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/T1_0 1 Tf -0.0243 Tc 3 Tr 9.5 0 0 9.5 70.46 537.85 Tm (7. )Tj /T1_1 1 Tf 0.05 Tc 8.881 0 0 6.9001 84.07 537.85 Tm (AN )Tj 7.7375 0 0 6.9001 101.17 537.85 Tm (ALTERNATIVE )Tj 7.4126 0 0 6.9001 161.89 537.85 Tm (CONSTRUCTION )Tj 7.7856 0 0 6.9001 229.83 537.85 Tm (IN )Tj /T1_2 1 Tf 9.8733 0 0 9.5 242.36 537.85 Tm (PG\(5, )Tj -0.0136 Tc 10.2 0 0 10.2 270.66 537.85 Tm (q\), )Tj 0 Tc 1.5 0 Td (q )Tj /T1_1 1 Tf 0.05 Tc 7.3785 0 0 6.9001 294.38 537.85 Tm (ODD )Tj /T1_0 1 Tf 9.7592 0 0 9.4 30.52 516.24 Tm (To )Tj 9.5064 0 0 9.4 45.45 516.24 Tm (obtain )Tj 0 Tc 9.4 0 0 9.4 74.96 516.24 Tm (a )Tj 0.0426 Tc 0.852 0 Td (result )Tj 0.0335 Tc 2.821 0 Td (similar )Tj -0.035 Tc 9.3616 0 0 9.4 141.02 516.24 Tm (for )Tj /T1_2 1 Tf 0 Tc 8.6 0 0 8.6 155.11 516.24 Tm (q )Tj /T1_0 1 Tf 0.0453 Tc 9.4 0 0 9.4 162.99 516.24 Tm (odd )Tj 0.05 Tc 9.6041 0 0 9.4 181.42 516.24 Tm (to )Tj 0.0496 Tc 9.4 0 0 9.4 193.06 516.24 Tm (Theorem )Tj 0.0061 Tc 4.285 0 Td (6.2, )Tj 0.0445 Tc 1.937 0 Td (consider )Tj 0.05 Tc 9.5625 0 0 9.4 289.96 516.24 Tm (the )Tj 0.0187 Tc 9.4 0 0 9.4 306.27 516.24 Tm (chords )Tj /T1_2 1 Tf -0.0279 Tc 9.8 0 0 9.8 142.21 497.89 Tm (1\(S2, )Tj 0.0376 Tc 2.179 0 Td (rs, )Tj -0.035 Tc 8.8654 0 0 9.8 176.89 497.89 Tm (r2 )Tj /T1_0 1 Tf 0 Tc 9.8 0 0 9.8 187.99 497.89 Tm (-)Tj /T1_2 1 Tf -0.0097 Tc 0.951 0 Td (s, )Tj -0.035 Tc 9.6137 0 0 9.8 206.31 497.89 Tm (s, )Tj 0.05 Tc 12.1252 0 0 9.8 214.83 497.89 Tm (-r, )Tj /T1_3 1 Tf -0.035 Tc 8.6974 0 0 9.8 230.38 497.89 Tm (1\) )Tj /T1_0 1 Tf 0.0491 Tc 9.4 0 0 9.4 18.81 478.63 Tm (of )Tj 0.05 Tc 10.2456 0 0 9.4 30.03 478.63 Tm (the )Tj 0.0292 Tc 9.4 0 0 9.4 47.07 478.63 Tm (cubic )Tj 0 Tc 2.622 0 Td (C )Tj 0.05 Tc 9.7524 0 0 9.4 80.72 478.63 Tm (and )Tj 9.6991 0 0 9.4 99.52 478.63 Tm (the )Tj 0.0184 Tc 9.4 0 0 9.4 116 478.63 Tm (axes )Tj /T1_2 1 Tf 0.033 Tc 9.7 0 0 9.7 139.51 459.91 Tm (1\(v)Tj 0 Tc 6.5001 0 0 6.5001 153.15 463.87 Tm (2)Tj 0.728 -0.609 Td (, )Tj 0.0229 Tc 9.7 0 0 9.7 161.56 459.91 Tm (uv, )Tj 0.05 Tc 7.3475 0 0 6.5001 175.77 459.91 Tm (V, )Tj 0 Tc 9.7 0 0 9.7 185.32 459.91 Tm (u)Tj 6.5001 0 0 6.5001 190.77 464.05 Tm (2 )Tj /T1_0 1 Tf 1.018 -0.637 Td (-)Tj /T1_2 1 Tf 0.05 Tc 6.9504 0 0 6.5001 206.38 459.91 Tm (V, )Tj 12.0515 0 0 9.7 215.91 459.91 Tm (-u, )Tj /T1_3 1 Tf -0.035 Tc 8.6974 0 0 9.8 232.9 459.91 Tm (1\) )Tj /T1_0 1 Tf 0.0491 Tc 9.4 0 0 9.4 18.99 441.37 Tm (of )Tj 0.05 Tc 10.3822 0 0 9.4 30.03 441.37 Tm (the )Tj 0.0238 Tc 9.4 0 0 9.4 47.25 441.37 Tm (developable )Tj /T1_1 1 Tf 0.0301 Tc 12.1 0 0 12.1 98.77 441.37 Tm (r, )Tj /T1_0 1 Tf 0.0177 Tc 9.4 0 0 9.4 110.51 441.37 Tm (which )Tj 0.0322 Tc 2.883 0 Td (correspond )Tj 0.0488 Tc 5.12 0 Td (to )Tj 0.0224 Tc 1.217 0 Td (each )Tj 0.05 Tc 9.6749 0 0 9.4 218.25 441.37 Tm (other )Tj 9.5985 0 0 9.4 243.9 441.37 Tm (under )Tj 9.8357 0 0 9.4 271.6 441.37 Tm (the )Tj 0.0193 Tc 9.4 0 0 9.4 288.53 441.37 Tm (null )Tj 0.0389 Tc 1.974 0 Td (polarity )Tj 0.032 Tc -30.63 -3.964 Td (defined )Tj 0.0436 Tc 3.611 0 Td (by )Tj 0.05 Tc 9.5625 0 0 9.4 66.76 404.11 Tm (the )Tj 0.0348 Tc 9.4 0 0 9.4 83.44 404.11 Tm (linear )Tj 0.0268 Tc 2.871 0 Td (complex )Tj /T1_2 1 Tf 0.05 Tc 7.0796 0 0 6.6 147.88 404.11 Tm (l03 )Tj /T1_0 1 Tf 0 Tc 13 0 0 13 161.93 404.11 Tm (= )Tj -0.035 Tc 10.1135 0 0 11.8 172.07 404.11 Tm (h2 )Tj 0.03 Tc 9.4 0 0 9.4 186.39 404.11 Tm (of )Tj /T1_2 1 Tf 0.0474 Tc 9.5 0 0 9.5 197.53 404.11 Tm (PG\(3, )Tj /T1_3 1 Tf -0.035 Tc 8.6043 0 0 10 224.87 404.11 Tm (q\) )Tj /T1_0 1 Tf 0.05 Tc 9.5989 0 0 9.4 236.61 404.11 Tm (or )Tj 0.0421 Tc 9.4 0 0 9.4 248.84 404.11 Tm (equivalently )Tj 0.0436 Tc 5.795 0 Td (by )Tj 0.05 Tc 9.4259 0 0 9.4 316.96 404.11 Tm (the )Tj 0.021 Tc 9.4 0 0 9.4 333.05 404.11 Tm (section )Tj 0 Tc 9.5 0 0 9.5 19.24 392.59 Tm (X)Tj 6.8001 0 0 6.8001 27.5 390.97 Tm (2 )Tj 12.1 0 0 12.1 34.86 392.59 Tm (= )Tj -0.035 Tc 9.1424 0 0 9.5 45.34 392.59 Tm (X3 )Tj 0.03 Tc 9.4 0 0 9.4 60.39 392.59 Tm (of )Tj 0.05 Tc 7.5219 0 0 6.8001 71.02 392.59 Tm (1{5 )Tj 0.0434 Tc 9.4 0 0 9.4 86.86 392.59 Tm (in )Tj /T1_2 1 Tf 0.0474 Tc 9.5 0 0 9.5 98.35 392.59 Tm (PG\(5, )Tj /T1_3 1 Tf -0.035 Tc 9.0101 0 0 10 125.69 392.59 Tm (q\). )Tj /T1_0 1 Tf 0.05 Tc 10.3894 0 0 9.4 19.2 376.39 Tm (LeIllma )Tj 9.6346 0 0 9.4 59.3 376.39 Tm (7.1. )Tj /T1_2 1 Tf 0.0462 Tc 9.8 0 0 9.8 82.24 376.39 Tm (The )Tj 0.0357 Tc 1.952 0 Td (set )Tj 0.05 Tc 10.9308 0 0 9.8 116.37 376.39 Tm (of )Tj 0.0207 Tc 9.8 0 0 9.8 127.05 376.39 Tm (points )Tj -0.023 Tc -5.821 -1.873 Td ({\(S2, )Tj 0.0376 Tc 2.182 0 Td (rs, )Tj -0.035 Tc 9.0765 0 0 9.8 104.89 358.03 Tm (r2 )Tj /T1_0 1 Tf 0 Tc 9.8 0 0 9.8 115.99 358.03 Tm (-)Tj /T1_2 1 Tf -0.028 Tc 0.951 0 Td [(s, )-95(s, )]TJ 0.05 Tc 11.7837 0 0 9.8 143.01 358.03 Tm (-r, )Tj /T1_1 1 Tf -0.035 Tc 8.6905 0 0 8.7 158.3 358.03 Tm (1\) )Tj 0 Tc 8.7 0 0 8.7 169.15 358.03 Tm (: )Tj /T1_2 1 Tf -0.035 Tc 9.5562 0 0 9.8 174.01 358.03 Tm (r, )Tj 0 Tc 9.8 0 0 9.8 182.55 358.03 Tm (s )Tj /T1_1 1 Tf 8.7 0 0 8.7 189.52 358.03 Tm (E )Tj 0.02 Tc 0.983 0 Td ('\)'}U )Tj /T1_2 1 Tf 0.0425 Tc 9.7 0 0 9.7 70 342.55 Tm ({\(v)Tj 0 Tc 6.5001 0 0 6.5001 83.49 346.51 Tm (2)Tj 0.7 -0.609 Td (, )Tj 0.0415 Tc 9.7 0 0 9.7 91.72 342.55 Tm (uv, )Tj 0.05 Tc 7.5461 0 0 6.5001 106.46 342.55 Tm (V, )Tj 0 Tc 9.7 0 0 9.7 116.02 342.55 Tm (u)Tj 6.5001 0 0 6.5001 121.47 346.51 Tm (2 )Tj /T1_0 1 Tf 1.018 -0.609 Td (-)Tj /T1_2 1 Tf 0.05 Tc 7.5461 0 0 6.5001 136.7 342.55 Tm (V, )Tj 11.897 0 0 9.7 146.79 342.55 Tm (-u, )Tj /T1_1 1 Tf -0.035 Tc 8.9254 0 0 9.8 163.33 342.55 Tm (1\) )Tj 0 Tc 9.8 0 0 9.8 174.16 342.55 Tm (: )Tj /T1_2 1 Tf 0.0064 Tc 9.7 0 0 9.7 179.2 342.55 Tm (u, )Tj 0 Tc 1.004 0 Td (v )Tj /T1_1 1 Tf 7.8001 0 0 7.8001 196.74 342.55 Tm (E )Tj -0.035 Tc 9.7831 0 0 9.8 205.26 342.55 Tm ('\)'}U )Tj /T1_2 1 Tf 0.05 Tc 10.5551 0 0 9.8 70.17 327.43 Tm ({\(s2,s,I,0,0,0\),\(s2,s,0,1,0,0\): )Tj 0 Tc 9.8 0 0 9.8 208.11 327.43 Tm (s )Tj /T1_0 1 Tf 8.4 0 0 8.4 215.23 327.43 Tm (E )Tj 0.05 Tc 8.8711 0 0 8.4 223.64 327.43 Tm ('\)'}U )Tj 10.2279 0 0 9.8 245.1 327.43 Tm ({\(1,0,0,0,0,0\)} )Tj /T1_2 1 Tf -0.0245 Tc 9.8 0 0 9.8 19.32 309.25 Tm (is )Tj 0.05 Tc 10.138 0 0 9.8 29.76 309.25 Tm (the )Tj 0.0121 Tc 9.8 0 0 9.8 46.32 309.25 Tm (intersection )Tj 0.05 Tc 10.7077 0 0 9.8 97.83 309.25 Tm (of )Tj 0.0267 Tc 9.8 0 0 9.8 108.96 309.25 Tm (the )Tj -0.0017 Tc 1.641 0 Td (quadrics )Tj -0.035 Tc 9.6163 0 0 9.8 133.04 290.17 Tm (XOX5 )Tj /T1_1 1 Tf 0 Tc 12.2 0 0 12.2 159.28 290.17 Tm (+ )Tj /T1_0 1 Tf 9.5 0 0 9.5 168.46 290.17 Tm (X)Tj 6.6 0 0 6.6 176.72 289.45 Tm (I)Tj 9.5 0 0 9.5 180.52 290.17 Tm (X)Tj 6.6 0 0 6.6 188.43 289.45 Tm (4 )Tj /T1_1 1 Tf 12.2 0 0 12.2 194.74 290.17 Tm (+ )Tj /T1_2 1 Tf 9.8 0 0 9.8 204.68 290.17 Tm (X)Tj 0.765 -0.073 Td (2)Tj 0.429 0.073 Td (X)Tj 0.797 -0.092 Td (3 )Tj /T1_0 1 Tf 13 0 0 13 231.41 290.17 Tm (= )Tj -0.0273 Tc 9.5 0 0 9.5 241.28 290.17 Tm (0, )Tj /T1_2 1 Tf -0.002 Tc 9.8 0 0 9.8 133.18 275.05 Tm (\(X2 )Tj /T1_1 1 Tf 0 Tc 13.2 0 0 13.2 150.62 275.05 Tm (+ )Tj /T1_2 1 Tf 9.8 0 0 9.8 160.4 275.05 Tm (X)Tj 0.779 -0.11 Td (3)Tj 0.05 Tc 11.1046 0 0 9.8 172.81 275.05 Tm (\)X)Tj 0 Tc 9.8 0 0 9.8 183.68 273.97 Tm (5 )Tj /T1_0 1 Tf 0.679 0.11 Td (-)Tj /T1_2 1 Tf 0.05 Tc 15.0243 0 0 14.4 199.78 275.05 Tm (xl )Tj -0.035 Tc 9.5801 0 0 9.8 224.83 275.05 Tm (0, )Tj -0.002 Tc 9.8 0 0 9.8 133.18 259.57 Tm (\(X2 )Tj /T1_1 1 Tf 0 Tc 13.2 0 0 13.2 150.44 259.57 Tm (+ )Tj /T1_2 1 Tf -0.0243 Tc 9.8 0 0 9.8 160.4 259.57 Tm (X3\)XO )Tj /T1_0 1 Tf 0 Tc 3.054 0 Td (-)Tj 0.0073 Tc 15.3 0 0 15.3 199.38 259.57 Tm (xi )Tj -0.035 Tc 9.3453 0 0 9.4 224.9 259.57 Tm (0. )Tj /T1_2 1 Tf 0.0406 Tc 9.2 0 0 9.2 19.69 237.25 Tm (Proof. )Tj /T1_0 1 Tf 0.0171 Tc 9.4 0 0 9.4 50.32 237.25 Tm (To )Tj 0.0173 Tc 1.484 0 Td (prove )Tj 0.0369 Tc 2.735 0 Td (this, )Tj 0.05 Tc 9.4259 0 0 9.4 111.4 237.25 Tm (the )Tj 0.0436 Tc 9.4 0 0 9.4 127.7 237.25 Tm (arguments )Tj 0.0491 Tc 4.865 0 Td (of )Tj 0.0432 Tc 1.169 0 Td (Theorem )Tj 0.0001 Tc 4.247 0 Td (6.2 )Tj 0.05 Tc 9.7003 0 0 9.4 239.85 237.25 Tm (can )Tj 9.7011 0 0 9.4 257.95 237.25 Tm (be )Tj 0.0254 Tc 9.4 0 0 9.4 271.26 237.25 Tm (used. )Tj 0 Tc 3.321 0 Td (0 )Tj 0.05 Tc 11.1993 0 0 9.4 19.16 216.37 Tm (Theorem )Tj 9.7454 0 0 9.4 66.86 216.37 Tm (7.2. )Tj /T1_2 1 Tf 0.037 Tc 9.8 0 0 9.8 89.8 216.37 Tm (The )Tj 0.0265 Tc 1.934 0 Td (set )Tj -0.0019 Tc 1.513 0 Td (considered )Tj -0.0253 Tc 4.698 0 Td (in )Tj 0.0495 Tc 1.106 0 Td (Lemma )Tj /T1_0 1 Tf -0.035 Tc 8.8801 0 0 9.4 215.01 216.37 Tm (7.1 )Tj /T1_2 1 Tf -0.0062 Tc 9.8 0 0 9.8 229.38 216.37 Tm (is )Tj /T1_0 1 Tf 0 Tc 9.4 0 0 9.4 239.12 216.37 Tm (a )Tj /T1_2 1 Tf -0.035 Tc 9.3104 0 0 9.8 247.31 216.37 Tm (\(2q2 )Tj /T1_1 1 Tf 0 Tc 13.2 0 0 13.2 266.72 216.37 Tm (+ )Tj /T1_2 1 Tf 0.0063 Tc 9.8 0 0 9.8 276.44 216.37 Tm (2\)-cap )Tj 0.05 Tc 10.9308 0 0 9.8 305.73 216.37 Tm (of )Tj 0.0426 Tc 9.5 0 0 9.5 316.15 216.37 Tm (PG\(5, )Tj -0.0291 Tc 9.8 0 0 9.8 343.2 216.37 Tm (q\), )Tj 0 Tc 1.378 0 Td (q )Tj 0.0295 Tc -34.422 -1.176 Td (odd. )Tj 0.0367 Tc 9.2 0 0 9.2 19.69 188.47 Tm (Proof. )Tj /T1_0 1 Tf 0.0283 Tc 9.4 0 0 9.4 50.23 188.47 Tm (Suppose )Tj 0.05 Tc 9.5184 0 0 9.4 87.82 188.47 Tm (three )Tj 0.03 Tc 9.4 0 0 9.4 112.77 188.47 Tm (of )Tj 0.05 Tc 9.5625 0 0 9.4 124 188.47 Tm (the )Tj 0.0379 Tc 9.4 0 0 9.4 140.77 188.47 Tm (points )Tj 0.0279 Tc 3.071 0 Td (are )Tj 0.0207 Tc 1.705 0 Td (collinear )Tj 0.05 Tc 9.6154 0 0 9.4 224.01 188.47 Tm (on )Tj 0 Tc 9.4 0 0 9.4 237.86 188.47 Tm (a )Tj 0.0295 Tc 0.921 0 Td (line )Tj /T1_2 1 Tf -0.035 Tc 8.1967 0 0 9.2 265.41 188.47 Tm (l; )Tj /T1_0 1 Tf 0.05 Tc 9.8306 0 0 9.4 275.2 188.47 Tm (then )Tj 0.0496 Tc 9.4 0 0 9.4 297.52 188.47 Tm (this )Tj 0.004 Tc 2.023 0 Td (line )Tj -0.035 Tc 9.3682 0 0 9.4 334.54 188.47 Tm (is )Tj -0.0108 Tc 9.4 0 0 9.4 344.25 188.47 Tm (con\255)Tj 0.05 Tc 9.8451 0 0 9.4 19.24 176.95 Tm (tained )Tj 0.0243 Tc 9.4 0 0 9.4 48.7 176.95 Tm (in )Tj 0.05 Tc 9.4259 0 0 9.4 59.38 176.95 Tm (the )Tj 0.0392 Tc 9.4 0 0 9.4 74.98 176.95 Tm (intersection )Tj 0.03 Tc 5.399 0 Td (of )Tj 0.05 Tc 9.4259 0 0 9.4 136.06 176.95 Tm (the )Tj 0.0473 Tc 9.4 0 0 9.4 151.54 176.95 Tm (three )Tj 0.0256 Tc 2.52 0 Td (quadrics. )Tj -0.0066 Tc 4.377 0 Td (So )Tj 0.05 Tc 9.7985 0 0 9.4 229.24 176.95 Tm (it )Tj 0.0405 Tc 9.4 0 0 9.4 238.23 176.95 Tm (consists )Tj 0.04 Tc 3.791 0 Td (only )Tj 0.0491 Tc 2.183 0 Td (of )Tj 0.0379 Tc 1.102 0 Td (points )Tj 0.0032 Tc 2.938 0 Td (defined )Tj 0.0342 Tc -33.32 -1.206 Td (above. )Tj 0.0284 Tc 1.237 -1.245 Td (Since )Tj 0.05 Tc 9.6991 0 0 9.4 57.04 153.91 Tm (the )Tj 9.4277 0 0 9.4 74.03 153.91 Tm (set )Tj 0.0296 Tc 9.4 0 0 9.4 89.73 153.91 Tm (consists )Tj 0.03 Tc 3.83 0 Td (of )Tj -0.0015 Tc 1.233 0 Td (two )Tj /T1_2 1 Tf -0.035 Tc 8.4707 0 0 9.8 156.43 153.91 Tm (\(q2 )Tj /T1_0 1 Tf 0 Tc 11.1 0 0 11.1 171.12 153.91 Tm (+ )Tj /T1_2 1 Tf 9.8 0 0 9.8 180.84 153.91 Tm (q )Tj /T1_0 1 Tf 11.1 0 0 11.1 188.22 153.91 Tm (+ )Tj 0.0313 Tc 9.4 0 0 9.4 198.47 153.91 Tm (I\)-caps; )Tj 0.0354 Tc 3.836 0 Td (necessarily )Tj /T1_1 1 Tf -0.035 Tc 8.9217 0 0 13.2 284.88 153.91 Tm (III )Tj /T1_0 1 Tf 7.2233 0 0 11.9 296.64 153.91 Tm (:s; )Tj 9.0039 0 0 9.4 307.58 153.91 Tm (4. )Tj 9.3061 0 0 9.4 321.31 153.91 Tm (So )Tj /T1_2 1 Tf 0 Tc 9.8 0 0 9.8 334.92 153.91 Tm (q )Tj /T1_0 1 Tf 11.1 0 0 11.1 343.2 153.91 Tm (= )Tj -0.035 Tc 9.0253 0 0 9.4 354.14 153.91 Tm (3. )Tj 0.05 Tc 9.9631 0 0 9.4 19.23 142.75 Tm (When )Tj /T1_3 1 Tf 0 Tc 8.1 0 0 8.1 47.94 142.75 Tm (q )Tj /T1_0 1 Tf 11.1 0 0 11.1 55.38 142.75 Tm (= )Tj -0.035 Tc 9.2907 0 0 9.4 65.23 142.75 Tm (3, )Tj 0.05 Tc 9.4923 0 0 9.4 75.88 142.75 Tm (it )Tj 0.0008 Tc 9.4 0 0 9.4 85.31 142.75 Tm (was )Tj 0.0069 Tc 1.964 0 Td (checked )Tj 0.0245 Tc 3.706 0 Td (by )Tj 0.0465 Tc 1.387 0 Td (computer )Tj 0.05 Tc 10.1785 0 0 9.4 193.84 142.75 Tm (that )Tj 9.5625 0 0 9.4 214.36 142.75 Tm (the )Tj 9.4277 0 0 9.4 230.63 142.75 Tm (set )Tj -0.0179 Tc 9.4 0 0 9.4 245.98 142.75 Tm (is )Tj 0 Tc 1.07 0 Td (a )Tj 0.0358 Tc 0.844 0 Td (cap. )Tj 0.05 Tc 9.8989 0 0 9.4 31.06 131.41 Tm (The )Tj 0.0017 Tc 9.4 0 0 9.4 51.17 131.41 Tm (size )Tj 0.03 Tc 1.977 0 Td (of )Tj 0.05 Tc 9.5625 0 0 9.4 80.8 131.41 Tm (the )Tj 0.0447 Tc 9.4 0 0 9.4 97.65 131.41 Tm (cap )Tj -0.035 Tc 9.0754 0 0 9.4 115.49 131.41 Tm (is )Tj /T1_2 1 Tf 8.6447 0 0 9.8 125.24 131.41 Tm (2q2 )Tj /T1_1 1 Tf 0 Tc 12.2 0 0 12.2 141.1 131.41 Tm (+ )Tj /T1_0 1 Tf 9.4 0 0 9.4 150.6 131.41 Tm (2 )Tj 0.0008 Tc 0.854 0 Td (since )Tj 0.05 Tc 9.5625 0 0 9.4 181.96 131.41 Tm (the )Tj 0.0417 Tc 9.4 0 0 9.4 198.55 131.41 Tm (points )Tj 0.05 Tc 10.3708 0 0 9.8 227.76 131.41 Tm (\(1,0,0,0,0,0\), )Tj /T1_2 1 Tf -0.035 Tc 9.0605 0 0 9.8 292.5 131.41 Tm (\(S2, )Tj /T1_0 1 Tf 9.3453 0 0 9.8 308.78 131.41 Tm (0, )Tj /T1_2 1 Tf 0.05 Tc 12.1252 0 0 9.8 318.33 131.41 Tm (-s, )Tj -0.028 Tc 9.8 0 0 9.8 333.75 131.41 Tm (s, )Tj /T1_0 1 Tf 0.0293 Tc 0.832 0 Td (0,1\), )Tj /T1_2 1 Tf 0 Tc -32.901 -1.194 Td (s )Tj /T1_1 1 Tf 7.8001 0 0 7.8001 26.82 119.71 Tm (E )Tj 0.0176 Tc 1.164 0 Td ('\)', )Tj /T1_0 1 Tf 0.05 Tc 9.6349 0 0 9.4 47.6 119.71 Tm (and )Tj /T1_2 1 Tf -0.035 Tc 9.7855 0 0 9.8 66.58 119.71 Tm (\(r)Tj 0 Tc 6.5001 0 0 6.5001 74.28 123.31 Tm (4)Tj 0.0352 Tc 9.8 0 0 9.8 78.94 119.71 Tm (/4, )Tj 0 Tc 1.38 0 Td (r)Tj 0.493 0.367 Td (3)Tj 0.0443 Tc 0.442 -0.367 Td (/2, )Tj 0 Tc 1.398 0 Td (r)Tj 0.48 0.367 Td (2)Tj 0.0352 Tc 0.437 -0.367 Td (/2, )Tj 0 Tc 1.38 0 Td (r)Tj 0.498 0.367 Td (2)Tj 0.0352 Tc 0.418 -0.367 Td (/2, )Tj 0.05 Tc 11.7837 0 0 9.8 160.65 119.71 Tm (-r, )Tj /T1_0 1 Tf 0.0112 Tc 9.4 0 0 9.4 175.89 119.71 Tm (1\), )Tj /T1_2 1 Tf 0 Tc 9.8 0 0 9.8 189.66 119.71 Tm (r )Tj /T1_1 1 Tf 7.8001 0 0 7.8001 197.28 119.71 Tm (E )Tj -0.035 Tc 5.9826 0 0 7.8001 205.78 119.71 Tm (,\)" )Tj /T1_0 1 Tf 0.0158 Tc 9.4 0 0 9.4 216.99 119.71 Tm (define )Tj 0.05 Tc 10.3266 0 0 9.4 244.99 119.71 Tm (both )Tj 0.0416 Tc 9.4 0 0 9.4 268.11 119.71 Tm (chords )Tj 0.05 Tc 9.6349 0 0 9.4 298.7 119.71 Tm (and )Tj -0.0008 Tc 9.4 0 0 9.4 317.06 119.71 Tm (axes. )Tj 0 Tc 3.121 0 Td (0 )Tj 0.05 Tc 10.4702 0 0 9.4 19.39 98.83 Tm (ReIllark. )Tj 9.569 0 0 9.4 67.06 98.83 Tm (The )Tj 0.0272 Tc 9.4 0 0 9.4 86.92 98.83 Tm (two )Tj 0.05 Tc 9.7047 0 0 9.4 105.67 98.83 Tm 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23.7001 0 0 23.7001 250.66 466.21 Tm (\260 )Tj /T1_0 1 Tf 0.05 Tc 9.6349 0 0 9.4 258.74 466.21 Tm (and )Tj 0.0224 Tc 9.3 0 0 9.3 277.54 466.21 Tm (X3 )Tj 0 Tc 11.3 0 0 11.3 292.98 466.21 Tm (= )Tj -0.0199 Tc 9.4 0 0 9.4 303.2 466.21 Tm (0. )Tj 0.05 Tc 9.7963 0 0 9.4 315.46 466.21 Tm (Then )Tj 9.5625 0 0 9.4 340.72 466.21 Tm (the )Tj 0.0081 Tc 9.4 0 0 9.4 357.1 466.21 Tm (two )Tj 0.0391 Tc -35.087 -1.206 Td (imaginary )Tj 0.0493 Tc 4.786 0 Td (chords )Tj 0.0436 Tc 3.39 0 Td (intersect )Tj 0.05 Tc 9.5456 0 0 9.4 143.74 454.87 Tm (in )Tj 9.6991 0 0 9.4 155.68 454.87 Tm (the )Tj 0.0393 Tc 9.4 0 0 9.4 172.85 454.87 Tm (same )Tj 0.0441 Tc 2.6 0 Td (point )Tj 0.0108 Tc 2.689 0 Td (of )Tj -0.035 Tc 9.2947 0 0 9.3 234.16 454.87 Tm (Xo )Tj 0 Tc 11.3 0 0 11.3 250.14 454.87 Tm (= )Tj -0.035 Tc 9.2947 0 0 9.3 260.98 454.87 Tm (X3 )Tj 0 Tc 11.3 0 0 11.3 277.32 454.87 Tm (= )Tj -0.0235 Tc 9.1 0 0 9.1 288.63 454.87 Tm (0; )Tj 0.05 Tc 9.453 0 0 9.4 300.5 454.87 Tm (assume )Tj 10.2879 0 0 9.4 335.13 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Tm (\(n,2h\) )Tj /T1_0 1 Tf 0 Tc 11.3 0 0 11.3 352.92 420.31 Tm (= )Tj -0.035 Tc 9.0505 0 0 9.1 364.45 420.31 Tm (2, )Tj 0.0181 Tc 9.4 0 0 9.4 27.17 408.43 Tm (necessarily )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 74.5 408.43 Tm (h )Tj 13.2 0 0 13.2 84.92 408.43 Tm (+ )Tj /T1_1 1 Tf -0.035 Tc 9.0504 0 0 9.7 95.29 408.43 Tm (t2 )Tj /T1_0 1 Tf 0 Tc 8.4 0 0 8.4 106.87 408.43 Tm (E )Tj 0.0145 Tc 10.5 0 0 10.5 116.03 408.43 Tm ({I, )Tj /T1_1 1 Tf 0.0423 Tc 8.7 0 0 8.7 129.74 408.43 Tm (w, )Tj 0 Tc 1.241 0 Td (w)Tj 9.7 0 0 9.7 147.2 412.21 Tm (2)Tj -0.035 Tc 9.3533 0 0 9.7 151.95 408.43 Tm (}. )Tj /T1_0 1 Tf 0.0161 Tc 9.4 0 0 9.4 163.76 408.43 Tm (Hence )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 192.22 408.43 Tm (h )Tj 12.3 0 0 12.3 202.12 408.43 Tm (+ )Tj /T1_1 1 Tf -0.035 Tc 8.5612 0 0 9.7 211.76 408.43 Tm (t2 )Tj /T1_0 1 Tf 0 Tc 12.1 0 0 12.1 222.6 408.43 Tm (= )Tj -0.035 Tc 8.9497 0 0 10.5 232.79 408.43 Tm (1, )Tj 0.0151 Tc 9.4 0 0 9.4 243.23 408.43 Tm (since )Tj /T1_1 1 Tf 0 Tc 8.7 0 0 8.7 266.72 408.43 Tm (w )Tj /T1_2 1 Tf 9.5 0 0 9.5 276.88 408.43 Tm (\242 )Tj /T1_1 1 Tf -0.035 Tc 7.6577 0 0 10.4 285.98 408.43 Tm (ry, )Tj /T1_0 1 Tf 0.0465 Tc 9.4 0 0 9.4 298.07 408.43 Tm (which )Tj 0.0132 Tc 3.032 0 Td (shows )Tj 0.05 Tc 10.0691 0 0 9.4 354.58 408.43 Tm (that )Tj 9.8533 0 0 9.3 27.16 396.55 Tm (tf )Tj 14.0483 0 0 11.9 37.19 396.55 Tm (+h )Tj 0 Tc 11.9 0 0 11.9 56.28 396.55 Tm (+ )Tj 9.4 0 0 9.4 65.91 396.55 Tm (1 )Tj /T1_2 1 Tf 8.1 0 0 8.1 73.31 396.55 Tm (= )Tj /T1_0 1 Tf 0.0184 Tc 9.4 0 0 9.4 83.42 396.55 Tm (0. )Tj 0.05 Tc 9.6317 0 0 9.4 38.44 385.03 Tm (Then )Tj /T1_1 1 Tf -0.035 Tc 9.2118 0 0 9.7 63.61 385.03 Tm (t;.n+l )Tj /T1_0 1 Tf 0 Tc 11.3 0 0 11.3 89.04 385.03 Tm (= )Tj /C0_0 1 Tf 4.9051 0 0 9 100.09 385.03 Tm <0074007E002B006C0020>Tj /T1_0 1 Tf 0.0265 Tc 9.4 0 0 9.4 124.66 385.03 Tm (implies )Tj -0.035 Tc 10.1019 0 0 13.1 157.93 385.03 Tm (f'1 )Tj /T1_2 1 Tf 0 Tc 12.2 0 0 12.2 171.34 385.03 Tm (+ )Tj /T1_0 1 Tf 10.8 0 0 10.8 181.42 385.03 Tm (h )Tj /T1_2 1 Tf 12.2 0 0 12.2 191.86 385.03 Tm (+ )Tj 9 0 0 9 201.49 385.03 Tm (1 )Tj /T1_0 1 Tf 11.3 0 0 11.3 210.18 385.03 Tm (= )Tj /T1_2 1 Tf -0.035 Tc 7.9383 0 0 9 220.95 385.03 Tm (0; )Tj /T1_0 1 Tf 9.3394 0 0 9.4 232.25 385.03 Tm (so )Tj 10.289 0 0 13.1 244.33 385.03 Tm (f'1 )Tj 0 Tc 11.3 0 0 11.3 258.96 385.03 Tm (= )Tj 0.05 Tc 10.6744 0 0 9.3 269.97 385.03 Tm (tf )Tj 9.4179 0 0 9.4 281.69 385.03 Tm (which )Tj 0.0297 Tc 9.4 0 0 9.4 310.96 385.03 Tm (implies )Tj 0.05 Tc 11.0696 0 0 9.3 344.49 385.03 Tm (tl )Tj 0 Tc 11.3 0 0 11.3 356.16 385.03 Tm (= )Tj /T1_2 1 Tf 9 0 0 9 367.27 385.03 Tm (1 )Tj /T1_0 1 Tf 0.0055 Tc 9.4 0 0 9.4 27.23 373.51 Tm (since )Tj 0 Tc 2.463 0 Td (m )Tj 11.3 0 0 11.3 61.5 373.51 Tm (= )Tj /T1_3 1 Tf 9.3 0 0 9.3 71.48 373.51 Tm (2)Tj /T1_1 1 Tf 6.9001 0 0 6.9001 76.11 377.11 Tm (n)Tj 0.87 -0.522 Td (, )Tj /T1_3 1 Tf -0.0314 Tc 9.8 0 0 9.8 88.32 373.51 Tm (\(n, )Tj -0.035 Tc 9.2782 0 0 9.3 102.33 373.51 Tm (h\) )Tj /T1_0 1 Tf 0 Tc 11.3 0 0 11.3 114.24 373.51 Tm (= )Tj /T1_2 1 Tf 0.05 Tc 12.0296 0 0 8.8 124.51 373.51 Tm (l. )Tj /T1_0 1 Tf 9.4264 0 0 9.4 38.44 362.35 Tm (This )Tj 0.0228 Tc 9.4 0 0 9.4 59.27 362.35 Tm (shows )Tj 0.05 Tc 10.7257 0 0 9.4 86.91 362.35 Tm (that )Tj 9.9723 0 0 9.4 107.62 362.35 Tm (the )Tj 0.0378 Tc 9.4 0 0 9.4 123.75 362.35 Tm (chords )Tj 0.05 Tc 9.6349 0 0 9.4 153.8 362.35 Tm (and )Tj 0.0312 Tc 9.4 0 0 9.4 171.8 362.35 Tm (axes )Tj 0.0108 Tc 2.184 0 Td (of )Tj 0 Tc 9.8 0 0 9.8 202.22 362.35 Tm (C )Tj /T1_3 1 Tf -0.035 Tc 9.7073 0 0 9.8 208.38 362.35 Tm (\(m\) )Tj /T1_0 1 Tf 0.05 Tc 9.5174 0 0 9.4 226.16 362.35 Tm (and )Tj 0 Tc 14 0 0 14 244.06 362.35 Tm (r )Tj /T1_3 1 Tf -0.035 Tc 9.5813 0 0 9.8 250.5 362.35 Tm (\(m\) )Tj /T1_0 1 Tf 0.0235 Tc 9.4 0 0 9.4 268.29 362.35 Tm (define )Tj 0 Tc 2.967 0 Td (a )Tj /T1_1 1 Tf -0.035 Tc 9.3104 0 0 9.7 304.55 362.35 Tm (\(2q2 )Tj /T1_2 1 Tf 0 Tc 12.3 0 0 12.3 323.08 362.35 Tm (+ )Tj /T1_1 1 Tf 9.7 0 0 9.7 331.5 362.35 Tm (q )Tj /T1_2 1 Tf 12.3 0 0 12.3 337.3 362.35 Tm (+ )Tj /T1_0 1 Tf 9.8 0 0 9.8 345.98 362.35 Tm (1 )Tj 0.0327 Tc 9.4 0 0 9.4 350.58 362.35 Tm (\)-cap )Tj 0.0353 Tc -34.414 -1.111 Td (on )Tj 0.05 Tc 7.6677 0 0 7.5001 39.88 351.91 Tm (1{5. )Tj 0 Tc 9.4 0 0 9.4 64.7 351.91 Tm (0 )Tj 0.05 Tc 10.8291 0 0 9.4 27.27 329.95 Tm (Theorem )Tj 10.4098 0 0 9.3 72.59 329.95 Tm (6.2. )Tj /T1_1 1 Tf 0.0462 Tc 9.8 0 0 9.8 96.64 329.95 Tm (The )Tj 0.0216 Tc 9.7 0 0 9.7 115.73 329.95 Tm (\(2q2+q+ )Tj 0.0269 Tc 9.8 0 0 9.8 154.9 329.95 Tm (I\)-cap )Tj 0.0146 Tc 2.902 0 Td (constructed )Tj -0.007 Tc 5.065 0 Td (in )Tj 0.019 Tc 1.112 0 Td (Theorem )Tj /T1_0 1 Tf -0.0127 Tc 9.3 0 0 9.3 283.39 329.95 Tm (6.1 )Tj /T1_1 1 Tf 0.0122 Tc 9.8 0 0 9.8 298.14 329.95 Tm (is )Tj 0.0451 Tc 1.01 0 Td (the )Tj 0.0137 Tc 1.561 0 Td (intersection )Tj /T1_0 1 Tf 0.05 Tc 9.8076 0 0 9.6 27.63 318.79 Tm (of )Tj /T1_1 1 Tf 0.0175 Tc 9.8 0 0 9.8 38.58 318.79 Tm (the )Tj 0.0195 Tc 1.605 0 Td (hypersurfaces )Tj -0.0075 Tc 10 0 0 10 139.48 295.75 Tm (\(X2 )Tj /T1_2 1 Tf 0 Tc 12.3 0 0 12.3 157.3 295.75 Tm (+ )Tj 12.8 0 0 12.8 167.02 295.75 Tm (x)Tj /T1_0 1 Tf 9.3 0 0 9.3 174.85 294.13 Tm (3)Tj 0.0425 Tc 0.489 0.174 Td (\)m-1 )Tj -0.0163 Tc 2.172 0 Td (X5 )Tj /T1_2 1 Tf 0 Tc 12.3 0 0 12.3 213.82 295.75 Tm (+ )Tj /T1_0 1 Tf 0.05 Tc 10.548 0 0 9.3 223.18 295.75 Tm (X,r )Tj /T1_2 1 Tf 0 Tc 8.1 0 0 8.1 241.43 295.75 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 9.0857 0 0 9.6 251.73 295.75 Tm (0, )Tj /T1_1 1 Tf -0.0165 Tc 10 0 0 10 139.66 279.37 Tm (\(X2 )Tj /T1_2 1 Tf 0 Tc 12.3 0 0 12.3 157.48 279.37 Tm (+ )Tj /T1_0 1 Tf 14.8 0 0 14.8 166.99 279.37 Tm (x)Tj 9.3 0 0 9.3 175.03 277.75 Tm (3)Tj 0.0361 Tc 0.47 0.174 Td (\)m-1 )Tj -0.035 Tc 9.2947 0 0 9.3 199.78 279.37 Tm (Xo )Tj /T1_2 1 Tf 0 Tc 12.3 0 0 12.3 214 279.37 Tm (+ )Tj /T1_0 1 Tf 0.0372 Tc 9.3 0 0 9.3 223.36 279.37 Tm (X;n )Tj /T1_2 1 Tf 0 Tc 8.1 0 0 8.1 241.61 279.37 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 8.8261 0 0 9.6 251.91 279.37 Tm (0, )Tj /T1_1 1 Tf -0.0233 Tc 9.7 0 0 9.7 141.32 262.45 Tm (XOX5 )Tj /T1_2 1 Tf 0 Tc 12.3 0 0 12.3 167.92 262.45 Tm (+ )Tj /T1_0 1 Tf 9.3 0 0 9.3 177.46 262.45 Tm (X)Tj 6.6 0 0 6.6 185.9 261.55 Tm (I)Tj 9.3 0 0 9.3 189.7 262.45 Tm (X)Tj 6.6 0 0 6.6 197.43 261.73 Tm (4 )Tj /T1_2 1 Tf 12.3 0 0 12.3 203.74 262.45 Tm (+ )Tj /T1_1 1 Tf 9.7 0 0 9.7 213.5 262.45 Tm (X)Tj /T1_3 1 Tf 6.2 0 0 6.2 221.12 261.55 Tm (2)Tj /T1_1 1 Tf 9.7 0 0 9.7 225.38 262.45 Tm (X)Tj /T1_3 1 Tf 6.2 0 0 6.2 233 261.55 Tm (3 )Tj /T1_2 1 Tf 8.1 0 0 8.1 239.81 262.45 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 8.8261 0 0 9.3 250.11 262.45 Tm (0. )Tj /T1_1 1 Tf 0.0226 Tc 8.9 0 0 8.9 27.61 242.11 Tm (Proof. )Tj /T1_0 1 Tf 0.05 Tc 9.4943 0 0 9.4 56.84 242.11 Tm (By )Tj -0.035 Tc 9.3133 0 0 10.7 72.14 242.11 Tm ([4], )Tj 0.05 Tc 9.8357 0 0 9.4 88.54 242.11 Tm (the )Tj 0.047 Tc 9.4 0 0 9.4 105.21 242.11 Tm (coordinates )Tj 0.05 Tc 9.5989 0 0 9.4 156.51 242.11 Tm (of )Tj 9.6991 0 0 9.4 167.74 242.11 Tm (the )Tj 0.0148 Tc 9.4 0 0 9.4 184.23 242.11 Tm (chords )Tj 0.05 Tc 3.159 0 Td (and )Tj 0.0248 Tc 1.934 0 Td (axes )Tj 0.0447 Tc 2.222 0 Td (can )Tj 0.05 Tc 9.8842 0 0 9.4 270.19 242.11 Tm (be )Tj 9.7985 0 0 9.4 283.67 242.11 Tm (rewritten )Tj 0.0216 Tc 9.4 0 0 9.4 326.6 242.11 Tm (as )Tj /T1_1 1 Tf 0.0061 Tc 9.7 0 0 9.7 27.28 223.21 Tm (J\(R2m )Tj -0.0341 Tc 2.789 0 Td (pm, )Tj 0 Tc 1.662 0 Td (R)Tj 0.768 0.334 Td (m)Tj 0.757 -0.334 Td (+)Tj 0.665 0.334 Td (l )Tj -0.035 Tc 9.4851 0 0 9.7 95.72 223.21 Tm (p, )Tj 0.0401 Tc 9.7 0 0 9.7 105.01 223.21 Tm (Rm\(1 )Tj /T1_2 1 Tf 0 Tc 12.3 0 0 12.3 129.04 223.21 Tm (+ )Tj /T1_1 1 Tf 0.05 Tc 9.9431 0 0 9.7 137.67 223.21 Tm (p+ )Tj -0.035 Tc 8.3627 0 0 9.7 151.66 223.21 Tm (p2 )Tj /T1_2 1 Tf 0 Tc 13.1 0 0 13.1 161.25 223.21 Tm (+ )Tj /T1_1 1 Tf 0.0041 Tc 9.7 0 0 9.7 169.89 223.21 Tm (p4+ )Tj 0 Tc 1.868 0 Td (.)Tj /T1_0 1 Tf 0.05 Tc 10.2879 0 0 9.7 192.03 223.21 Tm (.. )Tj /T1_2 1 Tf 0 Tc 13.1 0 0 13.1 199.05 223.21 Tm (+ )Tj /T1_1 1 Tf -0.0055 Tc 9.7 0 0 9.7 207.69 223.21 Tm (pm/2\), )Tj 0.05 Tc 9.9604 0 0 9.7 234.97 223.21 Tm (Rm\(p+ )Tj -0.035 Tc 8.5445 0 0 9.7 267.05 223.21 Tm (p2 )Tj /T1_2 1 Tf 0 Tc 13.1 0 0 13.1 276.99 223.21 Tm (+ )Tj -0.011 Tc 0.663 0 Td (... )Tj 0 Tc 0.931 0 Td (+ )Tj /T1_1 1 Tf 0.013 Tc 9.7 0 0 9.7 306.69 223.21 Tm (pm/2\), )Tj 0 Tc (R)Tj 3.673 0.315 Td (m)Tj 0.739 -0.315 Td (-)Tj 0.608 0.315 Td (l)Tj 0.404 -0.315 Td (, )Tj /T1_2 1 Tf -0.035 Tc 8.9254 0 0 10.2 363.49 223.21 Tm (1\) )Tj /T1_0 1 Tf 0.05 Tc 9.4 0 0 9.4 27.26 203.59 Tm (and )Tj /T1_1 1 Tf 0.0198 Tc 9.7 0 0 9.7 27.46 185.59 Tm (J\(U)Tj -0.035 Tc 8.2872 0 0 9.7 43.53 189.01 Tm (2m)Tj 4.9282 0 0 9.7 54.24 185.59 Tm (J-t)Tj 0 Tc 9.7 0 0 9.7 59.9 189.01 Tm (m)Tj 0.805 -0.353 Td (, )Tj -0.035 Tc 9.3458 0 0 9.7 71.53 185.59 Tm (Um+IJ-t, )Tj -0.0267 Tc 9.7 0 0 9.7 106.98 185.59 Tm (Um\(J-t+ )Tj /T1_0 1 Tf -0.035 Tc 6.4943 0 0 11.9 141.99 185.59 Tm (J-t2 )Tj 0 Tc 11.9 0 0 11.9 153.3 185.59 Tm (+ )Tj 0.05 Tc 12.0388 0 0 11.9 162.29 185.59 Tm (... )Tj 0 Tc 11.9 0 0 11.9 174.72 185.59 Tm (+ )Tj /T1_1 1 Tf -0.035 Tc 8.3546 0 0 9.7 183.51 185.59 Tm (J-tm/2\) )Tj /T1_0 1 Tf 0 Tc 9.7 0 0 9.7 207.75 185.59 Tm (, )Tj /T1_1 1 Tf 0.393 0 Td (U)Tj 0.788 0.353 Td (m)Tj /T1_3 1 Tf -0.035 Tc 7.8097 0 0 9.8 226.61 185.59 Tm (\(1 )Tj /T1_0 1 Tf 0 Tc 11.9 0 0 11.9 235.92 185.59 Tm (+ )Tj -0.035 Tc 9.1935 0 0 11.9 244.75 185.59 Tm (J-t+ )Tj 6.4943 0 0 11.9 260.25 185.59 Tm (J-t2 )Tj 0 Tc 11.9 0 0 11.9 271.74 185.59 Tm (+ )Tj 0.05 Tc 12.4846 0 0 11.9 280.72 185.59 Tm (... )Tj 0 Tc 11.9 0 0 11.9 293.34 185.59 Tm (+ )Tj /T1_1 1 Tf -0.035 Tc 8.7524 0 0 9.7 302.67 185.59 Tm (J-tm/2\) )Tj /T1_0 1 Tf 0 Tc 9.7 0 0 9.7 327.99 185.59 Tm (, )Tj /T1_1 1 Tf 0.05 Tc 11.0765 0 0 9.7 332.19 185.59 Tm (um-I, )Tj /T1_3 1 Tf -0.035 Tc 9.2762 0 0 9.8 360.67 185.59 Tm (1\). )Tj /T1_0 1 Tf 0.013 Tc 9.4 0 0 9.4 38.48 166.51 Tm (For )Tj 0 Tc 1.87 0 Td (a )Tj 0.05 Tc 9.7818 0 0 9.4 64.46 166.51 Tm (point )Tj 0.0361 Tc 9.4 0 0 9.4 90.82 166.51 Tm (lying )Tj 0.0434 Tc 2.623 0 Td (in )Tj 0.05 Tc 9.8357 0 0 9.4 127.24 166.51 Tm (the )Tj 0.0375 Tc 9.4 0 0 9.4 144.64 166.51 Tm (intersection )Tj 0.0491 Tc 5.476 0 Td (of )Tj 0.05 Tc 9.4259 0 0 9.4 207.7 166.51 Tm (the )Tj 0.0285 Tc 9.4 0 0 9.4 224.45 166.51 Tm (hypersurfaces, )Tj 0.05 Tc 9.5054 0 0 9.4 287.56 166.51 Tm (if )Tj 0.0224 Tc 9.3 0 0 9.3 297.34 166.51 Tm (X5 )Tj /T1_2 1 Tf 0 Tc 8.7 0 0 8.7 313.78 166.51 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 9.3453 0 0 9.4 324.8 166.51 Tm (0, )Tj 0.05 Tc 9.7342 0 0 9.4 336.22 166.51 Tm (then )Tj 0.0422 Tc 9.4 0 0 9.4 358.54 166.51 Tm (the )Tj 0.0341 Tc -35.231 -1.226 Td (points )Tj 0.0471 Tc 3.148 0 Td (are )Tj 0.0137 Tc 1.914 0 Td (\(1, )Tj /T1_1 1 Tf 0 Tc 9.7 0 0 9.7 88.09 154.99 Tm (t)Tj 0.341 0.371 Td (m)Tj 0.05 Tc 18.2242 0 0 9.7 98.68 154.99 Tm (-\\ )Tj /T1_0 1 Tf -0.0199 Tc 9.4 0 0 9.4 112.94 154.99 Tm (0, )Tj /T1_1 1 Tf 0 Tc 9.7 0 0 9.7 122.11 154.99 Tm (t)Tj 0.36 0.371 Td (m)Tj 0.824 -0.371 Td (, )Tj /T1_0 1 Tf -0.0199 Tc 9.4 0 0 9.4 137.24 154.99 Tm (0, )Tj 0.015 Tc 0.996 0 Td (0\), )Tj 0.05 Tc 9.9982 0 0 9.4 163.14 154.99 Tm (\(0,0,0,1,0,0\), )Tj -0.0342 Tc 9.4 0 0 9.4 227.23 154.99 Tm (\(1, )Tj /T1_1 1 Tf 0 Tc 9.7 0 0 9.7 239.11 154.99 Tm (t)Tj 0.378 0.371 Td (m)Tj 0.05 Tc 17.3831 0 0 9.7 250.07 154.99 Tm (-\\ )Tj 0 Tc 9.7 0 0 9.7 263.77 154.99 Tm (t)Tj 0.36 0.371 Td (m)Tj 0.824 -0.371 Td (, )Tj /T1_0 1 Tf -0.0007 Tc 9.4 0 0 9.4 279.08 154.99 Tm (0, )Tj -0.035 Tc 9.3453 0 0 9.4 288.62 154.99 Tm (0, )Tj 0.0438 Tc 9.4 0 0 9.4 297.8 154.99 Tm (0\), )Tj 0.05 Tc 10.1181 0 0 9.4 314.88 154.99 Tm (\(0,0,1,0,0,0\) )Tj 0.013 Tc 9.4 0 0 9.4 27.17 143.47 Tm (which )Tj 0.05 Tc 9.4602 0 0 9.4 54.09 143.47 Tm (correspond )Tj 10.0407 0 0 9.4 103.84 143.47 Tm (to )Tj 9.6991 0 0 9.4 115.9 143.47 Tm (the )Tj 0.0312 Tc 9.4 0 0 9.4 132.56 143.47 Tm (axes )Tj 0.05 Tc 9.5456 0 0 9.4 153.82 143.47 Tm (in )Tj 0.003 Tc 9.3 0 0 9.3 165.04 143.47 Tm (X3 )Tj 0 Tc 11.3 0 0 11.3 180.12 143.47 Tm (= )Tj /T1_2 1 Tf 23.7001 0 0 23.7001 189.46 143.47 Tm (\260 )Tj /T1_0 1 Tf 0.05 Tc 9.6349 0 0 9.4 197.54 143.47 Tm (and )Tj 9.5625 0 0 9.4 215.98 143.47 Tm (the )Tj 0.0263 Tc 9.4 0 0 9.4 232.11 143.47 Tm (chords )Tj 0.05 Tc 9.7722 0 0 9.4 261.88 143.47 Tm (through )Tj /T1_1 1 Tf 10.258 0 0 9.6 298.78 143.47 Tm (Vo. )Tj /T1_0 1 Tf 0 Tc 9.4 0 0 9.4 38.66 131.95 Tm (H )Tj -0.035 Tc 9.1424 0 0 9.3 49.48 131.95 Tm (X5 )Tj 0 Tc 11.3 0 0 11.3 66.36 131.95 Tm (= )Tj 9.4 0 0 9.4 79.05 131.95 Tm (1 )Tj 0.05 Tc 9.7524 0 0 9.4 88.82 131.95 Tm (and )Tj 0 Tc 9.3 0 0 9.3 109.06 131.95 Tm (X)Tj 6.7 0 0 6.7 116.97 130.87 Tm (4 )Tj 11.3 0 0 11.3 126.3 131.95 Tm (= )Tj -0.035 Tc 9.3453 0 0 9.4 138.68 131.95 Tm (0, )Tj 0.05 Tc 9.8306 0 0 9.4 151 131.95 Tm (then )Tj /T1_3 1 Tf 10.3074 0 0 9 174.88 131.95 Tm (\(X)Tj /T1_1 1 Tf 0 Tc 10 0 0 10 185.86 130.69 Tm (o)Tj 0.48 0.126 Td (, )Tj 0.05 Tc 12.0791 0 0 10 194.46 131.95 Tm (... )Tj /T1_3 1 Tf 12.0614 0 0 9 208.72 131.95 Tm (,X)Tj 0 Tc 6.2 0 0 6.2 220.38 130.69 Tm (5)Tj 0.732 0.203 Td (\) )Tj /T1_0 1 Tf 11.3 0 0 11.3 233.22 131.95 Tm (= )Tj /T1_1 1 Tf -0.0282 Tc 9.7 0 0 9.7 245.87 131.95 Tm (\(t)Tj -0.035 Tc 8.2872 0 0 9.7 252.51 135.73 Tm (2m)Tj 0 Tc 9.7 0 0 9.7 263.73 131.95 Tm (, )Tj /T1_0 1 Tf -0.035 Tc 9.3453 0 0 9.4 267.74 131.95 Tm (0, )Tj /T1_1 1 Tf 0 Tc 9.7 0 0 9.7 276.91 131.95 Tm (t)Tj 0.36 0.39 Td (m)Tj 0.824 -0.39 Td [(, )106(t)]TJ 0.772 0.371 Td (m)Tj 0.824 -0.371 Td (, )Tj /T1_0 1 Tf 0.05 Tc 9.665 0 0 9.4 307.88 131.95 Tm (0,1\). )Tj 10.0101 0 0 9.6 336.35 131.95 Tm (If )Tj -0.035 Tc 9.2947 0 0 9.3 347.38 131.95 Tm (X5 )Tj 0 Tc 11.3 0 0 11.3 364.44 131.95 Tm (= )Tj 9.4 0 0 9.4 27.57 119.17 Tm (1 )Tj 0.05 Tc 0.944 0 Td (and )Tj 0 Tc 9.3 0 0 9.3 55.96 119.17 Tm (X)Tj 6.7 0 0 6.7 63.87 117.91 Tm (4 )Tj /T1_1 1 Tf -0.035 Tc 3.8594 0 0 7.1 72.97 119.17 Tm (=f=. )Tj /T1_0 1 Tf 9.3453 0 0 9.4 85.76 119.17 Tm (0, )Tj 0.05 Tc 9.5848 0 0 9.4 98.02 119.17 Tm (letting )Tj 0 Tc 9.3 0 0 9.3 130.12 119.17 Tm (X)Tj 6.7 0 0 6.7 138.21 117.91 Tm (4 )Tj 11.3 0 0 11.3 