if there be any , are obvious on inspection . 78. Factors found by comparing with ...
... divisible by that letter . Thus and 2ax + x2 = x ( 2a + x ) , ax + a2x2 = ax ( 1 + ax ) , 2a3b2x + 3a2b3y = a2b2 ( 2ax + 3by ) . Such monomial factors , if there be any , are obvious on inspection . 78. Factors found by comparing with ...
Σελίδα 65
... divisible by x - a , for all positive integral values of n . It is known that x - a , x2 - a2 and x3 divisible by x - α . We have " — an = x2 -- = 2-1 - - · an - - a3 are all · x2 - 1 ( x − a ) + a ( x2 − 1 — a1 - 1 ) . - Now if x a ...
... divisible by x - a , for all positive integral values of n . It is known that x - a , x2 - a2 and x3 divisible by x - α . We have " — an = x2 -- = 2-1 - - · an - - a3 are all · x2 - 1 ( x − a ) + a ( x2 − 1 — a1 - 1 ) . - Now if x a ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
a+b+c a₁ arithmetic mean arithmetical progression ax² b₁ binomial Binomial Theorem C₁ Cambridge coefficient contain continued fraction Crown 8vo denominator determinant digits divergent divide divisible divisor Edition equal equation ax example expansion Extra fcap Fcap Find the number Find the sum follows geometrical progression given expression Globe 8vo greater Hence the required infinity letters logarithm MACMILLAN'S Multiply negative nth convergent nth root nth term number of terms obtained P₁ periodic continued fraction positive integer powers prime number Professor prove quadratic equation quadratic surd quotient ratio remainder School Shew Solve the equation square root subtract suppose Theorem Trinity College u₁ unknown quantities white ball whole number zero
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