A Treatise on Algebra: By Charles SmithMacmillan and Company, 1888 - 571 sider |
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Side x
... solution Equations of the first degree with three unknown quantities Method of undetermined multipliers Equations with ... solutions of the corresponding equations . Examples XV .. CHAPTER XII . MISCELLANEOUS THEOREMS AND EXAMPLES . PAGE ...
... solution Equations of the first degree with three unknown quantities Method of undetermined multipliers Equations with ... solutions of the corresponding equations . Examples XV .. CHAPTER XII . MISCELLANEOUS THEOREMS AND EXAMPLES . PAGE ...
Side xvi
... solutions of ax + by = c can always be found if a and b are prime to one another General solution of ax - by = c , having given one solution General solution of ax + by = c , having given one solution Number of positive integral solutions ...
... solutions of ax + by = c can always be found if a and b are prime to one another General solution of ax - by = c , having given one solution General solution of ax + by = c , having given one solution Number of positive integral solutions ...
Side 105
... solution of equations frequent use is made of the following principles . I. An equation is equivalent to that formed by adding the same quantity to both its members . For it is clear that A + m = B + m when , and only when , A = B. II ...
... solution of equations frequent use is made of the following principles . I. An equation is equivalent to that formed by adding the same quantity to both its members . For it is clear that A + m = B + m when , and only when , A = B. II ...
Side 107
... solution of which is x = — The following are special cases . I. If b = 0 , the equation reduces to ax = 0 ; whence x = 0 . II . If b = 0 and also a = 0 , the equation is clearly satisfied for all values of x . III . If a = 0 , and b 0 ...
... solution of which is x = — The following are special cases . I. If b = 0 , the equation reduces to ax = 0 ; whence x = 0 . II . If b = 0 and also a = 0 , the equation is clearly satisfied for all values of x . III . If a = 0 , and b 0 ...
Side 108
... the system of alternative equations - α = 0 , or x − b = 0 , or x - c = 0 , & c . - From the above it will be apparent that the solution of an equation of any degree can be written down 108 ONE UNKNOWN QUANTITY . EQUATIONS .
... the system of alternative equations - α = 0 , or x − b = 0 , or x - c = 0 , & c . - From the above it will be apparent that the solution of an equation of any degree can be written down 108 ONE UNKNOWN QUANTITY . EQUATIONS .
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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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