147.36 119.17 Tm (= )Tj /T1_1 1 Tf 9.7 0 0 9.7 159.54 119.17 Tm (U)Tj 0.751 0.371 Td (m)Tj 0.758 -0.371 Td (-)Tj 0.627 0.371 Td (l )Tj /T1_0 1 Tf 0.0138 Tc 9.4 0 0 9.4 188.38 119.17 Tm (implies )Tj 0 Tc 9.3 0 0 9.3 221.56 119.17 Tm (X)Tj 6.7 0 0 6.7 229.46 117.91 Tm (2 )Tj /T1_2 1 Tf 13.1 0 0 13.1 236.31 119.17 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 9.1424 0 0 9.3 247.12 119.17 Tm (X3 )Tj 0 Tc 11.3 0 0 11.3 263.64 119.17 Tm (= )Tj /T1_1 1 Tf 9.7 0 0 9.7 276 119.17 Tm (U)Tj 0.788 0.353 Td (m )Tj /T1_0 1 Tf 0.05 Tc 9.9874 0 0 9.4 295.64 119.17 Tm (and )Tj /T1_1 1 Tf 0 Tc 9.7 0 0 9.7 316.54 119.17 Tm (u)Tj -0.035 Tc 8.0026 0 0 9.7 323.78 124.21 Tm (m2)Tj 0 Tc 9.7 0 0 9.7 334.73 119.17 Tm (-)Tj 0.578 0.371 Td (m )Tj /T1_0 1 Tf -0.035 Tc 9.2947 0 0 9.3 347.74 119.17 Tm (Xo )Tj 0 Tc 11.3 0 0 11.3 364.44 119.17 Tm (= )Tj 0.05 Tc 13.5709 0 0 9.3 27.34 107.64 Tm (Xl' )Tj 9.7654 0 0 9.4 50.76 107.64 Tm (Substituting )Tj 10.6967 0 0 9.3 107.08 107.64 Tm (Xl )Tj 0 Tc 11.3 0 0 11.3 122.88 107.64 Tm (= )Tj /T1_1 1 Tf -0.035 Tc 9.2384 0 0 9.7 133.63 107.64 Tm (Um+lJ-t )Tj /T1_0 1 Tf 0.0169 Tc 9.4 0 0 9.4 167.68 107.64 Tm (implies )Tj 0 Tc 9.3 0 0 9.3 200.32 107.64 Tm (X)Tj 6.3001 0 0 6.3001 208.22 106.38 Tm (2 )Tj /T1_2 1 Tf 12.2 0 0 12.2 214.72 107.64 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 9.2947 0 0 9.3 224.26 107.64 Tm (X3 )Tj 0 Tc 11.3 0 0 11.3 239.52 107.64 Tm (= )Tj /T1_1 1 Tf 0.05 Tc 10.2835 0 0 9.7 250.47 107.64 Tm (um, )Tj /T1_0 1 Tf 0.0224 Tc 9.3 0 0 9.3 271.24 107.64 Tm (Xo )Tj 0 Tc 11.3 0 0 11.3 287.4 107.64 Tm (= )Tj /T1_1 1 Tf 9.7 0 0 9.7 298.36 107.64 Tm (u)Tj -0.035 Tc 8.7476 0 0 9.7 306.14 111.24 Tm (2m)Tj 4.9282 0 0 9.7 317.76 107.64 Tm (J-t)Tj 0 Tc 9.7 0 0 9.7 323.06 111.24 Tm (m)Tj 0.824 -0.371 Td (, )Tj /T1_3 1 Tf 9.2 0 0 9.2 337.05 107.64 Tm (X)Tj /T1_1 1 Tf 9.7 0 0 9.7 345.02 106.56 Tm (2)Tj /T1_3 1 Tf 9.2 0 0 9.2 349.11 107.64 Tm (X)Tj /T1_1 1 Tf 6.6 0 0 6.6 357.06 106.21 Tm (3 )Tj 11.4 0 0 11.4 364.17 107.64 Tm (= )Tj 9.7 0 0 9.7 27.42 95.95 Tm (U)Tj -0.035 Tc 8.2872 0 0 9.7 35.07 99.73 Tm (2m)Tj 7.5455 0 0 9.7 46.29 95.95 Tm (\(J-tm )Tj /T1_2 1 Tf 0 Tc 12.3 0 0 12.3 64.6 95.95 Tm (+ )Tj /T1_1 1 Tf -0.035 Tc 7.736 0 0 9.7 74.24 95.95 Tm (J-t\). )Tj /T1_0 1 Tf -0.0257 Tc 9.4 0 0 9.4 38.71 84.78 Tm (So )Tj /T1_1 1 Tf 0 Tc 10 0 0 10 51.69 84.78 Tm (X)Tj 9.7 0 0 9.7 59.36 83.52 Tm (2)Tj 0.49 0.13 Td (, )Tj /T1_0 1 Tf 0.0224 Tc 9.3 0 0 9.3 68.02 84.78 Tm (X3 )Tj 0.05 Tc 9.4959 0 0 9.4 83.42 84.78 Tm (are )Tj 0.0427 Tc 9.4 0 0 9.4 99.23 84.78 Tm (solutions )Tj 0.05 Tc 10.0407 0 0 9.4 139.48 84.78 Tm (to )Tj 0 Tc 9.3 0 0 9.3 151 84.78 Tm (X)Tj 11.9 0 0 11.9 159.95 88.56 Tm (2 )Tj 0.47 -0.318 Td (+ )Tj /T1_1 1 Tf 9.7 0 0 9.7 174.12 84.78 Tm (U)Tj 0.788 0.371 Td (m )Tj /T1_0 1 Tf 9.3 0 0 9.3 188.98 84.78 Tm (X )Tj 11.9 0 0 11.9 198.84 84.78 Tm (+ )Tj /T1_1 1 Tf -0.035 Tc 7.4546 0 0 9.7 207.93 84.78 Tm (\(J-tm )Tj /T1_0 1 Tf 0 Tc 11.9 0 0 11.9 225.3 84.78 Tm (+ )Tj /T1_1 1 Tf -0.035 Tc 8.2483 0 0 9.7 233.91 84.78 Tm (J-t\)U)Tj 8.2872 0 0 9.7 250.89 88.38 Tm (2m )Tj /T1_2 1 Tf 0 Tc 8.1 0 0 8.1 264.47 84.78 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 9.3453 0 0 9.4 274.76 84.78 Tm (0. )Tj 0.0448 Tc 9.4 0 0 9.4 286.52 84.78 Tm (Hence )Tj 0.05 Tc 9.8357 0 0 9.4 315.52 84.78 Tm (the )Tj 0.0406 Tc 9.4 0 0 9.4 331.65 84.78 Tm (caps )Tj 0.0098 Tc 2.22 0 Td (form )Tj 0.05 Tc 9.5625 0 0 9.4 27.34 73.63 Tm (the )Tj 0.0479 Tc 9.4 0 0 9.4 43.48 73.63 Tm (intersection )Tj 0.0491 Tc 5.552 0 Td (of )Tj 0.05 Tc 9.8357 0 0 9.4 106.72 73.63 Tm (the )Tj 0.0329 Tc 9.4 0 0 9.4 123.47 73.63 Tm (hypersurfaces. )Tj 0 Tc 7.324 0 Td (0 )Tj 0.05 Tc 10.7233 0 0 9.4 27.49 52.93 Tm (Remark. )Tj 10.1189 0 0 9.4 73.89 52.93 Tm (The )Tj 9.5874 0 0 9.4 94.6 52.93 Tm (last )Tj 0.0465 Tc 9.4 0 0 9.4 113.57 52.93 Tm (result )Tj 0.0012 Tc 2.903 0 Td (is )Tj 0.05 Tc 9.6965 0 0 9.4 151.01 52.93 Tm (not )Tj 0.0191 Tc 9.4 0 0 9.4 168.64 52.93 Tm (valid )Tj -0.0086 Tc 2.462 0 Td (for )Tj 0.05 Tc 9.4581 0 0 9.4 206.73 52.93 Tm (odd )Tj 0.0398 Tc 9.4 0 0 9.4 225.63 52.93 Tm (characteristic. )Tj 0.05 Tc 10.1579 0 0 9.4 289.73 52.93 Tm (In )Tj /T1_1 1 Tf 0.0372 Tc 10 0 0 10 302.84 52.93 Tm (PG\(5, )Tj -0.0302 Tc 2.83 0 Td (q\), )Tj 0 Tc 1.458 0 Td (q )Tj /T1_0 1 Tf 0.0298 Tc 9.4 0 0 9.4 353.79 52.93 Tm (odd, )Tj 0.05 Tc 9.5625 0 0 9.4 27.52 41.41 Tm (the )Tj 0.0298 Tc 9.4 0 0 9.4 43.52 41.41 Tm (Klein )Tj 0.05 Tc 9.5868 0 0 9.4 68.85 41.41 Tm (quadric )Tj -0.0179 Tc 9.4 0 0 9.4 103.96 41.41 Tm (is )Tj 0.05 Tc 9.6991 0 0 9.4 113.56 41.41 Tm (the )Tj 0.04 Tc 9.4 0 0 9.4 130.05 41.41 Tm (only )Tj 0.0481 Tc 2.221 0 Td (quadric )Tj 0.0337 Tc 3.638 0 Td (containing )Tj 0.05 Tc 9.6991 0 0 9.4 230.74 41.41 Tm (the )Tj /T1_1 1 Tf -0.035 Tc 8.7932 0 0 9.7 247.68 41.41 Tm (\(2q2 )Tj /T1_2 1 Tf 0 Tc 12.3 0 0 12.3 266.02 41.41 Tm (+ )Tj /T1_1 1 Tf 9.7 0 0 9.7 275.34 41.41 Tm (q )Tj /T1_2 1 Tf 12.3 0 0 12.3 281.86 41.41 Tm (+ )Tj /T1_0 1 Tf 9.4 0 0 9.4 291.45 41.41 Tm (1 )Tj 0.05 Tc 9.5115 0 0 9.4 296.4 41.41 Tm (\)-cap )Tj 0.0409 Tc 9.4 0 0 9.4 321.21 41.41 Tm (constructed. )Tj 0.0038 Tc -13.64 -2.719 Td (109 )Tj ET endstream endobj 225 0 obj <>/Filter/CCITTFaxDecode/Height 1872/Length 46493/Name/Im0/Subtype/Image/Type/XObject/Width 2240>>stream )Du :JQDr(9RGQJ#@TV@TD 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13.7668 0 0 9.1 30.22 537.67 Tm (If )Tj /T1_1 1 Tf -0.035 Tc 8.4713 0 0 9.6 41.89 537.67 Tm (ao )Tj /T1_2 1 Tf 8.8261 0 0 9.3 65.97 537.67 Tm (0, )Tj 0.05 Tc 9.8306 0 0 9.3 77.02 537.67 Tm (then )Tj /T1_1 1 Tf 10.6883 0 0 9.6 99.65 537.67 Tm (alt)Tj 0 Tc 9.6 0 0 9.6 112.46 541.27 Tm (m )Tj /T1_0 1 Tf 12.3 0 0 12.3 122.02 537.67 Tm (+ )Tj /T1_1 1 Tf -0.0153 Tc 9.6 0 0 9.6 132.06 537.67 Tm (a2t )Tj /T1_2 1 Tf 0 Tc 11.5 0 0 11.5 148.08 537.67 Tm (= )Tj 9.3 0 0 9.3 158.84 537.67 Tm (0 )Tj 0.0449 Tc 0.892 0 Td (if )Tj 0.05 Tc 9.6349 0 0 9.3 176.48 537.67 Tm (and )Tj 0.0338 Tc 9.3 0 0 9.3 195.39 537.67 Tm (only )Tj 0.0449 Tc 2.304 0 Td (if )Tj /T1_1 1 Tf 0 Tc 9.6 0 0 9.6 226.15 537.67 Tm (t )Tj /T1_2 1 Tf 11.5 0 0 11.5 233.58 537.67 Tm (= )Tj 9.3 0 0 9.3 244.7 537.67 Tm (0 )Tj 0.05 Tc 9.5989 0 0 9.3 253.35 537.67 Tm (or )Tj /T1_1 1 Tf 11.0027 0 0 9.6 265.97 537.67 Tm (alt)Tj 0 Tc 9.6 0 0 9.6 279.32 541.45 Tm (m)Tj 0.766 -0.394 Td (-)Tj 0.615 0.394 Td (l )Tj /T1_0 1 Tf 12.3 0 0 12.3 299.14 537.67 Tm (+ )Tj /T1_1 1 Tf -0.035 Tc 8.283 0 0 9.6 309.01 537.67 Tm (a2 )Tj /T1_2 1 Tf 0 Tc 11.5 0 0 11.5 321.78 537.67 Tm (= )Tj -0.035 Tc 6.6904 0 0 9.3 332.39 537.67 Tm (O. )Tj 0.05 Tc 9.349 0 0 9.3 345.34 537.67 Tm (The )Tj 10.3994 0 0 9.3 18.99 526.51 Tm (latter )Tj 9.4053 0 0 9.3 46.16 526.51 Tm (equation )Tj 9.4532 0 0 9.3 85.31 526.51 Tm (has )Tj 10.1984 0 0 9.3 102.68 526.51 Tm (at )Tj 9.3079 0 0 9.3 114.28 526.51 Tm (most )Tj 0.0435 Tc 9.3 0 0 9.3 137.5 526.51 Tm (three )Tj 0.0359 Tc 2.524 0 Td (solutions )Tj 0.05 Tc 9.3236 0 0 9.3 200.8 526.51 Tm (in )Tj -0.035 Tc 8.8644 0 0 9.3 211.51 526.51 Tm ("\(' )Tj 0.0304 Tc 9.3 0 0 9.3 222.89 526.51 Tm (since )Tj 0.05 Tc 9.9378 0 0 9.3 247.2 526.51 Tm (\(m )Tj 0 Tc 9.3 0 0 9.3 261.97 526.51 Tm (-)Tj -0.0205 Tc 1.042 0 Td (1, )Tj /T1_1 1 Tf -0.035 Tc 8.899 0 0 9.6 280.76 526.51 Tm (22h )Tj /T1_2 1 Tf 0 Tc 9.6 0 0 9.6 297.07 526.51 Tm (-)Tj -0.0261 Tc 9.3 0 0 9.3 306.22 526.51 Tm (1\) )Tj 0 Tc 13 0 0 13 317.09 526.51 Tm (= )Tj -0.035 Tc 8.7598 0 0 9.3 326.96 526.51 Tm (3. )Tj 0.05 Tc 9.5758 0 0 9.3 30.79 514.45 Tm (So )Tj 9.5184 0 0 9.3 44.62 514.45 Tm (there )Tj 9.3582 0 0 9.3 69.02 514.45 Tm (are )Tj 10.1984 0 0 9.3 85.04 514.45 Tm (at )Tj 9.3941 0 0 9.3 96.64 514.45 Tm (most )Tj 0 Tc 9.3 0 0 9.3 119.66 514.45 Tm (4 )Tj 0.043 Tc 0.827 0 Td (distinct )Tj 0.0269 Tc 3.615 0 Td (solutions; )Tj 0.05 Tc 9.3464 0 0 9.3 203.38 514.45 Tm (together )Tj 9.7422 0 0 9.3 240.83 514.45 Tm (with )Tj 10.1089 0 0 9.3 262.96 514.45 Tm (the )Tj 0.0468 Tc 9.3 0 0 9.3 279.59 514.45 Tm (solution )Tj /T1_1 1 Tf 0 Tc 9.8 0 0 9.8 315.78 514.45 Tm (t )Tj /T1_2 1 Tf 13 0 0 13 321.95 514.45 Tm (= )Tj 0.05 Tc 8.1301 0 0 6.4001 331.66 514.45 Tm (00, )Tj 0.0359 Tc 9.3 0 0 9.3 346.48 514.45 Tm (this )Tj 0.028 Tc -35.194 -1.219 Td (gives )Tj 0.05 Tc 10.1984 0 0 9.3 43.64 503.11 Tm (at )Tj 9.3079 0 0 9.3 55.42 503.11 Tm (most )Tj 0 Tc 9.3 0 0 9.3 78.89 503.11 Tm (5 )Tj 0.0359 Tc 0.832 0 Td (solutions )Tj 0.05 Tc 9.3236 0 0 9.3 126.64 503.11 Tm (in )Tj -0.035 Tc 9.2871 0 0 9.3 137.52 503.11 Tm ("\('. )Tj 0.05 Tc 9.892 0 0 9.3 30.75 491.23 Tm (When )Tj /T1_1 1 Tf -0.035 Tc 8.6595 0 0 9.6 58.98 491.23 Tm (ao )Tj /T1_2 1 Tf 8.1396 0 0 12.6 71.01 491.23 Tm (-# )Tj -0.0316 Tc 9.3 0 0 9.3 81.08 491.23 Tm (0, )Tj 0.05 Tc 9.3426 0 0 9.3 91.27 491.23 Tm (by )Tj 0.0422 Tc 9.3 0 0 9.3 103.96 491.23 Tm (introducing )Tj 0.0278 Tc 5.349 0 Td (homogeneous )Tj 0.05 Tc 9.3453 0 0 9.3 210.87 491.23 Tm (coordinates )Tj /T1_1 1 Tf 0.0046 Tc 9.6 0 0 9.6 262.07 491.23 Tm (\(t, )Tj /T1_3 1 Tf 0.0282 Tc 9.8 0 0 9.8 273.53 491.23 Tm (l\) )Tj /T1_2 1 Tf 0.0429 Tc 9.3 0 0 9.3 282.83 491.23 Tm (such )Tj 0.05 Tc 10.0691 0 0 9.3 304 491.23 Tm (that )Tj /T1_1 1 Tf -0.0235 Tc 9.6 0 0 9.6 324.35 491.23 Tm (\(t, )Tj /T1_2 1 Tf -0.035 Tc 9.1661 0 0 9.3 335.02 491.23 Tm (1\) )Tj /T1_0 1 Tf 5.5768 0 0 11 345.87 491.23 Tm (== )Tj /T1_1 1 Tf 0.0041 Tc 9.6 0 0 9.6 355.39 491.23 Tm (t, )Tj /T1_2 1 Tf 0.05 Tc 9.3426 0 0 9.3 19.45 480.07 Tm (by )Tj 9.4371 0 0 9.3 34.9 480.07 Tm (making )Tj 9.6991 0 0 9.3 70.36 480.07 Tm (the )Tj 9.4053 0 0 9.3 88.28 480.07 Tm (equation )Tj 0.0239 Tc 9.3 0 0 9.3 128.87 480.07 Tm (homogeneous )Tj 0.05 Tc 9.6041 0 0 9.3 187.9 480.07 Tm (to )Tj /T1_1 1 Tf 0.0005 Tc 9.6 0 0 9.6 201 480.07 Tm (aotm+l )Tj /T1_0 1 Tf 0 Tc 12.3 0 0 12.3 233.8 480.07 Tm (+ )Tj /T1_1 1 Tf 0.05 Tc 10.8455 0 0 9.6 244.55 480.07 Tm (alt)Tj 0 Tc 9.6 0 0 9.6 