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" ... the locus of the centres of circles described through the origin to touch the inverse curve. Thus from the theorem that the locus of the foot of the perpendicular from the focus on the tangent of a conic is a circle, we deduce (as Mr. "
A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ... - Page 241
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 - Curves, Algebraic - 1852 - 329 pages
...circular infinite points for double points, and also the origin for another; the curve is the limaqon if the origin be the focus of the conic; the curve...touch the curve, is a circle;" or otherwise, " the limagon may be generated as the envelope of circles passing through a given point, and having their...
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Conic sections - 1852 - 334 pages
...where he also proves that the centre of gravity of these three points is the centre of the ellipse. To the foot of the perpendicular on a tangent will...touch the curve, is a circle ;" or otherwise, " the limagon may be generated as the envelope of circles passing through a given point, and having their...
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The Quarterly Journal of Pure and Applied Mathematics, Volume 5

James Joseph Sylvester, James Whitbread Lee Glaisher - Mathematics - 1862 - 408 pages
...the equation to the projection of this sphero-conic and this is the equation to the circle which is the locus of the foot of the perpendicular, from the focus, on the tangent to the projection of the line of curvature (II). PROP. 2. The locus of the point of intersection of...
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The Quarterly Journal of Pure and Applied Mathematics, Volume 5

Mathematics - 1862 - 428 pages
...equation to the projection of this sphero-conic and this is the equation to tke circle which is the loons of the foot of the perpendicular, from the focus, on the tangent to the projection ot the line of curvature (II). PROP. 2. The locus of tlie point of intersection of...
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An Introduction to Analytical Plane Geometry

W. P. Turnbull - Geometry, Analytic - 1867 - 276 pages
...— b 2 for b 2 . 149. As in Art. 126, Also S0. = e*x - ae = e. SP, and S'G = e 2 iť +oe = e. /8'P. The locus of the foot of the perpendicular from the focus on the tangent is the circle described on AA' as diameter. 150. Corresponding to the formula jf = a 2 cos 2 a,+1?...
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An introduction to analytical plane geometry

William Peveril Turnbull - 1867 - 294 pages
...•writing — J* for V. 149. As in Art. 126, CM.OT*-cf, Also SG = e*x-ae = e. SP, and S' G = e*x +ae=e. ST. The locus of the foot of the perpendicular from the focus on the tangent is the circle described on AA' as diameter. 150. Corresponding to the formula p* = a* cos* a -f Z>*...
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Elementary analytical geometry

Thomas Grenfell Vyvyan - Geometry, Analytic - 1867 - 290 pages
...have x ( m + — ] = 0. .-. x= 0. Ч т) \ " This is the equation to the tangent at the vertex : hence the locus of the foot of the perpendicular from the focus on a tangent is the tangent at the vertex. 86. To find the equation of the chord of contact of tangents...
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Conic Sections treated Geometrically

William Henry BESANT - Conic sections - 1869 - 300 pages
...perpendiculars drawn to the tangent and normal at any point, YZ i' parallel to the diameter. 24. Prove that the locus of the foot of the perpendicular from the focus on the normal is a parabola. 25. If PO be the normal, and GL the perpendicular from G upon SP, prove that...
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Solid Geometry and Conic Sections: With Appendices on Transversals, and ...

James Maurice Wilson - Conic sections - 1872 - 160 pages
...FY '= YM and FA = AX, AY is parallel to the directrix, and is therefore the tangent at A. Therefore the locus of the foot of the perpendicular from the focus on the tangent is the tangent at the vertex. COR. 4. Since FYM is perpendicular to the tangent and FY = YM, M is called...
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The Cone and Its Sections Treated Geometrically

S. A. Renshaw - Conic sections - 1875 - 220 pages
...be perpendiculars to the tangent and normal at any point, YZ is parallel to the axis. 45. — Prove that the locus of the foot of the perpendicular from the focus on the normal is a Parabola. 46. — If E be the centre of the circle described about the triangle POp, (fig....
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