ELLIPTOIDE

ELLIPTOIDE, an infinite or indefinite ellipse, defined by the indefinite equation $ay^\{m+n\}\; =\; bx^m\; \backslash cdot\; a\; -\; x^n$ when $m$ or $n$ are greater than 1: for when they are each = 1, it denotes the common ellipse.

There are several kinds or degrees of elliptoides, denominated from the exponent $m+n$ of the ordinate $y$. As the cubical elliptoid, expressed by $ay^3\; =\; bx^3\; \backslash cdot\; a\; -\; x^3$; the biquadratic, or fusolid $ay^4\; =\; bx^4\; \backslash cdot\; a\; -\; x^4$; &c.