An Essay On the Resolution of Equations
An Essay On the Resolution of Equations
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We thus perceive that «^=Ci(l + t'+0 +^0(^ + = l + ^' + t3 + Co(l + ^ + ^' + ^^ + ^^) = -(* + ^')- From which there will result, on writing t" instead of i, We might have arrived at the expression for ai from considering that y^-\-y -^^^VRi which, expressed as a function of / and Uj would become L'^{L^-{-L-\-a)t + L{L-\- L^+a^u, must in vanishing assume the form 0/ + Ow.
It appears, then, that a^n has only two different values, a^ and «^2. Hence all functions symmetrical relatively to a^ and «^...2 will remain unaltered when for l we substitute any one of the three roots 6^, L^, L^.
And in accordance with this we find «^ + «^, = ~(i + . 2 + t3 + t4)=-(-l), «j and «^2 arc in fact the roots of the equation a2— a— 1=0; which, solved as a quadratic equation, will give 72. Another consequence of the properties of a^' must here be pointed out.
Representing any one of the ten equations of the system by METHOD OF LAGRANGE AND VANDERMONDE.
and observing that we see that 55 (l^n — l~"^t2«> a, b, .
What to read after An Essay On the Resolution of Equations?
You can find similar books in the "Read Also" column, or choose other free books by G B George Birch Jerrard to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
We thus perceive that «^=Ci(l + t'+0 +^0(^ + = l + ^' + t3 + Co(l + ^ + ^' + ^^ + ^^) = -(* + ^')- From which there will result, on writing t" instead of i, We might have arrived at the expression for ai from considering that y^-\-y -^^^VRi which, expressed as a function of / and Uj would become L'^{L^-{-L-\-a)t + L{L-\- L^+a^u, must in vanishing assume the form 0/ + Ow.
It appears, then, that a^n has only two different values, a^ and «^2. Hence all functions symmetrical relatively to a^ and «^...2 will remain unaltered when for l we substitute any one of the three roots 6^, L^, L^.
And in accordance with this we find «^ + «^, = ~(i + . 2 + t3 + t4)=-(-l), «j and «^2 arc in fact the roots of the equation a2— a— 1=0; which, solved as a quadratic equation, will give 72. Another consequence of the properties of a^' must here be pointed out.
Representing any one of the ten equations of the system by METHOD OF LAGRANGE AND VANDERMONDE.
and observing that we see that 55 (l^n — l~"^t2«> a, b, .
What to read after An Essay On the Resolution of Equations?
You can find similar books in the "Read Also" column, or choose other free books by G B George Birch Jerrard to read onlineMoreLess
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