The elements of algebra1857 |
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Page 94
... side , and In this equation it is asserted , that a certain unknown quantity ( x ) is so connected with two known quantities ( a and b ) , that it exceeds the one ( a ) by as much as it falls short of the other ( b ) . Again , x2 + x ...
... side , and In this equation it is asserted , that a certain unknown quantity ( x ) is so connected with two known quantities ( a and b ) , that it exceeds the one ( a ) by as much as it falls short of the other ( b ) . Again , x2 + x ...
Page 95
... side to the other , if their signs be changed , and the two sides will still be equal . For let + 10 = 15 ; then by subtracting 10 from each side , ( Art . 80 ) , x + 10-10-15-10 , or a = 15-10 . Let -4-6 ; by adding 4 to each side ...
... side to the other , if their signs be changed , and the two sides will still be equal . For let + 10 = 15 ; then by subtracting 10 from each side , ( Art . 80 ) , x + 10-10-15-10 , or a = 15-10 . Let -4-6 ; by adding 4 to each side ...
Page 96
... side of an equation be raised to the same power , the results will be equal . ( Art . 81. ) Let -9 ; then = 9 × 9 = 81 . = Also , if the same root be extracted on both sides , the results will be equal . Let = 81 ; then 9 ( Art . 143 ) ...
... side of an equation be raised to the same power , the results will be equal . ( Art . 81. ) Let -9 ; then = 9 × 9 = 81 . = Also , if the same root be extracted on both sides , the results will be equal . Let = 81 ; then 9 ( Art . 143 ) ...
Page 97
... side , and the rational quantities the other , and then raising both sides to that power which will rationalize the surd . Thus , if √a + x - b - c , by transposition Ja + x = b + c , and a + x = ( b + c ) 2 . ( Art . 81. ) If the ...
... side , and the rational quantities the other , and then raising both sides to that power which will rationalize the surd . Thus , if √a + x - b - c , by transposition Ja + x = b + c , and a + x = ( b + c ) 2 . ( Art . 81. ) If the ...
Page 98
James Wood Thomas Lund. quantity to one side of the equation , and the known quantities to the other ( Art . 186 ) ; divide both sides by the coefficient , or sum of the coefficients , of the unknown quantity ( Art . 190 ) , and the ...
James Wood Thomas Lund. quantity to one side of the equation , and the known quantities to the other ( Art . 186 ) ; divide both sides by the coefficient , or sum of the coefficients , of the unknown quantity ( Art . 190 ) , and the ...
Common terms and phrases
algebraical quantities annuity Arithmetical Progression Binomial Theorem coefficient common denominator Comp contain continued fraction convergent cube root denary difference digits divided divisible divisor Edition equal equation EXERCISES expressed Extract the square factors Find the G.C.M. find the number Find the square find the sum Find the value given greater Greatest Common Measure Hence hour latter Least Common Multiple less lowest terms miles Mult multiplied N₁ negative nth root number of combinations number of terms numerator and denominator positive integers Post 8vo Present Value prime number proportion proposed quantities prove quadratic quadratic equation quotient radix ratio reduced remainder represented rule scale shew shillings square root ST JOHN'S COLLEGE subtracted suppose surd unknown quantities vols vulgar fraction whole number Woodcuts
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