...equation will be equal to the sum of all those roots so changed ; the co-efficient of the second term equal to the sum of all the products that can be formed with them, taken two and two at a time ; the co-efficient of the third term equal to the sum of all...

...formed by taking the roots two at a time. The coefficient of the fourth term, with its sign changed, is equal to the sum of all the products that can be formed by taking the roots three at a time. The coefficient of the fifth term is equal to the sum of all the...

...products that can be formed by taking the roots three at a time. The coefficient of the fifth term is equal to the sum of all the products that can be formed by taking the roots four at a time ; and so on. If the number of roots is even., the last term is equal...

...• - - Vn) = -Vn-l)— —• dx The derivative of the product of a finite number of variable» is equal to the sum of all the products that can be formed by multiplying the derivative of each variable by all the other variables. 53. Differentiation of a variable...

...the fourth and higher orders. 475. Thus the symbol is a determinant of the fourth order, and it is equal to the sum of all the products that can be formed by talcing one, and only one, element from each column and from each row, considering the sign of each...

...fourth and higher orders. 475. Thus the symbol Ci dl is a determinant of the fourth order, and it is equal to the sum of all the products that can be formed by taking one, and only one, element from each column and from each row, considering the sign of each...