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Books Books 1 - 6 of 6 on OlOjO ,8 is therefore self-polar. COROLLARY 1. Given any two involutions, there exists....  Take our survey New!
" 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 228
by Oswald Veblen, John Wesley Young - 1910
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Philosophical Magazine

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...
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An Elementary Treatise on Conic Sections

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...
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The Collected Mathematical Papers of Arthur Cayley, Volume 3

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...
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PROJECTIVE GEOMETRY

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...
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the methods of plane projective geometry based on the use of general ...

...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'...
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The Principles of Projective Geometry

...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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