OlOjO ,8 is therefore self-polar. COROLLARY 1. Given any two involutions, there exists a third involution which is harmonic with each of the given involutions. For if we take the two involutions on a conic, the involution whose center is the pole with... Projective Geometry - Page 228by Oswald Veblen, John Wesley Young - 1910Full view - About this book
| Science - 1857
...ff"> * ) we points in the conic and the second condition expresses that each of the points in question **is the pole with respect to the conic of the line joining the** other two points, ie that the three points are a system of conjugate points with respect to the last-mentioned... | |
| Charles Smith - Conic sections - 1883 - 352 pages
...a conic, and QP, RS meet in A, QS, PR in B, and PS, QR in G; then of the three points A, B, G each **is the pole with respect to the conic of the line joining the** other two. Take A for origin, and the two lines ASR, APQ for axes of x and y respectively. Let the... | |
| Arthur Cayley, Andrew Russell Forsyth - Mathematics - 1890 - 568 pages
...h") are points in the conic and the second condition expresses that each of the points in question **is the pole with respect to the conic of the line joining the** other two points, ie that the three points are a system of conjugate points with respect to the last-mentioned... | |
| OSWALD VEBLEN - 1910
...therefore self-polar. COROLLARY 1. Given any two involutions, there exists a third involution ivhich **is harmonic with each of the given involutions. For...involutions are collinear. THEOREM 22. The set of all** projectivities to which belongs the same involution I forms a commutative group. Proof. If II, Hj are... | |
| ...c$ + d = 0, where o, 6, c, d are constants and ad — bc 4= 0. Prove that, in general, the locus of **the pole with respect to the conic of the line joining the** points is a conic. What happens if 6 = c ? [MT L] 47. S is a conic inscribed in a triangle ABC. S'... | |
| ...conic circumscribing a triangle ABC, the polar of P, with respect to the triangle ABC, passes through **the pole, with respect to the' conic, of the line joining the** points, where the tangents at A, B and C to the conic meet the opposite sides of the triangle ABC.... | |
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