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

George Salmon - Conic sections - 1852 - 338 pages
...Cassini's ovals consist of two conjugate ovals within the parts of this figure ; when m is greater than c, of one continuous oval outside it. This lemniscata...the centre of any conic on the tangent is obviously p2 = a2 cos2i> + 62 sin2a>, a curve having the origin for a double point, and the two circular points...
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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...
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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...
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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...
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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...
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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...
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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...
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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...
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Scientific Papers, Volume 1

Peter Guthrie Tait - Kinetic theory of gases - 1898
...reciprocal in length, which gives one means of constructing the former. 2—2 It 'IB known also to be the locus of the foot of the perpendicular from the centre on the tangent plane to the other ellipsoid Tot = 1. In fact by (/i) v in the latter is — 5 ; therefore v~l = (—...
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The Analytical Theory of Light

James Walker - Light - 1904 - 448 pages
...whence the angle aNy is a right-angle, and the locus of N is a circle. Now the coordinates f, r), of the foot of the perpendicular from the centre on the tangent plane to the wave-surface at the point in which it is met by the ray a- with the direction-cosines...
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