Elements of Projective Geometry
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In our eReader you can find the full English version of the book. Read Elements of Projective Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Elements of Projective Geometry
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(2). But if this case be excluded, i. e. if no three of the eight vertices lie in a straight line, then a conic can be drawn through any five of them. Let a conic be drawn through ^,^,C,i^,J'(Fig. 185); then shall B', C, B' lie on the same conic. For since F,F,G are the diagonal points of the inscribed quadrangle ABCB, G is the pole of FF, and therefore G and the point where its polar FF meets the transversal GB' A' are harmonically conjugate with regard to the points where this transversal cut...s the conic. But one of these last points is A', therefore the other is B' \ for since F ,F,G are also the diagonal points of the quadrangle A'B' C'B', the points A' and B' are harmonically conjugate with regard to G and the point where FF cuts A'B'. In a similar manner it can be shown that C' and B' also lie on the same conic. The eight vertices A,B ,C ,B ,A',B',C',B' therefore lie on a conic, and the proposition is proved.
p a Fig. J85.
212 POLE AND POLAE. [266 Since the straight lines AJB and A'£' meet in G, therefore AA' and BB', as also AB' and A'B, wiU meet on BF, the polar of G.
What to read after Elements of Projective Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Cremona, Luigi, 1830-1903 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
(2). But if this case be excluded, i. e. if no three of the eight vertices lie in a straight line, then a conic can be drawn through any five of them. Let a conic be drawn through ^,^,C,i^,J'(Fig. 185); then shall B', C, B' lie on the same conic. For since F,F,G are the diagonal points of the inscribed quadrangle ABCB, G is the pole of FF, and therefore G and the point where its polar FF meets the transversal GB' A' are harmonically conjugate with regard to the points where this transversal cut...s the conic. But one of these last points is A', therefore the other is B' \ for since F ,F,G are also the diagonal points of the quadrangle A'B' C'B', the points A' and B' are harmonically conjugate with regard to G and the point where FF cuts A'B'. In a similar manner it can be shown that C' and B' also lie on the same conic. The eight vertices A,B ,C ,B ,A',B',C',B' therefore lie on a conic, and the proposition is proved.
p a Fig. J85.
212 POLE AND POLAE. [266 Since the straight lines AJB and A'£' meet in G, therefore AA' and BB', as also AB' and A'B, wiU meet on BF, the polar of G.
What to read after Elements of Projective Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Cremona, Luigi, 1830-1903 to read onlineMoreLess
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