A new method of resolving cubic equations ... Read, 6th May 1799 / [Sir James Ivory].

  • Ivory, James, Sir, 1765-1842.
Date:
[1805]
Catalogue details

Licence: Public Domain Mark

Credit: A new method of resolving cubic equations ... Read, 6th May 1799 / [Sir James Ivory]. Source: Wellcome Collection.

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    The terms of this expreffion are now to be evolved and ar¬ ranged, according to the powers of z: which being done, we {hall find, ' - a1 + 3 a2Xz + + iXz3 -f Aa2b -\-2AabXz + Abxz2 + Aa7Xz -{-2AaXz2 + AX23 + Bab2 + Bb2 X z Y — o. -f- 2BabXz + 2Bbxz2 + BaXz2 -f BX2j + Gb* + 3Cb>Xz +3CbXz* + CX2J ' In order to reduce this equation to our forms, we mufl e- quate three times the coefficient of z3 to the coefficient of z, either with the fame or different figns : and alfo the coefficient of to three times the abfolute term, likewife with the fame or different figns. For in the forms the coefficient of 2;3 and 2 are R and ip 3R : and the coefficient of %2 and the abfolute term are, 3r and + r. Now, in the transformed equation above, three times the coefficient of is 3-{-3A-b 3B + 3C, which I write thus, (3 -f- 2A -f* B) -f- (A -f 2B -f- 3C): And in like manner, for three times the abfolute term, I write (3^3 -f 2Art2£ Bab2) -{- {Aa2b -f- zBab* + 3C^?). This be¬ ing obferved, we fhall have thefe two equations for determining a and b: 3 + 2A+B7_+ 2Aai + ~Bb2 + A + 2B + 3cj — + LAa2 + 2B ab + 3C b2, $a2Aa-\rBa l___r 3^3 + 2 AcPb + Bab2 + AI> -f aBi + 3Cb$ ~ + 1+ AaV+ zBab2 + 3Cb\ 6. It is manifeft, from the manner in which I have written the two equations for determining a and b, that they depend upon;