| 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 cos2«i> + 62 sin2a>, a curve having the origin for a double point, and the two circular points... | |
| 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... | |
| 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... | |
| 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 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... | |
| 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
...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 = (—... | |
| 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), Ç **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... | |
| |