257.54 483.31 Tm (m)Tj 0.791 -0.338 Td ([ )Tj /T1_0 1 Tf 12.3 0 0 12.3 271.6 480.07 Tm (+ )Tj /T1_1 1 Tf 0.0051 Tc 9.6 0 0 9.6 282.36 480.07 Tm (a2tlm )Tj /T1_2 1 Tf 0 Tc 13 0 0 13 310.79 480.07 Tm (= )Tj 9.3 0 0 9.3 323 480.07 Tm (0 )Tj 0.05 Tc 9.3999 0 0 9.3 332.18 480.07 Tm (and )Tj 0.0161 Tc 9.3 0 0 9.3 351.73 480.07 Tm (by )Tj 0.05 Tc 9.3305 0 0 9.3 19.36 468.55 Tm (interchanging )Tj /T1_1 1 Tf 0 Tc 9.6 0 0 9.6 79.27 468.55 Tm (t )Tj /T1_2 1 Tf 0.05 Tc 9.6349 0 0 9.3 85.76 468.55 Tm (and )Tj /T1_3 1 Tf 0.0165 Tc 9 0 0 9 104.15 468.55 Tm (l, )Tj /T1_2 1 Tf 0.05 Tc 9.5322 0 0 9.3 112.76 468.55 Tm (an )Tj 0.0478 Tc 9.3 0 0 9.3 125.18 468.55 Tm (equation )Tj /T1_1 1 Tf -0.035 Tc 7.555 0 0 9.6 163.39 468.55 Tm (aoZ)Tj 0 Tc 9.6 0 0 9.6 175.46 471.79 Tm (m)Tj 0.708 -0.338 Td (+)Tj 6.5001 0 0 6.5001 188.53 471.97 Tm (1 )Tj /T1_0 1 Tf 12.3 0 0 12.3 193.84 468.55 Tm (+ )Tj /T1_1 1 Tf 0.05 Tc 9.7854 0 0 9.6 202.44 468.55 Tm (altlm )Tj /T1_0 1 Tf 0 Tc 12.3 0 0 12.3 226.78 468.55 Tm (+ )Tj /T1_1 1 Tf 0.0285 Tc 9.6 0 0 9.6 235.74 468.55 Tm (a2tml )Tj /T1_2 1 Tf 0 Tc 9.3 0 0 9.3 272.42 468.55 Tm (0 )Tj -0.0111 Tc 0.834 0 Td (is )Tj 0.0445 Tc 1.005 0 Td (obtained. )Tj 0.044 Tc 4.553 0 Td (Letting )Tj /T1_3 1 Tf 0 Tc -33.602 -1.239 Td (l )Tj /T1_2 1 Tf 11.5 0 0 11.5 25.5 457.03 Tm (= )Tj -0.0012 Tc 9.3 0 0 9.3 36.4 457.03 Tm (1, )Tj 0.05 Tc 9.6991 0 0 9.3 47.32 457.03 Tm (the )Tj 9.453 0 0 9.3 63.8 457.03 Tm (equation )Tj /T1_1 1 Tf -0.035 Tc 8.6595 0 0 9.6 103.44 457.03 Tm (ao )Tj /T1_0 1 Tf 0 Tc 12.3 0 0 12.3 115 457.03 Tm (+ )Tj /T1_1 1 Tf 0.05 Tc 10.5312 0 0 9.6 124.31 457.03 Tm (alt )Tj /T1_0 1 Tf 0 Tc 12.3 0 0 12.3 139.3 457.03 Tm (+ )Tj /T1_1 1 Tf -0.0196 Tc 9.6 0 0 9.6 148.62 457.03 Tm (a2tm )Tj /T1_2 1 Tf 0 Tc 11.5 0 0 11.5 171.3 457.03 Tm (= )Tj 9.3 0 0 9.3 181.34 457.03 Tm (0 )Tj -0.035 Tc 9.0754 0 0 9.3 189.47 457.03 Tm (is )Tj 0.0445 Tc 9.3 0 0 9.3 199.17 457.03 Tm (obtained. )Tj 0.003 Tc 4.675 0 Td (So, )Tj 0.0461 Tc 1.789 0 Td (again, )Tj 0.0327 Tc 3.117 0 Td (in )Tj -0.0226 Tc 1.189 0 Td ("\(', )Tj 0.0387 Tc 1.527 0 Td (there )Tj 0.0347 Tc 2.567 0 Td (are )Tj 0.05 Tc 9.9612 0 0 9.3 353.06 457.03 Tm (at )Tj 9.7389 0 0 9.3 19.42 445.69 Tm (most )Tj 0 Tc 9.3 0 0 9.3 43.79 445.69 Tm (5 )Tj 0.0342 Tc 0.813 0 Td (solutions. )Tj 0.05 Tc 9.5709 0 0 9.3 30.75 433.99 Tm (We )Tj 0.0213 Tc 9.3 0 0 9.3 48.23 433.99 Tm (now )Tj 0.0131 Tc 2.14 0 Td (check )Tj 0.05 Tc 10.2879 0 0 9.3 94.11 433.99 Tm (that )Tj -0.0096 Tc 9.3 0 0 9.3 115.01 433.99 Tm (no )Tj 0.0435 Tc 1.392 0 Td (three )Tj 0.0246 Tc 2.567 0 Td (chords )Tj -0.0167 Tc 3.195 0 Td (lie )Tj 0.05 Tc 9.3236 0 0 9.3 194.14 433.99 Tm (in )Tj 0 Tc 9.3 0 0 9.3 205.47 433.99 Tm (a )Tj 0.0241 Tc 0.843 0 Td (pencil. )Tj /T1_0 1 Tf 0.05 Tc 13.439 0 0 9.1 30.59 422.11 Tm (If )Tj /T1_2 1 Tf 0 Tc 9.3 0 0 9.3 42.39 422.11 Tm (a )Tj 0.047 Tc 0.94 0 Td (plane )Tj 0.05 Tc 9.5989 0 0 9.3 77.49 422.11 Tm (of )Tj /T1_1 1 Tf 0.0478 Tc 9.7 0 0 9.7 89.89 422.11 Tm (PG\(3, )Tj -0.035 Tc 8.9618 0 0 9.6 117.49 422.11 Tm (q\) )Tj /T1_2 1 Tf 0.0333 Tc 9.3 0 0 9.3 129.87 422.11 Tm (contains )Tj 0.0454 Tc 4.044 0 Td (exactly )Tj 0 Tc 3.635 0 Td (5 )Tj 0.05 Tc 9.322 0 0 9.3 210.07 422.11 Tm (points )Tj 9.5456 0 0 9.3 239.86 422.11 Tm (in )Tj /T1_1 1 Tf 9.9418 0 0 9.7 252.44 422.11 Tm (PG\(3, )Tj -0.0165 Tc 9.6 0 0 9.6 280.92 422.11 Tm (q2\), )Tj /T1_2 1 Tf 0.05 Tc 10.1984 0 0 9.3 300.68 422.11 Tm (at )Tj 0.0304 Tc 9.3 0 0 9.3 313.3 422.11 Tm (least )Tj 0.0145 Tc 2.418 0 Td (one )Tj 0.039 Tc 1.935 0 Td (of )Tj 0.05 Tc 10.2395 0 0 9.3 19.24 410.59 Tm (them )Tj -0.0305 Tc 9.3 0 0 9.3 45.1 410.59 Tm (is )Tj 0.0215 Tc 1.102 0 Td (defined )Tj 0.0213 Tc 3.581 0 Td (over )Tj -0.035 Tc 8.1611 0 0 9.3 109.47 410.59 Tm ("\(. )Tj /T1_0 1 Tf 0.05 Tc 12.7834 0 0 9.1 122.95 410.59 Tm (If )Tj /T1_2 1 Tf 0.0435 Tc 9.3 0 0 9.3 133.54 410.59 Tm (three )Tj 0.0197 Tc 2.625 0 Td (of )Tj 0.05 Tc 9.7359 0 0 9.3 169 410.59 Tm (them )Tj 9.3582 0 0 9.3 193.76 410.59 Tm (are )Tj 0.0247 Tc 9.3 0 0 9.3 209.97 410.59 Tm (defined )Tj 0.0342 Tc 3.619 0 Td (over )Tj -0.035 Tc 8.1749 0 0 9.3 264.83 410.59 Tm (,,\(, )Tj 0.05 Tc 9.5157 0 0 9.3 277.39 410.59 Tm (by )Tj 9.6991 0 0 9.3 291.4 410.59 Tm (the )Tj 0.0421 Tc 9.3 0 0 9.3 308.41 410.59 Tm (3-transitivity )Tj 0.05 Tc 9.3902 0 0 9.3 19.17 399.07 Tm (of )Tj 10.2456 0 0 9.3 30.39 399.07 Tm (the )Tj 0.0495 Tc 9.3 0 0 9.3 47.62 399.07 Tm (group )Tj 0.05 Tc 9.3902 0 0 9.3 74.97 399.07 Tm (of )Tj /T1_3 1 Tf -0.0342 Tc 9.8 0 0 9.8 85.6 399.07 Tm (C\(m\) )Tj /T1_2 1 Tf -0.035 Tc 8.4698 0 0 9.3 111.4 399.07 Tm ([5, )Tj -0.0055 Tc 9.3 0 0 9.3 124.03 399.07 Tm (p. )Tj -0.0273 Tc 1.368 0 Td (249], )Tj -0.035 Tc 8.9557 0 0 9.3 158.93 399.07 Tm (we )Tj 0.05 Tc 9.4547 0 0 9.3 172.89 399.07 Tm (can )Tj 0.0334 Tc 9.3 0 0 9.3 190.53 399.07 Tm (assume )Tj 0.05 Tc 10.2879 0 0 9.3 223.35 399.07 Tm (that )Tj 9.7319 0 0 9.3 244.24 399.07 Tm (this )Tj 9.5583 0 0 9.3 263.53 399.07 Tm (plane )Tj -0.0305 Tc 9.3 0 0 9.3 289.9 399.07 Tm (is )Tj 0.05 Tc 10.5242 0 0 9.7 299.5 399.07 Tm (Xl )Tj /T1_0 1 Tf 0 Tc 8.7 0 0 8.7 314.68 399.07 Tm (= )Tj /T1_3 1 Tf 9.8 0 0 9.8 324.82 399.07 Tm (X)Tj /T1_1 1 Tf 6.1 0 0 6.1 332.26 397.63 Tm (2)Tj 0.687 0.236 Td (\225 )Tj /T1_2 1 Tf 0.0393 Tc 9.3 0 0 9.3 343.18 399.07 Tm (This )Tj 0.05 Tc 9.3057 0 0 9.3 19.53 387.55 Tm (does )Tj 0.0488 Tc 9.3 0 0 9.3 41.67 387.55 Tm (contain )Tj 0.05 Tc 9.6991 0 0 9.3 74.86 387.55 Tm (the )Tj 0.0162 Tc 9.3 0 0 9.3 91.24 387.55 Tm (two )Tj 0.0474 Tc 1.9 0 Td (points )Tj /T1_1 1 Tf 0.0341 Tc 9.6 0 0 9.6 137.23 387.55 Tm (P\(w)Tj 0 Tc 1.751 0.375 Td (2)Tj 0.05 Tc 9.7605 0 0 9.6 158.98 387.55 Tm (,w,w, )Tj 9.9771 0 0 9.6 183.96 387.55 Tm (1\),P\(w,w)Tj 0 Tc 9.6 0 0 9.6 224.06 391.15 Tm (2)Tj 0.05 Tc 10.0226 0 0 9.6 228.82 387.55 Tm (,w)Tj 0 Tc 9.6 0 0 9.6 239 391.33 Tm (2)Tj 0.495 -0.394 Td (, )Tj /T1_2 1 Tf 0.0361 Tc 9.3 0 0 9.3 247.72 387.55 Tm (1\), )Tj 0.05 Tc 9.3532 0 0 9.3 261.89 387.55 Tm (where )Tj /T1_1 1 Tf 0 Tc 9.6 0 0 9.6 289.76 387.55 Tm (w)Tj 0.675 0.375 Td (2)Tj 0.05 Tc 11.7915 0 0 9.6 301.9 387.55 Tm (+w+l )Tj /T1_2 1 Tf 0 Tc 12.1 0 0 12.1 334.2 387.55 Tm (= )Tj -0.0316 Tc 9.3 0 0 9.3 343.7 387.55 Tm (0, )Tj 0.0327 Tc 1.086 0 Td (in )Tj /T1_1 1 Tf 0.05 Tc 10.0104 0 0 9.7 19.52 376.39 Tm (PG\(3, )Tj -0.035 Tc 9.0842 0 0 9.6 48.19 376.39 Tm (q2\) )Tj /T1_2 1 Tf 0.05 Tc 9.8728 0 0 9.3 63.73 376.39 Tm (but )Tj 0.0291 Tc 9.3 0 0 9.3 81.17 376.39 Tm (no )Tj 0.05 Tc 9.4364 0 0 9.3 94.48 376.39 Tm (three )Tj 9.3902 0 0 9.3 118.53 376.39 Tm (of )Tj 9.5625 0 0 9.3 129.4 376.39 Tm (the )Tj 0.0369 Tc 9.3 0 0 9.3 145.43 376.39 Tm (real )Tj 0.0323 Tc 1.927 0 Td (chords )Tj 0.05 Tc 9.6349 0 0 9.3 193.22 376.39 Tm (and )Tj 9.5625 0 0 9.3 211.66 376.39 Tm (the )Tj 9.4997 0 0 9.3 227.98 376.39 Tm (imaginary )Tj 9.3081 0 0 9.3 273.51 376.39 Tm (chord )Tj 0.0444 Tc 9.3 0 0 9.3 300.15 376.39 Tm (are )Tj 0.0298 Tc 1.665 0 Td (concurrent. )Tj 0.05 Tc 10.5234 0 0 9.3 30.89 364.69 Tm (If )Tj 9.5625 0 0 9.3 42.28 364.69 Tm (the )Tj 0.047 Tc 9.3 0 0 9.3 59.41 364.69 Tm (plane )Tj 0.0443 Tc 2.815 0 Td (contains )Tj 0.0242 Tc 4.123 0 Td (one )Tj 0.0404 Tc 1.966 0 Td (point )Tj 0.039 Tc 2.699 0 Td (of )Tj /T1_1 1 Tf 0.0432 Tc 9.7 0 0 9.7 178.99 364.69 Tm (PG\(3, )Tj /T1_3 1 Tf -0.035 Tc 9.1769 0 0 10 206.5 364.69 Tm (q\), )Tj /T1_2 1 Tf 0.05 Tc 9.7524 0 0 9.3 221.48 364.69 Tm (and )Tj 9.8357 0 0 9.3 241.18 364.69 Tm (the )Tj 9.7293 0 0 9.3 258.82 364.69 Tm (tangent )Tj 9.6041 0 0 9.3 295.18 364.69 Tm (to )Tj /T1_3 1 Tf -0.035 Tc 9.5537 0 0 9.8 307.18 364.69 Tm (C\(m\) )Tj /T1_2 1 Tf 0.05 Tc 9.9612 0 0 9.3 332.36 364.69 Tm (at )Tj 9.9596 0 0 9.3 344.5 364.69 Tm (that )Tj 9.6189 0 0 9.3 19.45 353.17 Tm (point, )Tj 9.7342 0 0 9.3 47.32 353.17 Tm (then )Tj 9.5625 0 0 9.3 68.56 353.17 Tm (the )Tj 0.047 Tc 9.3 0 0 9.3 84.43 353.17 Tm (plane )Tj 0.0388 Tc 2.68 0 Td (contains )Tj 0.05 Tc 9.7241 0 0 9.3 145.88 353.17 Tm (at )Tj 0.0441 Tc 9.3 0 0 9.3 156.58 353.17 Tm (most )Tj 0.0242 Tc 2.392 0 Td (one )Tj 0.05 Tc 9.6773 0 0 9.3 195.56 353.17 Tm (extra )Tj 9.5413 0 0 9.3 219.43 353.17 Tm (point )Tj 9.3902 0 0 9.3 243.99 353.17 Tm (of )Tj /T1_3 1 Tf -0.0122 Tc 9.8 0 0 9.8 254.26 353.17 Tm (C\(m\). )Tj /T1_2 1 Tf 0.0271 Tc 9.3 0 0 9.3 283.46 353.17 Tm (For, )Tj -0.035 Tc 9.2755 0 0 9.3 302.75 353.17 Tm (we )Tj 0.0428 Tc 9.3 0 0 9.3 316.17 353.17 Tm (can )Tj 0.0256 Tc 1.761 0 Td (assume )Tj 0.05 Tc 10.7257 0 0 9.3 19.59 341.65 Tm (that )Tj 9.3924 0 0 9.3 40.84 341.65 Tm (this )Tj 9.3809 0 0 9.3 59.23 341.65 Tm (point )Tj -0.0305 Tc 9.3 0 0 9.3 83.8 341.65 Tm (is )Tj 0 Tc 1.033 0 Td (U)Tj 6.6 0 0 6.6 101.8 340.21 Tm (3)Tj 0.706 0.218 Td (, )Tj 0.05 Tc 9.3999 0 0 9.3 111.68 341.65 Tm (and )Tj 9.5625 0 0 9.3 129.58 341.65 Tm (the )Tj 0.0295 Tc 9.3 0 0 9.3 145.45 341.65 Tm (planes )Tj 0.05 Tc 9.5081 0 0 9.3 173.86 341.65 Tm (through )Tj 9.5625 0 0 9.3 209.32 341.65 Tm (the )Tj 9.7293 0 0 9.3 225.34 341.65 Tm (tangent )Tj 0.0351 Tc 9.3 0 0 9.3 260.38 341.65 Tm (line )Tj /T1_1 1 Tf -0.0349 Tc 10 0 0 10 279.03 341.65 Tm (Xo )Tj /T1_0 1 Tf 0 Tc 8.1 0 0 8.1 293.81 341.65 Tm (= )Tj /T1_2 1 Tf 0.05 Tc 10.5242 0 0 9.7 303.82 341.65 Tm (Xl )Tj /T1_0 1 Tf 0 Tc 8.1 0 0 8.1 318.65 341.65 Tm (= )Tj /T1_2 1 Tf 9.3 0 0 9.3 328.4 341.65 Tm (0 )Tj 0.05 Tc 9.3858 0 0 9.3 335.5 341.65 Tm (to )Tj 0.0359 Tc 9.3 0 0 9.3 346.66 341.65 Tm (this )Tj 0.05 Tc 9.862 0 0 9.3 19.64 330.13 Tm (point )Tj 9.3356 0 0 9.3 45.63 330.13 Tm (contain )Tj 10.4356 0 0 9.3 79.45 330.13 Tm (at )Tj 9.3941 0 0 9.3 91.6 330.13 Tm (most )Tj 0.0145 Tc 9.3 0 0 9.3 115.11 330.13 Tm (one )Tj 0.05 Tc 9.3524 0 0 9.3 132.57 330.13 Tm (other )Tj 0.0452 Tc 9.3 0 0 9.3 157.33 330.13 Tm (point )Tj 0.039 Tc 2.66 0 Td (of )Tj /T1_0 1 Tf 0 Tc 9.2 0 0 9.2 192.65 330.13 Tm (C )Tj /T1_3 1 Tf -0.0283 Tc 9.8 0 0 9.8 199.02 