| 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... | |
| George Salmon - Conic sections - 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... | |
| James Maurice Wilson - 1872 - 160 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... | |
| Philip Kelland - 1873 - 248 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... | |
| 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... | |
| Benjamin Williamson - Calculus - 1877 - 372 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... | |
| 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... | |
| 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... | |
| 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... | |
| Peter Guthrie Tait - Kinetic theory of gases - 1898 - 548 pages
...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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