A Treatise on Algebra: By Charles SmithMacmillan and Company, 1888 - 571 páginas |
Dentro del libro
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Página 9
... seen that it is not necessary to invent any new signs to distinguish between quantities of directly opposite kinds , for this can be done by means of the old signs + and - The signs and are therefore used in Algebra with two entirely ...
... seen that it is not necessary to invent any new signs to distinguish between quantities of directly opposite kinds , for this can be done by means of the old signs + and - The signs and are therefore used in Algebra with two entirely ...
Página 20
... seen to be included in Art . 29 ( C ) . 35. Since a3 × a2 = a3 , and a2 × a3 = a10 ; we have con- versely a ÷ a3 = a3 , and a1o ÷ a3 = a3 . And , in general , and m > n , we have for by Art . 31 10 when m and n are any positive integers ...
... seen to be included in Art . 29 ( C ) . 35. Since a3 × a2 = a3 , and a2 × a3 = a10 ; we have con- versely a ÷ a3 = a3 , and a1o ÷ a3 = a3 . And , in general , and m > n , we have for by Art . 31 10 when m and n are any positive integers ...
Página 26
... seen that any term is added by writing it down , with its sign unchanged , after the expres- sion to which it is to be added ; and we have also seen that to add any expression as a whole gives the same result as to add all its terms in ...
... seen that any term is added by writing it down , with its sign unchanged , after the expres- sion to which it is to be added ; and we have also seen that to add any expression as a whole gives the same result as to add all its terms in ...
Página 27
... seen that any term may be sub- tracted by writing it down , with its sign changed , after the expression from which it is to be subtracted ; and we have also seen that to subtract any expression as a whole gives the same result as to ...
... seen that any term may be sub- tracted by writing it down , with its sign changed , after the expression from which it is to be subtracted ; and we have also seen that to subtract any expression as a whole gives the same result as to ...
Página 28
... seen in Art . 46 , to add any algebraical expression we have only to write down the terms in suc- cession with their signs unchanged . Hence , when a bracket is preceded by a + sign , the bracket may be omitted . Thus + ( 2a5b + 7c ) ...
... seen in Art . 46 , to add any algebraical expression we have only to write down the terms in suc- cession with their signs unchanged . Hence , when a bracket is preceded by a + sign , the bracket may be omitted . Thus + ( 2a5b + 7c ) ...
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Términos y frases comunes
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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