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Generally the reciprocal of a curve is the locus of the centres of circles through the origin to touch the inverse curve. Thus, " the envelope of a circle passing through a given point, and having its centre on a parabola, is a circular cubic with a double...
A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ... - Page 241
by George Salmon - 1852 - 316 pages

## A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Curves, Algebraic - 1852 - 329 pages
...through the double point of the limagon to touch the curve, is a circle;" or otherwise, " the limagon may be generated as the envelope of circles passing...transformations ; viz., when p = 0o> is altered to p n = (j)(nw). It is unnecessary to write down the effect of the transformation for curves of the form...

## A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Conic sections - 1852 - 334 pages
...through the double point of the limagon to touch the curve, is a circle ;" or otherwise, " the limagon may be generated as the envelope of circles passing...case of M. Chasles's transformations ; viz., when p = 0to is altered to p" = <p (nw). It is unnecessary to write down the effect of the transformation...

## Geometrical Exercises for Beginners

Samuel Constable - Geometry - 1882 - 218 pages
...in general, be drawn passing through two given points and touching a given circle. PKOP. 89. Every circle, passing through a given point, and having its centre on a given straight line, passes also through, another fixed point. Draw PD perpendicular to LM, and produce...

## The first six books of the Elements of Euclid, and propositions i.-xxi. of ...

Euclides - 1885 - 340 pages
...circle subtend a right angle at a given point, the locus of its middle point is a circle. 2. Every circle passing through a given point, and having its centre on a given fine, passes through another given point. 3. Draw a chord in a given circle which shall subtend...