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yJ = Ct ( * = l , 2 , . . , n ) , (45) with the essential proviso t h a t these equations are soluble with respect t o yv y2, .

E. a curve of the family and not the envelope; so t h a t t o obtain the envelope we must put dyj(xyyfC) dC __ ft ~""U- This equation also defines C as a function of (x, y). e. the equation of the envelope of family (IS) can be obtained by eliminating G from the two equations: V(x,y,C) = 0; » < y ° > =0. (82) As we move along the envelope, we touch different curves of family (78), each curve being defined by its value of constant C; this makes it clear why the equation of the envelope was sought in the form (78), with 0, however, taken as variable.

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A Course of Higher Mathematics. Volume II by V. I. Smirnov and A. J. Lohwater (Auth.)


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