 | George Salmon - Conic sections - 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... | |
 | George Salmon - Conic sections - 1852 - 338 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... | |
 | Samuel Constable - Geometry - 1882 - 222 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... | |
 | 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... | |
 | Euclid, John Casey - Euclid's Elements - 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 lone, passes through another given point. 3. Draw a chord in a given circle which shall subtend... | |
 | 1895 - 142 pages
...shall cut it at right angles : and, conversely, if it cut it at right angles, it shall bisect it. Every circle passing through a given point, and having its centre on a given line, passes through another fixed point. 2. If two chords of a circle cut one another, the rectangle... | |
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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... 