A Treatise on Algebra: By Charles Smith |
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Page xii
... term . 295 Examples XXIV . 297 Properties of the coefficients of a binomial expansion 299 Continued product of n binomial factors of the form x + a , x + b , & c . 302 Vandermonde's Theorem [ see also p . 282 ] 304 The multinomial ...
... term . 295 Examples XXIV . 297 Properties of the coefficients of a binomial expansion 299 Continued product of n binomial factors of the form x + a , x + b , & c . 302 Vandermonde's Theorem [ see also p . 282 ] 304 The multinomial ...
Page 35
... terms in vertical columns will thus be avoided . 60 . Definitions . A term which is the product of n letters is said to be of n dimensions , or of the nth degree . Thus 3abc is of three dimensions , or of the third degree ; and 5a b'c ...
... terms in vertical columns will thus be avoided . 60 . Definitions . A term which is the product of n letters is said to be of n dimensions , or of the nth degree . Thus 3abc is of three dimensions , or of the third degree ; and 5a b'c ...
Page 70
... n - 1 ( a− p ) x " + ( b − q ) x2 - 1 + ( c − r ) x2 - 2 + ...... , · - will ... nth degree in x are equal to one another for more than n values of x , the ... term which does -- not contain the letter a is put first , and the other ...
... n - 1 ( a− p ) x " + ( b − q ) x2 - 1 + ( c − r ) x2 - 2 + ...... , · - will ... nth degree in x are equal to one another for more than n values of x , the ... term which does -- not contain the letter a is put first , and the other ...
Page 96
... term of A ; then Xb‚a bß by . will be the corresponding term of B ; and since the expres- sions A and B are homogeneous and of the nth degree , a + B + y + ... = n . a λα α β Now λa , a , a , ... = λ ( b ̧x ) a ( b ̧x ) 3 ( b2x ) ...
... term of A ; then Xb‚a bß by . will be the corresponding term of B ; and since the expres- sions A and B are homogeneous and of the nth degree , a + B + y + ... = n . a λα α β Now λa , a , a , ... = λ ( b ̧x ) a ( b ̧x ) 3 ( b2x ) ...
Page 123
... nth degree n - 2 n - 3 ax " + bx " 1 + cx " 2 + dx " 3 + .... vanish for the n values x = α , x = B , x = y , & c ... term one degree lower than the highest is absent . We may make use of the above to prove certain identical rela- tions ...
... nth degree n - 2 n - 3 ax " + bx " 1 + cx " 2 + dx " 3 + .... vanish for the n values x = α , x = B , x = y , & c ... term one degree lower than the highest is absent . We may make use of the above to prove certain identical rela- tions ...
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Common terms and phrases
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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