Books Books ... a curve having the origin for a double point, and the two circular points at infinity for ordinary double points. As a generalization of the ovals of Cassini, we might seek the locus of a point, the product of whose distances from m given points shall... A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ... - Page 204
by George Salmon - 1852 - 316 pages ## A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Conic sections - 1852 - 338 pages
...Cayley's paper, Liouville, vol. xv. p. 354. 2c2 cos 2w, the origin If c4 = TO4, the equation becomes is a double point, and the curve is the lemniscata...the centre of any conic on the tangent is obviously p* = cf cos- + 62 siu2oj, a curve having the origin for a double point, and the two circular points... ## A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Curves, Algebraic - 1852 - 329 pages
...Cassini's ovals consist of two conjugate ovals within the parts of this figure ; when m is greater than o, of one continuous oval outside it. This lemniscata...the centre of any conic on the tangent is obviously p 2 = a 2 cos 2 <*> + 6 2 sin 2 w, a curve having the origin for a double point, and the two circular... ## Solid Geometry and Conic Sections: With Appendices on Transversals, and ...

James Maurice Wilson - Conic sections - 1872 - 162 pages
...perpendicular to FP. 31. With a given focus, and three given points on the curve, find the other focus. 32. The locus of the foot of the perpendicular from the centre on any chord that subtends a right angle at the centre is a circle. 33. Shew that the areas of the ellipse... ## Introduction to quaternions, by P. Kelland and P.G. Tait

Philip Kelland - 1873 - 250 pages
...whose distance from a given line is proportional to its distance from a given plane. 3. Prove that the locus of the foot of the perpendicular from the centre on the tangent plane- of an ellipsoid is (ax)' + (by)' + (cz)' = (a? + if + z')'. 4. The sum of the squares of the... ## An elementary treatise on the integral calculus, containing applications to ...

Benjamin Williamson - Calculus, Integral - 1875 - 288 pages
...9 corresponding to the limiting points A and B. For example, let it be proposed to find the area of the locus of the foot of the perpendicular from the centre on a tangent to an ellipse. £.2 yi Writing the equation of the ellipse in the form — + -^ = i, the... ## An Elementary Treatise on the Integral Calculus ...

Benjamin Williamson - Calculus of variations - 1877 - 370 pages
...136. Area of Pedals of Ellipse and Hyperbola. — For example, let it be proposed to find the area of the locus of the foot of the perpendicular from the centre on a tangent to an ellipse. g» yz Writing the equation of the ellipse in the form — z + T-2 = I> do... ## An Elementary Treatise on the Integral Calculus: Containing Applications to ...

Benjamin Williamson - Calculus of variations - 1884 - 424 pages
...Area of Pedals of ЖШрве and Hyperbola. — For example, let it be proposed to find the area of the locus of the foot of the perpendicular from the centre on a tangent to an ellipse. я? 1? Writing the equation of the ellipse in the form— a + j-*= i, Hence... ## Solid Geometry and Conic Sections: With Appendices on Transversals, and ...

James Maurice Wilson - Conic sections - 1885 - 180 pages
...FP, (Th. 8.) 31. With a given focus, and three given points on the curve, find the other focus. 32. The locus of the foot of the perpendicular from the centre on any chord that subtends a right angle at the centre is a circle. 33. Shew that the areas of the ellipse... ## A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic ...

John Casey - Geometry, Analytic - 1893 - 604 pages
...opposite side lie on a confocal. 15. A circle touching an ellipse passes through its centre ; prove that the locus of the foot of the perpendicular from the centre on the chord of intersection is a concentric and homothetic ellipse. 1C. If a variable triangle of given species... 