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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    A New Method of refolding Cubic Equations. By James Ivory, Esq^ Communicated by John PLAYFAiRt F.R. S. Ed in. and Profeffor of Mathematics in the Unfa erf ity of Edinburgh. [Read, 6th May 1799.] 1. T Divide cubic equations into two varieties or fpecies : the A one, comprehending all cubic equations with three real roots ; the other, all thofe with only one real root. 2. Let <p denote any angle whatever, and let r zi tan (p, the radius being unity : let alfo 2 1= tan - : then from the doctrine 3 of angular fedlions we have 32-2 5 T i — 3^} which being reduced to the form of an equation, is %3 — $rz1 — 3% -f- r =z o. Now, from what is commonly taught in angular fedlions, z, in this equation, may denote, not only tan -, but alfo 3 . % tan (|+i2o°), or tan ^-f-2400). It is to be remarked, too, that any value whatfoever may be ailigned to r, pofitive or negative, and without limit or reftridlion as to magnitude. The equation, then, has three different values of % for every given value of r ; and it belongs to the fpecies of cubic equations, ha¬ ving three real roots.
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