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The condition that the family of surfaces φ(x, y, z, λ) = 0 may be one of an orthogonal triad
Published online by Cambridge University Press: 20 January 2009
Extract
Cayley has shown that if the family of surfaces φ(x, y, z) = λ is one of an orthogonal triad, φ satisfies a differential equation of the third order. If, however, the parameter λ is involved implicitly in the equation of the family, the condition requires modification: for example, although
is one of an orthogonal triad, φ does not satisfy Cayley's equation.
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- Research Article
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- Copyright © Edinburgh Mathematical Society 1911
References
* Proc. Edin. Math. Soc., vol. xxix.Google Scholar