 | George Salmon - Conic sections - 1855 - 376 pages
...Given four points on a conic, the polar of a fixed point passes through a fixed point. (Ex. 3, p. 137.) Given four points on a conic, the locus of the pole of a fixed right line is a conic section. (Ex. 2, p. 241.) The lines joining the vertices of a triangle... | |
 | George Salmon - Conic sections - 1855 - 376 pages
...between these right lines : thus we obtain the theorem of p. 208. same manner it may be proved that the locus of the pole of a given line is a conic section. In general, if the equation of a conic section involve an indeterminate in the second degree,... | |
 | George Salmon - Conic sections - 1863 - 412 pages
...a circle are cut in a given ratio is an ellipse having dSuble contact with the circle. (Art. 163.) Given four points on a conic, the locus of the pole of any fixed line is a conic passing through the fourth harmonic to the point in which this line meets... | |
 | William Peveril Turnbull - Geometry, Analytic - 1867 - 298 pages
...sections by planes at right angles to VN' are circles. 16. Given four points on a conic, the locos of the pole of a given line is a conic passing through...converse, 19. Deduce a property of the circle from Euclid ill. 31. 20. Prove from the properties of the circle that if parallel tangents be drawn to a conic... | |
 | Charles Taylor - Mathematics - 1881 - 512 pages
...diagonals of a complete quadrilateral are a conjugate triad with respect to every conic inscribed in it. Given four points on a conic, the locus of the pole of a given line is a conic, &c. [Ex. 788. If two triangles circumscribe a conic, their six summits lie on a conic. The envelope... | |
 | George Shoobridge Carr - Mathematics - 1886 - 1036 pages
...true in this case. Hence, by a converse projection, the more general theorem is inferred. Ex. 2. — Given four points on a conic, the locus of the pole of any fixed line is a conic passing through the fourth harmonic to the point in which this line meets... | |
 | Sidney Luxton Loney - Coordinates - 1896 - 447 pages
...four fixed points; prove that (1) the polars of a given point all pass through a fixed point, and (2) the locus of the pole of a given line is a conic section. 5. Find the equation to the conic passing through the origin and the points (1, 1), ( - 1,... | |
 | George Salmon - Conic sections - 1904 - 426 pages
...+ kQ' is the pole with respect to S+kS' of the line joining the two given points. And we see that, given four points on a conic, the locus of the pole of a given lint; is a conic (Ex. 1, Art. '278). If an indeterminate enter in the second degree into the equation... | |
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Given four points on a conic, the locus of the pole of a given line is a conic passing through the four points (Chap. 