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V. A New Method of resolving Cubic Equations

Published online by Cambridge University Press:  17 January 2013

James Ivory
James Ivory
Affiliation:
Professor of Mathematics in theUniversity of Edinburgh.
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Extract

1. I Divide cubic equations into two varieties or species: the one, comprehending all cubic equations with three real roots; the other, all those with only one real root.

2. Let φ denote any angle whatever, and let τ = tan φ, the radius being unity: let also : then from the doctrine of angular sections we have

which being reduced to the form of an equation, is

Z3-3τZ2-3Z+τ=0.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 5 , Issue 1 , 1805 , pp. 99 - 116
Copyright
Copyright © Royal Society of Edinburgh 1805

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