The Journal of the Indian Mathematical Society

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The Theory of Envelopes of Plane Curves


     

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Ths envelope of a family of plane curves f (x, y, c) = 0 is defined in many text-books as the locus of the ultimate intersections of f(x, y, c) = 0 and f(x, y, c + δc) = 0. This definition has one serious disadvantage; for, it is easily prove J that if the family possess any double points, these will appear in the c-discriminant.
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  • The Theory of Envelopes of Plane Curves

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Abstract


Ths envelope of a family of plane curves f (x, y, c) = 0 is defined in many text-books as the locus of the ultimate intersections of f(x, y, c) = 0 and f(x, y, c + δc) = 0. This definition has one serious disadvantage; for, it is easily prove J that if the family possess any double points, these will appear in the c-discriminant.