330.13 Tm (\(m\). )Tj /T1_0 1 Tf 0.05 Tc 12.4556 0 0 9.1 221.24 330.13 Tm (If )Tj /T1_2 1 Tf 9.6991 0 0 9.3 231.46 330.13 Tm (the )Tj 9.4818 0 0 9.3 248.23 330.13 Tm (plane )Tj 0.0499 Tc 9.3 0 0 9.3 274.59 330.13 Tm (contains )Tj 0.0145 Tc 4.084 0 Td (one )Tj 0.0404 Tc 1.849 0 Td (point )Tj 0.039 Tc 2.602 0 Td (of )Tj /T1_1 1 Tf 0.05 Tc 9.9418 0 0 9.7 19.7 318.61 Tm (PG\(3, )Tj /T1_3 1 Tf -0.035 Tc 9.3438 0 0 9.8 48.28 318.61 Tm (q\), )Tj /T1_2 1 Tf 0.05 Tc 9.5174 0 0 9.3 62.72 318.61 Tm (and )Tj 0.0355 Tc 9.3 0 0 9.3 81.34 318.61 Tm (two )Tj 0.0442 Tc 1.977 0 Td (pairs )Tj 0.05 Tc 9.5989 0 0 9.3 123.03 318.61 Tm (of )Tj 0.0268 Tc 9.3 0 0 9.3 134.19 318.61 Tm (complex )Tj 0.0446 Tc 3.968 0 Td (conjugate )Tj 0.05 Tc 9.322 0 0 9.3 214.21 318.61 Tm (points )Tj 9.3236 0 0 9.3 243.28 318.61 Tm (in )Tj /T1_1 1 Tf 9.8733 0 0 9.7 255.14 318.61 Tm (PG\(3, )Tj -0.0228 Tc 9.6 0 0 9.6 283.44 318.61 Tm (q2\), )Tj /T1_2 1 Tf 0.05 Tc 9.5414 0 0 9.3 302.2 318.61 Tm (then )Tj 0.0492 Tc 9.3 0 0 9.3 323.8 318.61 Tm (the )Tj 0.0325 Tc 1.726 0 Td (plane )Tj 0.05 Tc 9.5353 0 0 9.3 19.53 307.09 Tm (only )Tj 0.0416 Tc 9.3 0 0 9.3 41.49 307.09 Tm (contains )Tj 0.0355 Tc 4.014 0 Td (two )Tj 0.0474 Tc 1.987 0 Td (imaginary )Tj 0.0143 Tc 4.78 0 Td (chords. )Tj /T1_0 1 Tf 0.05 Tc 13.7668 0 0 9.1 30.94 295.39 Tm (If )Tj /T1_2 1 Tf 9.5625 0 0 9.3 43 295.39 Tm (the )Tj 0.0421 Tc 9.3 0 0 9.3 60.67 295.39 Tm (plane )Tj 0.0443 Tc 2.854 0 Td (contains )Tj 0.0389 Tc 4.16 0 Td (exactly )Tj -0.0004 Tc 3.619 0 Td (four )Tj 0.0474 Tc 2.218 0 Td (points )Tj 0.0197 Tc 3.202 0 Td (of )Tj /T1_3 1 Tf -0.0342 Tc 9.8 0 0 9.8 221.5 295.39 Tm (C\(m\) )Tj /T1_2 1 Tf 0.05 Tc 9.7676 0 0 9.3 247.78 295.39 Tm (in )Tj /T1_1 1 Tf 9.8733 0 0 9.7 260.9 295.39 Tm (PG\(3, )Tj -0.029 Tc 9.6 0 0 9.6 289.2 295.39 Tm (q2\), )Tj /T1_2 1 Tf 0.05 Tc 9.5414 0 0 9.3 309.04 295.39 Tm (then )Tj 0.0255 Tc 9.3 0 0 9.3 331.3 295.39 Tm (if )Tj 0.0247 Tc 1.052 0 Td (these )Tj 0.0447 Tc -34.557 -1.239 Td (four )Tj 0.05 Tc 9.322 0 0 9.3 41.59 283.87 Tm (points )Tj 0.0376 Tc 9.3 0 0 9.3 71.01 283.87 Tm (consist )Tj 0.05 Tc 9.3902 0 0 9.3 103.41 283.87 Tm (of )Tj 0.0065 Tc 9.3 0 0 9.3 115.18 283.87 Tm (two )Tj 0.0345 Tc 1.997 0 Td (pairs )Tj 0.0197 Tc 2.563 0 Td (of )Tj 0.0332 Tc 1.219 0 Td (complex )Tj 0.047 Tc 4.084 0 Td (conjugate )Tj 0.05 Tc 9.4103 0 0 9.3 251.11 283.87 Tm (points, )Tj 9.4364 0 0 9.3 284.38 283.87 Tm (there )Tj 0.0251 Tc 9.3 0 0 9.3 309.87 283.87 Tm (are )Tj 0.008 Tc 1.761 0 Td (only )Tj 0.0065 Tc 2.253 0 Td (two )Tj 0.05 Tc 9.5403 0 0 9.3 19.72 272.35 Tm (imaginary )Tj 0.0362 Tc 9.3 0 0 9.3 65.61 272.35 Tm (chords )Tj 0.05 Tc 9.3236 0 0 9.3 95.68 272.35 Tm (in )Tj 9.5625 0 0 9.3 106.72 272.35 Tm (the )Tj 0.034 Tc 9.3 0 0 9.3 122.77 272.35 Tm (plane, )Tj 0.05 Tc 9.5174 0 0 9.3 150.56 272.35 Tm (and )Tj 0.0236 Tc 9.3 0 0 9.3 168.53 272.35 Tm (similarly, )Tj 0.0255 Tc 4.38 0 Td (if )Tj 0.05 Tc 9.8357 0 0 9.3 217.78 272.35 Tm (the )Tj 9.4818 0 0 9.3 234.37 272.35 Tm (plane )Tj 9.4454 0 0 9.3 260.19 272.35 Tm (contains )Tj 0.0162 Tc 9.3 0 0 9.3 298.6 272.35 Tm (two )Tj 0.0305 Tc 1.898 0 Td (real )Tj 0.0301 Tc 1.918 0 Td (points, )Tj 0.05 Tc 10.1049 0 0 9.3 19.7 261.01 Tm (and )Tj 0.0259 Tc 9.3 0 0 9.3 39.04 261.01 Tm (two )Tj 0.0494 Tc 1.947 0 Td (conjugate )Tj 0.0474 Tc 4.666 0 Td (imaginary )Tj 0.0333 Tc 4.752 0 Td (points, )Tj 0.05 Tc 9.3543 0 0 9.3 175.3 261.01 Tm (there )Tj 0.0347 Tc 9.3 0 0 9.3 199.71 261.01 Tm (are )Tj 0.05 Tc 9.4135 0 0 9.3 215.18 261.01 Tm (again )Tj 9.3465 0 0 9.3 240.75 261.01 Tm (only )Tj 0.0452 Tc 9.3 0 0 9.3 262.24 261.01 Tm (two )Tj 0.0362 Tc 1.967 0 Td (chords )Tj 0.0327 Tc 3.233 0 Td (in )Tj 0.0492 Tc 1.168 0 Td (the )Tj 0.0224 Tc 1.706 0 Td (plane. )Tj 0.05 Tc 10.7801 0 0 9.3 31.06 249.49 Tm (If )Tj 0 Tc 9.3 0 0 9.3 42.93 249.49 Tm (a )Tj 0.0421 Tc 0.94 0 Td (plane )Tj 0.0471 Tc 2.834 0 Td (contains )Tj 0.0421 Tc 4.16 0 Td (exactly )Tj 0.05 Tc 9.3543 0 0 9.3 149.92 249.49 Tm (three )Tj 0.0398 Tc 9.3 0 0 9.3 174.97 249.49 Tm (points, )Tj 0.0145 Tc 3.492 0 Td (one )Tj 0.05 Tc 9.3902 0 0 9.3 225.81 249.49 Tm (of )Tj 9.9877 0 0 9.3 237.76 249.49 Tm (them )Tj -0.0305 Tc 9.3 0 0 9.3 263.8 249.49 Tm (is )Tj 0.0329 Tc 1.169 0 Td (real. )Tj /T1_0 1 Tf 0.05 Tc 12.1279 0 0 9.1 299.91 249.49 Tm (If )Tj /T1_2 1 Tf 0.0199 Tc 9.3 0 0 9.3 310.77 249.49 Tm (all )Tj 0.0387 Tc 1.498 0 Td (three )Tj 0.0251 Tc 2.663 0 Td (are )Tj 0.05 Tc 9.3437 0 0 9.3 19.61 237.97 Tm (real, )Tj 9.4451 0 0 9.3 42.82 237.97 Tm (they )Tj 0.0234 Tc 9.3 0 0 9.3 64.88 237.97 Tm (form )Tj 0 Tc 2.478 0 Td (a )Tj 0.0207 Tc 0.946 0 Td (3-cap, )Tj 0.05 Tc 9.5174 0 0 9.3 125.36 237.97 Tm (and )Tj 0.0061 Tc 9.3 0 0 9.3 144.28 237.97 Tm (if )Tj 0.0274 Tc 0.967 0 Td (only )Tj 0.0242 Tc 2.284 0 Td (one )Tj -0.0305 Tc 1.937 0 Td (is )Tj 0.0184 Tc 1.091 0 Td (real, )Tj 0.05 Tc 9.7342 0 0 9.3 224.62 237.97 Tm (then )Tj 9.6187 0 0 9.3 247.12 237.97 Tm (this )Tj 9.5583 0 0 9.3 266.77 237.97 Tm (plane )Tj 0.0338 Tc 9.3 0 0 9.3 293.49 237.97 Tm (only )Tj 0.0305 Tc 2.303 0 Td (contains )Tj 0.05 Tc 9.5322 0 0 9.3 351.98 237.97 Tm (an )Tj 9.5809 0 0 9.3 19.54 226.45 Tm (imaginary )Tj 0.0291 Tc 9.3 0 0 9.3 65.43 226.45 Tm (chord. )Tj 0.05 Tc 9.8034 0 0 9.3 31.06 214.75 Tm (This )Tj 0.0152 Tc 9.3 0 0 9.3 53.33 214.75 Tm (shows )Tj 0.05 Tc 10.5068 0 0 9.3 80.97 214.75 Tm (that )Tj 0.0291 Tc 9.3 0 0 9.3 102.05 214.75 Tm (no )Tj 0.0421 Tc 1.415 0 Td (plane )Tj 0.0333 Tc 2.718 0 Td (contains )Tj 0.05 Tc 9.3543 0 0 9.3 177.1 214.75 Tm (three )Tj 9.3026 0 0 9.3 201.33 214.75 Tm (concurrent )Tj 0.0401 Tc 9.3 0 0 9.3 249.03 214.75 Tm (chords. )Tj -0.015 Tc 3.766 0 Td (So )Tj 0.05 Tc 9.5625 0 0 9.3 297.34 214.75 Tm (the )Tj 0.0168 Tc 9.3 0 0 9.3 313.65 214.75 Tm (chords )Tj 0.0169 Tc 3.115 0 Td (form )Tj 0 Tc -34.721 -1.239 Td (a )Tj /T1_1 1 Tf -0.035 Tc 9.1765 0 0 9.3 28.08 203.23 Tm (\(q2 )Tj /T1_0 1 Tf 0 Tc 12.3 0 0 12.3 43.36 203.23 Tm (+ )Tj /T1_1 1 Tf 9.3 0 0 9.3 52.68 203.23 Tm (q )Tj /T1_0 1 Tf 12.3 0 0 12.3 59.56 203.23 Tm (+ )Tj /T1_2 1 Tf 0.05 Tc 9.369 0 0 9.3 69.6 203.23 Tm (I\)-cap. )Tj 9.7092 0 0 9.3 31.1 191.53 Tm (From )Tj 9.6991 0 0 9.3 57.04 191.53 Tm (the )Tj 0.0315 Tc 9.3 0 0 9.3 73.61 191.53 Tm (null )Tj 0.05 Tc 9.3446 0 0 9.3 92.53 191.53 Tm (polarity )Tj /T1_3 1 Tf -0.022 Tc 9.4 0 0 9.4 127.71 191.53 Tm (U, )Tj /T1_2 1 Tf 0.0028 Tc 9.3 0 0 9.3 141.03 191.53 Tm (also )Tj 0.05 Tc 9.4259 0 0 9.3 159.82 191.53 Tm (the )Tj 0.0249 Tc 9.3 0 0 9.3 175.95 191.53 Tm (axes )Tj 0.0058 Tc 2.245 0 Td (define )Tj 0 Tc 2.942 0 Td (a )Tj /T1_1 1 Tf -0.035 Tc 8.6118 0 0 9.6 232.93 191.53 Tm (\(q2 )Tj /T1_0 1 Tf 0 Tc 12.3 0 0 12.3 247.3 191.53 Tm (+ )Tj /T1_1 1 Tf 9.6 0 0 9.6 257.16 191.53 Tm (q )Tj /T1_0 1 Tf 12.3 0 0 12.3 264.04 191.53 Tm (+ )Tj /T1_2 1 Tf 0.05 Tc 9.6173 0 0 9.3 274.43 191.53 Tm (I\)-cap )Tj 0.0462 Tc 9.3 0 0 9.3 303.39 191.53 Tm (on )Tj -0.035 Tc 7.3923 0 0 7.6 316.19 191.53 Tm (1-{5. )Tj 0.05 Tc 9.3284 0 0 9.3 31.22 179.83 Tm (Consider )Tj 0.0116 Tc 9.3 0 0 9.3 70.91 179.83 Tm (now )Tj 0.05 Tc 9.6991 0 0 9.3 90.16 179.83 Tm (the )Tj 0.0323 Tc 9.3 0 0 9.3 105.75 179.83 Tm (chords )Tj 0.0485 Tc 3.155 0 Td (and )Tj 0.05 Tc 9.4259 0 0 9.3 152.26 179.83 Tm (the )Tj 0.0143 Tc 9.3 0 0 9.3 167.67 179.83 Tm (axes. )Tj 0.0379 Tc 2.604 0 Td (Suppose )Tj 0.05 Tc 9.6378 0 0 9.3 228.58 179.83 Tm (they )Tj 9.5101 0 0 9.3 249.21 179.83 Tm (do )Tj 9.8275 0 0 9.3 262.25 179.83 Tm (not )Tj 0.0174 Tc 9.3 0 0 9.3 278.73 179.83 Tm (define )Tj 0 Tc 2.903 0 Td (a )Tj /T1_1 1 Tf 0.0349 Tc 9.6 0 0 9.6 313.37 179.83 Tm (\(2q2+q+l\)\255)Tj /T1_2 1 Tf 0.05 Tc 9.3775 0 0 9.3 19.35 168.49 Tm (cap. )Tj 0.0346 Tc 9.3 0 0 9.3 44.62 168.49 Tm (Assume )Tj 0.05 Tc 10.3974 0 0 9.3 80.97 168.49 Tm (that )Tj 0.0484 Tc 9.3 0 0 9.3 103.12 168.49 Tm (three )Tj 0.0397 Tc 2.694 0 Td (points )Tj 0.0347 Tc 3.163 0 Td (are )Tj 0.0304 Tc 1.761 0 Td (collinear )Tj 0.0344 Tc 4.209 0 Td (where )Tj 0.0452 Tc 3.096 0 Td (two )Tj 0.05 Tc 9.3863 0 0 9.3 261.27 168.49 Tm (correspond )Tj 9.3858 0 0 9.3 311.74 168.49 Tm (to )Tj 0.0207 Tc 9.3 0 0 9.3 324.09 168.49 Tm (chords )Tj 0.039 Tc 3.232 0 Td (of )Tj /T1_3 1 Tf -0.003 Tc 9.8 0 0 9.8 19.18 157.15 Tm (C\(m\). )Tj /T1_0 1 Tf 0.05 Tc 13.439 0 0 9.1 30.77 145.27 Tm (If )Tj /T1_2 1 Tf 9.5625 0 0 9.3 41.56 145.27 Tm (the )Tj 0.0162 Tc 9.3 0 0 9.3 57.94 145.27 Tm (two )Tj 0.04 Tc 1.928 0 Td (chords )Tj 0.0347 Tc 3.29 0 Td (are )Tj 0.0434 Tc 1.692 0 Td (real )Tj 0.0143 Tc 2.004 0 Td (chords, )Tj 0.0383 Tc 3.441 0 Td (suppose )Tj 0.05 Tc 9.4451 0 0 9.3 208.78 145.27 Tm (they )Tj 9.3582 0 0 9.3 230.12 145.27 Tm (are )Tj 0 Tc 9.3 0 0 9.3 246.41 145.27 Tm (U )Tj /T1_0 1 Tf 6.2 0 0 6.2 255.17 145.27 Tm (0 )Tj /T1_2 1 Tf 9.3 0 0 9.3 259.55 145.27 Tm (U )Tj /T1_0 1 Tf 6.2 0 0 6.2 267.95 145.27 Tm (3 )Tj /T1_2 1 Tf 0.05 Tc 9.7524 0 0 9.3 276.02 145.27 Tm (and )Tj 0 Tc 9.3 0 0 9.3 294.83 145.27 Tm (U )Tj /T1_0 1 Tf 6.2 0 0 6.2 303.23 145.27 Tm (3 )Tj /T1_2 1 Tf 0.05 Tc 9.559 0 0 9.3 307.61 145.27 Tm (U. )Tj 9.349 0 0 9.3 322.66 145.27 Tm (The )Tj 9.4117 0 0 9.3 341.8 145.27 Tm (third )Tj 9.862 0 0 9.3 19.46 133.75 Tm (point )Tj 9.6378 0 0 9.3 45.34 133.75 Tm (then )Tj 9.3941 0 0 9.3 67.12 133.75 Tm (must )Tj 0.0443 Tc 9.3 0 0 9.3 90.81 133.75 Tm (correspond )Tj 0.0383 Tc 5.233 0 Td (to )Tj 0.05 Tc 9.7155 0 0 9.3 150.56 133.75 Tm (an )Tj 0.0222 Tc 9.3 0 0 9.3 163.53 133.75 Tm (axis )Tj 0.0373 Tc 2.043 0 Td (passing )Tj 0.05 Tc 9.6137 0 0 9.3 215.8 133.75 Tm (through )Tj 0 Tc 9.3 0 0 9.3 252.53 133.75 Tm (U )Tj 0.05 Tc 7.5482 0 0 6.9001 261.27 133.75 Tm (3. )Tj 9.8989 0 0 9.3 272.62 133.75 Tm (The )Tj 0.0338 Tc 9.3 0 0 9.3 292.59 133.75 Tm (only )Tj 0.0157 Tc 2.245 0 Td (axis )Tj 0.0244 Tc 2.024 0 Td (passing )Tj 0.05 Tc 9.825 0 0 9.3 19.42 122.22 Tm (through )Tj 0.0488 Tc 9.3 0 0 9.3 56.32 122.22 Tm (this )Tj 0.05 Tc 9.5413 0 0 9.3 74.35 122.22 Tm (point )Tj -0.0305 Tc 9.3 0 0 9.3 99.46 122.22 Tm (is )Tj 0.0398 Tc 1.006 0 Td (its )Tj 0.05 Tc 9.3957 0 0 9.3 121.66 122.22 Tm (tangent )Tj 9.6041 0 0 9.3 155.68 122.22 Tm (to )Tj /T1_0 1 Tf 0 Tc 9.2 0 0 9.2 166.55 122.22 Tm (C )Tj /T1_3 1 Tf -0.0161 Tc 9.8 0 0 9.8 172.74 122.22 Tm (\(m\), )Tj /T1_2 1 Tf 0.05 Tc 10.0045 0 0 9.3 193.51 122.22 Tm (but )Tj 9.3924 0 0 9.3 210.76 122.22 Tm (this )Tj 0.0375 Tc 9.3 0 0 9.3 229.05 122.22 Tm (does )Tj 0.05 Tc 9.8275 0 0 9.3 250.73 122.22 Tm (not )Tj 0.022 Tc 9.3 0 0 9.3 267.76 122.22 Tm (lie )Tj 0.05 Tc 9.5456 0 0 9.3 280.54 122.22 Tm (in )Tj 0 Tc 9.3 0 0 9.3 291.51 122.22 Tm (a )Tj 0.0325 Tc 0.824 0 Td (pencil )Tj 0.0417 Tc 2.94 0 Td (with )Tj 0.0065 Tc 2.244 0 Td (two )Tj 0.05 Tc 9.6251 0 0 9.3 19.61 110.71 Tm (real )Tj 0.0272 Tc 9.3 0 0 9.3 38.97 110.71 Tm (chords. )Tj 0.05 Tc 10.7801 0 0 9.3 31.06 98.82 Tm (If )Tj 9.5625 0 0 9.3 42.46 98.82 Tm (the )Tj 0.0162 Tc 9.3 0 0 9.3 59.74 98.82 Tm (two )Tj 0.04 Tc 2.005 0 Td (chords )Tj 0.0347 Tc 3.368 0 Td (are )Tj 0.0242 Tc 1.781 0 Td (one )Tj 0.0305 Tc 1.963 0 Td (real )Tj 0.0312 Tc 2.043 0 Td (chord )Tj 0.05 Tc 9.7524 0 0 9.3 190.34 98.82 Tm (and )Tj 0 Tc 9.3 0 0 9.3 209.79 98.82 Tm (a )Tj 0.05 Tc 9.5148 0 0 9.3 218.32 98.82 Tm (tangent, )Tj 9.3183 0 0 9.3 257.5 98.82 Tm (let )Tj 9.9723 0 0 9.3 272.5 98.82 Tm (the )Tj 9.4513 0 0 9.3 290.14 98.82 Tm (tangent )Tj 0.015 Tc 9.3 0 0 9.3 325.45 98.82 Tm (be )Tj /T1_1 1 Tf -0.035 Tc 9.6831 0 0 10 339.14 98.82 Tm (Xo )Tj 0 Tc 11.4 0 0 11.4 354.63 98.82 Tm (= )Tj /T1_3 1 Tf 9 0 0 9 19.71 87.31 Tm (X )Tj /T1_2 1 Tf 6.6 0 0 6.6 28.04 87.31 Tm (I )Tj /T1_0 1 Tf 8.1 0 0 8.1 36.23 87.31 Tm (= )Tj /T1_2 1 Tf 9.3 0 0 9.3 47.42 87.31 Tm (0 )Tj 0.05 Tc 9.5174 0 0 9.3 56.24 87.31 Tm (and )Tj 9.5625 0 0 9.3 75.4 87.31 Tm (the )Tj 0.0457 Tc 9.3 0 0 9.3 92.43 87.31 Tm (chord )Tj 0.05 Tc 9.335 0 0 9.3 119.53 87.31 Tm (be )Tj 0 Tc 9.3 0 0 9.3 133.19 87.31 Tm (U )Tj 6.6 0 0 6.6 141.59 87.31 Tm (0 )Tj 9.3 0 0 9.3 145.79 87.31 Tm (U )Tj 0.05 Tc 7.5482 0 0 6.6 153.81 87.31 Tm (3. )Tj 0.0279 Tc 9.3 0 0 9.3 166.66 87.31 Tm (Again, )Tj 0.0484 Tc 3.329 0 Td (there )Tj 0.0082 Tc 2.665 0 Td (is )Tj 0.0485 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q9Nm-a #GԮ1Ҵ{ ݊q Ƭ0HFI~."* ! &a0L9C#q3X"El X"?":!bVmz"hoFY pҊtI;&Qdc.UHnQҔ9(r&։DDE$6&JIJ@TF@T]G *PVR (EK JdEr 29Qu:@T]G *. *R1 r莢9RJ9QtGQF@T]F@TBc-P$GD"0b(%Lp$8b22Dqa !A6Z{bGRxqƓe(Б]K( WGP{QZª":vBGUVC:0X[H88i;F%.# k + GcIXM ":{k :#& oMQ,a$Z˰aXRʙPb"JQ(QQ)Q(Q(Q(VPA(Q (JDrB@TG *P endstream endobj 213 0 obj <> endobj 214 0 obj <> endobj 215 0 obj <> endobj 216 0 obj <> endobj 205 0 obj <>stream q 403.1999969 0 0 336.9600067 0 239.0399933 cm /Im0 Do Q q 403.1999969 0 0 239.0399933 0 0 cm /Im1 Do Q BT /T1_0 1 Tf 0.0343 Tc 3 Tr 9.5 0 0 9.5 27.11 546.31 Tm (In )Tj 0.004 Tc 1.266 0 Td (fact, )Tj 0.05 Tc 9.6005 0 0 9.5 60.46 546.31 Tm (there )Tj 0.0323 Tc 9.5 0 0 9.5 85.42 546.31 Tm (is )Tj 0 Tc 1.078 0 Td (a )Tj 0.05 Tc 9.9685 0 0 9.5 103.67 546.31 Tm (natural )Tj 0.0381 Tc 9.5 0 0 9.5 137.71 546.31 Tm (bijection )Tj 0.0217 Tc 4.149 0 Td (between )Tj 0.0135 Tc 3.835 0 Td (any )Tj 0.0096 Tc 1.865 0 Td (two )Tj 0.0021 Tc 1.944 0 Td (of )Tj 0.0449 Tc 1.125 0 Td (the )Tj 0.0256 Tc 1.735 0 Td (four 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Tm (C\(m\) )Tj /T1_2 1 Tf 0 Tc 8.1 0 0 8.1 134.15 401.77 Tm (= )Tj /T1_1 1 Tf 0.05 Tc 10.1958 0 0 10.1 144.51 401.77 Tm ({pet\) )Tj /T1_2 1 Tf 0 Tc 8.1 0 0 8.1 170.33 401.77 Tm (= )Tj /T1_1 1 Tf 0.05 Tc 10.1482 0 0 10.1 180.62 401.77 Tm (P\(t)Tj 0 Tc 10.1 0 0 10.1 194.89 405.55 Tm (m)Tj 0.05 Tc 11.6656 0 0 10.1 201.46 401.77 Tm (+\\ )Tj 0 Tc 10.1 0 0 10.1 215.34 401.77 Tm (t)Tj 0.363 0.392 Td (m)Tj 0.757 -0.392 Td (, )Tj -0.004 Tc 0.341 0 Td (t, )Tj /T1_2 1 Tf -0.035 Tc 9.1603 0 0 10.2 238.21 401.77 Tm (1\) )Tj 0 Tc 10.2 0 0 10.2 249.57 401.77 Tm (: )Tj 8.6 0 0 8.6 254.3 401.77 Tm (t )Tj 7.8001 0 0 7.8001 260.82 401.77 Tm (E )Tj /T1_0 1 Tf 0.0091 Tc 9.6 0 0 9.6 268.99 401.77 Tm ('\)'+}, )Tj 0.0161 Tc 9.5 0 0 9.5 26.99 381.07 Tm (where )Tj 0 Tc 9.3 0 0 9.3 54.52 381.07 Tm (m )Tj 11.6 0 0 11.6 65.64 381.07 Tm (= )Tj /T1_3 1 Tf 9.3 0 0 9.3 75.8 381.07 Tm (2)Tj /T1_1 1 Tf 6.9001 0 0 6.9001 80.79 384.67 Tm (n)Tj 0.87 -0.522 Td (, )Tj /T1_3 1 Tf -0.0293 Tc 9.6 0 0 9.6 91.38 381.07 Tm (\(n, 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/T1_0 1 Tf 9.569 0 0 9.5 38.26 295.39 Tm (The )Tj 0.0231 Tc 9.5 0 0 9.5 57.86 295.39 Tm (axis )Tj 0.0202 Tc 6.3001 0 0 6.3001 77.69 295.39 Tm (7r )Tj 0 Tc 1.057 0 Td (\( )Tj /T1_3 1 Tf -0.035 Tc 9.4534 0 0 9.9 87.85 295.39 Tm (u\) )Tj /T1_2 1 Tf 0 Tc 10.8 0 0 10.8 99.15 295.39 Tm (n )Tj /T1_0 1 Tf 0.0487 Tc 6.3001 0 0 6.3001 107.57 295.39 Tm (7r )Tj 0 Tc 1.086 0 Td (\( )Tj /T1_3 1 Tf -0.035 Tc 9.5446 0 0 9.9 117.32 295.39 Tm (v\) )Tj /T1_0 1 Tf -0.0246 Tc 9.5 0 0 9.5 129.52 295.39 Tm (is )Tj /T1_1 1 Tf 0.05 Tc 11.2837 0 0 10.1 309.72 327.61 Tm (rm+sm )Tj /T1_2 1 Tf 18.8347 0 0 10 309.43 319.87 Tm (---,1\). )Tj /T1_1 1 Tf 13.0002 0 0 10.1 317.27 313.03 Tm (r+s )Tj /T1_0 1 Tf 9.569 0 0 9.5 38.44 243.37 Tm (The )Tj 9.8961 0 0 9.5 58.48 243.37 Tm (tangent )Tj 10.4356 0 0 9.5 94.93 243.37 Tm (at )Tj /T1_1 1 Tf 10.2077 0 0 10.1 107.62 243.37 Tm (pet\) )Tj /T1_0 1 Tf -0.0246 Tc 9.5 0 0 9.5 129.88 243.37 Tm (is )Tj /T1_1 1 Tf -0.0143 Tc 10.1 0 0 10.1 140.29 243.37 Tm (let\) )Tj /T1_0 1 Tf 0 Tc 11.6 0 0 11.6 158.16 243.37 Tm (= )Tj /T1_1 1 Tf -0.0222 Tc 10.1 0 0 10.1 169.09 243.37 Tm (let, )Tj -0.0336 Tc 1.425 0 Td (t\) )Tj /T1_0 1 Tf 0 Tc 11.6 0 0 11.6 193.98 243.37 Tm (= )Tj /T1_1 1 Tf 0.05 Tc 11.3535 0 0 10.1 204.71 243.37 Tm (l\(t)Tj -0.035 Tc 8.2872 0 0 10.1 216.87 246.97 Tm (2m)Tj 0 Tc 10.1 0 0 10.1 228.1 243.37 Tm (, )Tj /T1_0 1 Tf -0.0316 Tc 9.3 0 0 9.3 231.92 243.37 Tm (0, )Tj /T1_1 1 Tf 0 Tc 10.1 0 0 10.1 240.9 243.37 Tm (t)Tj 0.381 0.356 Td (m)Tj 0.74 -0.356 Td [(, )142(t)]TJ 0.704 0.356 Td (m)Tj 0.74 -0.356 Td (, )Tj /T1_0 1 Tf 0.0071 Tc 9.3 0 0 9.3 270.62 243.37 Tm (0, )Tj 0.0458 Tc (1\), )Tj 0.05 Tc 10.1049 0 0 9.5 295.46 243.37 Tm (and )Tj 0.044 Tc 9.5 0 0 9.5 315.34 243.37 Tm (this )Tj 0.0071 Tc 2.039 0 Td (coincides )Tj 0.0474 Tc -32.392 -1.175 Td (with )Tj 0.05 Tc 9.6991 0 0 9.5 48.58 232.21 Tm (the )Tj 9.6554 0 0 9.5 64.9 232.21 Tm (generator )Tj 9.5989 0 0 9.5 108.63 232.21 Tm (of )Tj 10.8267 0 0 10.2 119.76 232.21 Tm (f\(m\) )Tj 9.5456 0 0 9.5 145.36 232.21 Tm (in )Tj /T1_1 1 Tf -0.035 Tc 9.766 0 0 10.1 156.45 232.21 Tm (7r\(t\). )Tj /T1_0 1 Tf 0.05 Tc 9.569 0 0 9.5 38.26 220.51 Tm (The )Tj 9.7426 0 0 9.5 57.4 220.51 Tm (tangents )Tj 0.0217 Tc 9.5 0 0 9.5 96.56 220.51 Tm (form )Tj 0 Tc 2.368 0 Td (a )Tj 0.0308 Tc 0.805 0 Td (regulus )Tj 0.0114 Tc 3.498 0 Td (lying )Tj 0.0246 Tc 2.386 0 Td (on )Tj /T1_3 1 Tf -0.035 Tc 7.9512 0 0 9.7 194.77 220.51 Tm (1-l)Tj /T1_1 1 Tf 0 Tc 6.7 0 0 6.7 203.52 223.93 Tm (3 )Tj /T1_0 1 Tf 1.004 -0.51 Td (: )Tj /T1_1 1 Tf 0.05 Tc 8.7592 0 0 6.7 215.64 220.51 Tm (XOX3 )Tj /T1_0 1 Tf 12.1005 0 0 11 241.14 220.51 Tm (+X)Tj 0 Tc 6.8001 0 0 6.8001 257.71 218.89 Tm (I)Tj 11 0 0 11 261.52 220.51 Tm (X)Tj 6.8001 0 0 6.8001 269.42 219.07 Tm (2 )Tj /T1_2 1 Tf 8.1 0 0 8.1 276.71 220.51 Tm (= )Tj /T1_0 1 Tf 11 0 0 11 286.99 220.51 Tm (0 )Tj 0.0305 Tc 9.5 0 0 9.5 294.65 220.51 Tm (whose )Tj 0.0248 Tc 3.004 0 Td (correspond\255)Tj 0.0138 Tc -31.167 -1.232 Td (ing )Tj 0.0136 Tc 1.599 0 Td (null )Tj 0.05 Tc 9.6578 0 0 9.5 60.31 208.81 Tm (polarity )Tj /T1_3 1 Tf 0 Tc 9.6 0 0 9.6 95.85 208.81 Tm (U )Tj /T1_0 1 Tf -0.0056 Tc 9.5 0 0 9.5 106.12 208.81 Tm (is )Tj /T1_1 1 Tf 0.0106 Tc 10.1 0 0 10.1 115.46 208.81 Tm (P\(ao, )Tj 0.0154 Tc 2.498 0 Td (aI, )Tj -0.035 Tc 9.3752 0 0 10.1 154.56 208.81 Tm (a2, )Tj 9.3289 0 0 10.1 168.06 208.81 Tm (a3\) )Tj /T1_2 1 Tf 8.0434 0 0 11 183.83 208.81 Tm (+---+ )Tj /T1_1 1 Tf 8.8811 0 0 10.1 203.1 208.81 Tm (7r\(a3, )Tj 9.5289 0 0 10.1 226.02 208.81 Tm (a2, )Tj 0.0065 Tc 10.1 0 0 10.1 239.69 208.81 Tm (aI, )Tj -0.035 Tc 9.5564 0 0 10.1 253.38 208.81 Tm (ao\). )Tj /T1_0 1 Tf -0.0172 Tc 9.5 0 0 9.5 272.89 208.81 Tm (So )Tj /T1_3 1 Tf 0 Tc 9.6 0 0 9.6 285.21 208.81 Tm (U )Tj /T1_0 1 Tf 0.0386 Tc 9.5 0 0 9.5 295.66 208.81 Tm (interchanges )Tj /T1_3 1 Tf -0.0321 Tc 9.6 0 0 9.6 350.02 208.81 Tm (C\(m\) )Tj /T1_0 1 Tf 0.05 Tc 9.5174 0 0 9.5 27.26 197.47 Tm (and )Tj 10.5025 0 0 10.2 45.24 197.47 Tm (f\(m\). )Tj 10.8754 0 0 9.5 27.27 180.91 Tm (Theorem )Tj 10.2991 0 0 9.3 74.75 180.91 Tm (6.1. )Tj /T1_1 1 Tf 9.8654 0 0 9.3 98.8 180.91 Tm (The )Tj 0.0353 Tc 9.3 0 0 9.3 119.27 180.91 Tm (chords )Tj 0.05 Tc 9.5024 0 0 9.3 150.6 180.91 Tm (and )Tj /T1_0 1 Tf 0.0183 Tc 9.5 0 0 9.5 170 180.91 Tm (axes )Tj 0.05 Tc 10.0163 0 0 9 191.6 180.91 Tm (of )Tj /T1_1 1 Tf 0.0414 Tc 9.3 0 0 9.3 203.65 180.91 Tm (the )Tj -0.035 Tc 8.6667 0 0 9.3 220.51 180.91 Tm (\(q )Tj /T1_2 1 Tf 0 Tc 12.6 0 0 12.6 230.91 180.91 Tm (+ )Tj /T1_1 1 Tf 0.0268 Tc 9.3 0 0 9.3 241.83 180.91 Tm (I\)-arc )Tj 0.0132 Tc 2.913 0 Td (C\(rn\) )Tj 0.05 Tc 9.8418 0 0 9.3 295.68 180.91 Tm (and )Tj 9.6488 0 0 9.3 315.78 180.91 Tm (its )Tj 0.0343 Tc 9.3 0 0 9.3 330.4 180.91 Tm (osculating )Tj 0.0287 Tc -32.571 -1.219 Td (developable )Tj /T1_0 1 Tf -0.035 Tc 12.029 0 0 14.4 78.64 169.57 Tm (rem\) )Tj /T1_1 1 Tf 0.0242 Tc 9.3 0 0 9.3 105.07 169.57 Tm (form )Tj /T1_0 1 Tf 0 Tc 2.434 0 Td (a )Tj /T1_1 1 Tf -0.035 Tc 9.207 0 0 9.4 136.08 169.57 Tm (\(2q2 )Tj /T1_2 1 Tf 0 Tc 12.6 0 0 12.6 155.49 169.57 Tm (+ )Tj /T1_1 1 Tf 9.3 0 0 9.3 165 169.57 Tm (q )Tj /T1_2 1 Tf 12.6 0 0 12.6 171.69 169.57 Tm (+ )Tj /T1_1 1 Tf 0.0395 Tc 9.3 0 0 9.3 181.71 169.57 Tm (I\)-cap )Tj /T1_0 1 Tf 0.0075 Tc 3.058 0 Td (on )Tj /T1_3 1 Tf -0.035 Tc 7.5814 0 0 9.7 222.51 169.57 Tm (1-l)Tj /T1_1 1 Tf 0 Tc 9.4 0 0 9.4 231.02 172.99 Tm (5)Tj 0.518 -0.364 Td (. )Tj /T1_3 1 Tf -0.035 Tc 9.556 0 0 9.6 27.42 152.83 Tm (Proof. )Tj /T1_0 1 Tf 0.05 Tc 9.7889 0 0 9.5 56.8 152.83 Tm (The )Tj 9.6112 0 0 9.5 77.66 152.83 Tm (arguments )Tj 0.04 Tc 9.5 0 0 9.5 125.91 152.83 Tm (of )Tj 0.0465 Tc 1.237 0 Td (Proposition )Tj -0.0205 Tc 5.476 0 Td (4.2 )Tj 0.037 Tc 1.662 0 Td (can )Tj 0.05 Tc 9.5181 0 0 9.5 223.21 152.83 Tm (be )Tj 0.0133 Tc 9.5 0 0 9.5 236.97 152.83 Tm (copied )Tj 0.0314 Tc 3.165 0 Td (if )Tj /T1_3 1 Tf -0.0011 Tc 9.6 0 0 9.6 277.14 152.83 Tm (\(n, )Tj -0.0302 Tc 1.452 0 Td (2h\) )Tj /T1_2 1 Tf 0 Tc 8.7 0 0 8.7 309.64 152.83 Tm (= )Tj /T1_0 1 Tf 9.5 0 0 9.5 320.79 152.83 Tm (1 )Tj 0.0096 Tc 0.893 0 Td (since )Tj 0.05 Tc 9.5414 0 0 9.5 353.32 152.83 Tm (then )Tj -0.035 Tc 10.3859 0 0 10.4 26.89 141.13 Tm (C\(rn\), )Tj 0 Tc 9.5 0 0 9.5 54.7 141.13 Tm (m )Tj /T1_3 1 Tf 9 0 0 9 77.79 141.13 Tm (2)Tj /T1_1 1 Tf 6.9001 0 0 6.9001 82.77 144.73 Tm (n)Tj 0.922 -0.522 Td (, )Tj /T1_0 1 Tf 0.0101 Tc 9.5 0 0 9.5 94.77 141.13 Tm (defines )Tj 0 Tc 3.428 0 Td (a )Tj /T1_1 1 Tf -0.035 Tc 8.889 0 0 10.1 136.44 141.13 Tm (\(q )Tj /T1_2 1 Tf 0 Tc 12.6 0 0 12.6 146.85 141.13 Tm (+ )Tj /T1_0 1 Tf 0.05 Tc 9.5382 0 0 9.5 157.25 141.13 Tm (I\)-arc )Tj -0.003 Tc 9.5 0 0 9.5 184.78 141.13 Tm (in )Tj /T1_1 1 Tf 0.013 Tc 10.1 0 0 10.1 196.1 141.13 Tm (PG\(3, )Tj -0.035 Tc 8.9618 0 0 10.1 223.51 141.13 Tm (q\) )Tj /T1_0 1 Tf 0.05 Tc 9.6349 0 0 9.5 235.52 141.13 Tm (and )Tj 0 Tc 9.5 0 0 9.5 254.6 141.13 Tm (a )Tj /T1_1 1 Tf -0.035 Tc 8.8942 0 0 10.1 262.98 141.13 Tm (\(q2 )Tj /T1_2 1 Tf 0 Tc 12.6 0 0 12.6 277.89 141.13 Tm (+ )Tj /T1_0 1 Tf 0.05 Tc 9.9051 0 0 9.5 288.65 141.13 Tm (I\)-arc )Tj 0.0349 Tc 9.5 0 0 9.5 317.26 141.13 Tm (in )Tj /T1_1 1 Tf 0.013 Tc 10.1 0 0 10.1 329.48 141.13 Tm (PG\(3, )Tj -0.035 Tc 9.3486 0 0 10.1 356.88 141.13 Tm (q2\). )Tj /T1_0 1 Tf -0.0009 Tc 9.5 0 0 9.5 27.32 129.61 Tm (Hence, )Tj -0.035 Tc 9.2755 0 0 9.5 57.77 129.61 Tm (we )Tj 0.046 Tc 9.5 0 0 9.5 72.09 129.61 Tm (only )Tj 0.0336 Tc 2.293 0 Td (consider )Tj 0.05 Tc 9.8357 0 0 9.5 131.92 129.61 Tm (the )Tj 0.0151 Tc 9.5 0 0 9.5 148.77 129.61 Tm (case )Tj /T1_3 1 Tf -0.035 Tc 9.5361 0 0 9.8 169.5 129.61 Tm (\(n, )Tj 9.0063 0 0 9.6 182.91 129.61 Tm (2h\) )Tj /T1_0 1 Tf 0 Tc 13 0 0 13 199.19 129.61 Tm (= )Tj -0.035 Tc 8.4636 0 0 9.5 209.11 129.61 Tm (2; )Tj 0.05 Tc 10.1785 0 0 9.5 219.4 129.61 Tm (that )Tj -0.0331 Tc 9.5 0 0 9.5 240.22 129.61 Tm (is, )Tj /T1_3 1 Tf 0 Tc 9.6 0 0 9.6 252.63 129.61 Tm (h )Tj /T1_0 1 Tf -0.035 Tc 9.3682 0 0 9.5 260.74 129.61 Tm (is )Tj 0.05 Tc 9.9139 0 0 9.5 270.26 129.61 Tm (odd )Tj 9.9874 0 0 9.5 289.88 129.61 Tm (and )Tj /T1_3 1 Tf 0 Tc 9.8 0 0 9.8 309.15 129.61 Tm (n )Tj /T1_0 1 Tf -0.0246 Tc 9.5 0 0 9.5 318.34 129.61 Tm (is )Tj 0.0015 Tc 1.021 0 Td (even. )Tj 0.05 Tc 9.5362 0 0 9.5 38.49 118.09 Tm (When )Tj /T1_3 1 Tf 0.0368 Tc 9.6 0 0 9.6 67.98 118.09 Tm (\(n,2h\) )Tj /T1_2 1 Tf 0 Tc 8.7 0 0 8.7 100.66 118.09 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 9.3091 0 0 9.5 112.99 118.09 Tm (2, )Tj 0.05 Tc 9.927 0 0 9.5 124.9 118.09 Tm (then )Tj /T1_3 1 Tf -0.0259 Tc 9.6 0 0 9.6 147.88 118.09 Tm (C\(m\) )Tj /T1_0 1 Tf 0.005 Tc 9.5 0 0 9.5 173.97 118.09 Tm (does )Tj 0.0453 Tc 2.339 0 Td (not )Tj -0.001 Tc 1.867 0 Td (define )Tj 0.05 Tc 9.5322 0 0 9.5 242.9 118.09 Tm (an )Tj 0.0118 Tc 9.5 0 0 9.5 256.94 118.09 Tm (arc )Tj 0.0349 Tc 1.783 0 Td (in )Tj /T1_1 1 Tf 0.0397 Tc 10.1 0 0 10.1 286.64 118.09 Tm (PG\(3, )Tj -0.0185 Tc 9.4 0 0 9.4 315.3 118.09 Tm (q2\). )Tj /T1_0 1 Tf -0.0341 Tc 9.5 0 0 9.5 338.01 118.09 Tm (We )Tj 0.0051 Tc 1.831 0 Td (first )Tj 0.0373 Tc -34.54 -1.214 Td (determine )Tj 0.05 Tc 10.2456 0 0 9.5 72.15 106.56 Tm (the )Tj 9.6491 0 0 9.5 89.8 106.56 Tm (maximum )Tj 0.0494 Tc 9.5 0 0 9.5 135.71 106.56 Tm (number )Tj 0.04 Tc 3.705 0 Td (of )Tj 0.0324 Tc 1.185 0 Td (points )Tj 0.0211 Tc 3.002 0 Td (of )Tj 0 Tc 1.155 0 Td [(C )255(\( )]TJ /T1_3 1 Tf 0.0332 Tc 9.4 0 0 9.4 231.21 106.56 Tm (m\), )Tj /T1_0 1 Tf 0.048 Tc 9.5 0 0 9.5 249.56 106.56 Tm (extended )Tj 0.05 Tc 10.2589 0 0 9.5 291.03 106.56 Tm (to )Tj -0.0159 Tc 9.5 0 0 9.5 303.37 106.56 Tm ('\)", )Tj 0.05 Tc 9.5456 0 0 9.5 318.52 106.56 Tm (in )Tj 0 Tc 9.5 0 0 9.5 330.2 106.56 Tm (a )Tj 0.0299 Tc 0.883 0 Td (plane )Tj 0.0021 Tc 2.699 0 Td (of )Tj /T1_1 1 Tf 0.0085 Tc 10.1 0 0 10.1 27.44 95.23 Tm (PG\(3, )Tj -0.035 Tc 10.0969 0 0 10.1 54.66 95.23 Tm (q\). )Tj /T1_0 1 Tf 0.0232 Tc 9.5 0 0 9.5 38.65 83.7 Tm (Let )Tj /T1_2 1 Tf -0.0068 Tc 5.9001 0 0 5.9001 55 83.7 Tm (7r )Tj /T1_1 1 Tf -0.035 Tc 9.2776 0 0 10.1 73.67 83.7 Tm (7r\(ao, )Tj 0.0154 Tc 10.1 0 0 10.1 97.85 83.7 Tm (aI, )Tj -0.035 Tc 9.3752 0 0 10.1 111.9 83.7 Tm (a2, )Tj 9.924 0 0 10.1 125.76 83.7 Tm (a3\). )Tj /T1_0 1 Tf 0.05 Tc 9.5206 0 0 9.5 145.72 83.7 Tm (This )Tj 0.027 Tc 9.5 0 0 9.5 167.14 83.7 Tm (intersects )Tj /T1_3 1 Tf -0.0321 Tc 9.6 0 0 9.6 208 83.7 Tm (C\(m\) )Tj /T1_0 1 Tf 0.0161 Tc 9.5 0 0 9.5 232.37 83.7 Tm (where )Tj /T1_1 1 Tf -0.0281 Tc 10.1 0 0 10.1 259.31 83.7 Tm (aot)Tj 0 Tc 1.267 0.34 Td (m)Tj 0.672 -0.34 Td (+)Tj 0.658 0.357 Td (l )Tj /T1_0 1 Tf 11 0 0 11 291.01 83.7 Tm (+ )Tj /T1_1 1 Tf 0.05 Tc 11.1599 0 0 10.1 299.81 83.7 Tm (alt)Tj 0 Tc 10.1 0 0 10.1 312.97 87.31 Tm (m )Tj /T1_0 1 Tf 11 0 0 11 321.61 83.7 Tm (+ )Tj /T1_1 1 Tf -0.0281 Tc 10.1 0 0 10.1 330.23 83.7 Tm (a2t )Tj /T1_0 1 Tf 0 Tc 11 0 0 11 344.47 83.7 Tm (+ )Tj /T1_1 1 Tf -0.035 Tc 8.6595 0 0 10.1 352.74 83.7 Tm (a3 )Tj /T1_3 1 Tf 0 Tc 8.7 0 0 8.7 364.81 83.7 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 7.0839 0 0 11 27.29 72.55 Tm (O. )Tj 0.0303 Tc 9.5 0 0 9.5 38.66 61.03 Tm (By )Tj 0.05 Tc 9.6483 0 0 9.5 53.02 61.03 Tm (letting )Tj 0 Tc 10.1 0 0 10.1 83.86 61.03 Tm (t )Tj 13 0 0 13 90.29 61.03 Tm (= )Tj /T1_3 1 Tf 0.05 Tc 8.6993 0 0 8.5 100.12 61.03 Tm (tf )Tj /T1_0 1 Tf 0 Tc 11.9 0 0 11.9 108.12 61.03 Tm (+ )Tj /T1_1 1 Tf 0.05 Tc 10.0104 0 0 10 117.11 61.03 Tm (a, )Tj /T1_0 1 Tf 9.7422 0 0 9.5 129.05 61.03 Tm (with )Tj /T1_1 1 Tf 0 Tc 10 0 0 10 150.95 61.03 Tm (a )Tj /T1_0 1 Tf 9.5 0 0 9.5 160.1 61.03 Tm (a )Tj 0.0308 Tc 0.755 0 Td (solution )Tj 0.0021 Tc 3.737 0 Td (of )Tj 0.0377 Tc 1.087 0 Td (this )Tj 0.0419 Tc 1.905 0 Td (equation )Tj 0.0349 Tc 4.057 0 Td (in )Tj -0.0096 Tc 1.134 0 Td ('\)", )Tj -0.0048 Tc 1.526 0 Td (we )Tj 0.05 Tc 9.5775 0 0 9.5 309.51 61.03 Tm (can )Tj 0.0247 Tc 9.5 0 0 9.5 326.87 61.03 Tm (reduce )Tj 0.0314 Tc 3.144 0 Td (this )Tj 0.0392 Tc -34.682 -1.232 Td (equation )Tj 0.05 Tc 10.0407 0 0 9.5 66.22 49.33 Tm (to )Tj 0.0466 Tc 9.5 0 0 9.5 78.21 49.33 Tm (one )Tj 0.05 Tc 9.7422 0 0 9.5 96.47 49.33 Tm (with )Tj /T1_1 1 Tf -0.035 Tc 8.8478 0 0 10.1 118.92 49.33 Tm (a3 )Tj /T1_2 1 Tf 0 Tc 8.7 0 0 8.7 131.44 49.33 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 7.0839 0 0 9.5 141.77 49.33 Tm (O. )Tj -0.0172 Tc 9.5 0 0 9.5 153.91 49.33 Tm (So )Tj 0.05 Tc 9.7985 0 0 9.5 167.32 49.33 Tm (it )Tj -0.018 Tc 9.5 0 0 9.5 176.81 49.33 Tm (suffices )Tj 0.05 Tc 9.6041 0 0 9.5 208.96 49.33 Tm (to )Tj 9.8431 0 0 9.5 220.36 49.33 Tm (study )Tj 9.5322 0 0 9.5 247.22 49.33 Tm (an )Tj 9.6917 0 0 9.5 260 49.33 Tm (equation )Tj /T1_1 1 Tf -0.0108 Tc 10.1 0 0 10.1 300.53 49.33 Tm (aotm+l )Tj /T1_2 1 Tf 0 Tc 12.6 0 0 12.6 332.97 49.33 Tm (+ )Tj /T1_1 1 Tf 0.05 Tc 10.6883 0 0 10.1 342.65 49.33 Tm (alt)Tj 0 Tc 10.1 0 0 10.1 355.45 52.75 Tm (m )Tj 0.922 -0.339 Td (+ )Tj -0.0281 Tc -33.413 -1.212 Td (a2t )Tj /T1_0 1 Tf 0 Tc 13 0 0 13 42.77 37.09 Tm (= )Tj -0.035 Tc 6.8872 0 0 9.6 52.67 37.09 Tm (O. )Tj 9.9368 0 0 10.1 192.98 14.76 Tm (107 )Tj ET endstream endobj 210 0 obj <>/Filter/CCITTFaxDecode/Height 1872/Length 33108/Name/Im0/Subtype/Image/Type/XObject/Width 2240>>stream *PJDr $uR:BF@TD *PGQ(Q*P (A r9RGQB#@TG *P#(Du ":JDr $uc *V H2 2 2JCR!R@TBc *T1# (dJH2 $uR:BF@TYA@TD *PGQ(Q# +(rF# 2c&Fhp"h#:#A 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Tf 0 Tc 12.8 0 0 12.8 178.35 167.41 Tm (+ )Tj /T1_2 1 Tf 8.8 0 0 8.8 187.87 167.41 Tm (q )Tj /T1_3 1 Tf 12.8 0 0 12.8 194.91 167.41 Tm (+ )Tj /T1_0 1 Tf 9.5 0 0 9.5 205.05 167.41 Tm (1 )Tj 0.0438 Tc 0.811 0 Td (nondegenerate )Tj 0.0128 Tc 6.794 0 Td (conics )Tj 0.0263 Tc 2.994 0 Td (containing )Tj 0.0354 Tc 4.839 0 Td (the )Tj 0.05 Tc 9.9287 0 0 9.5 22.12 155.71 Tm (three )Tj 0.0201 Tc 9.5 0 0 9.5 46.78 155.71 Tm (vertices )Tj 0.04 Tc 3.536 0 Td (of )Tj 0 Tc 1.06 0 Td (a )Tj 0.0329 Tc 0.766 0 Td (triangle )Tj 0.0043 Tc 3.574 0 Td (defined )Tj -0.0041 Tc 3.316 0 Td (over )Tj 0 Tc 2.064 0 Td (a )Tj 0.0185 Tc 0.721 0 Td (cubic )Tj 0.0402 Tc 2.519 0 Td (extension )Tj 0.04 Tc 4.435 0 Td (of )Tj -0.035 Tc 7.3182 0 0 9.3 265.78 155.71 Tm ('Y. )Tj 0.05 Tc 9.5282 0 0 9.5 278.56 155.71 Tm (There )Tj -0.035 Tc 9.3682 0 0 9.5 305.38 155.71 Tm (is )Tj 0 Tc 9.5 0 0 9.5 314.18 155.71 Tm (a )Tj 0.0163 Tc 0.721 0 Td (connection )Tj 0.0469 Tc -31.461 -1.213 Td (between )Tj 0.0449 Tc (the )Tj 0.036 Tc 5.632 0 Td (set )Tj 0.04 Tc 1.558 0 Td (of )Tj 0.0205 Tc 1.118 0 Td (chords )Tj 0.04 Tc 3.107 0 Td (of )Tj 0 Tc 1.136 0 Td (a )Tj 0.0311 Tc 0.785 0 Td (twisted )Tj 0.0185 Tc 3.422 0 Td (cubic )Tj 0.0419 Tc 2.614 0 Td (and )Tj 0 Tc 1.914 0 Td (a )Tj 0.0458 Tc 0.788 0 Td (projective )Tj 0.0275 Tc 4.764 0 Td (circumscribed )Tj 0.0226 Tc 6.301 0 Td (bundle )Tj 0.04 Tc -33.131 -1.213 Td (of )Tj 0 Tc 1.212 0 Td (a )Tj 0.031 Tc 0.883 0 Td (projective )Tj 0.0299 Tc 4.661 0 Td (plane )Tj -0.0062 Tc 2.679 0 Td (as )Tj -0.0246 Tc 1.215 0 Td (is )Tj 0.012 Tc 0.999 0 Td (shown )Tj -0.0062 Tc 3.035 0 Td (as )Tj -0.0201 Tc 1.213 0 Td (follows. )Tj 0.05 Tc 9.5222 0 0 9.5 34.33 120.79 Tm (Let )Tj /T1_2 1 Tf -0.035 Tc 9.3543 0 0 10.2 52.61 120.79 Tm (Q={F'\\,I-\243,vl,X, )Tj /T1_1 1 Tf 7.1641 0 0 8.8 110.04 120.79 Tm (IL, )Tj /T1_0 1 Tf 0.0202 Tc 6.2 0 0 6.2 120.03 120.79 Tm (1/ )Tj /T1_3 1 Tf 0 Tc 7.8001 0 0 7.8001 128.52 120.79 Tm (E )Tj 0.05 Tc 8.0088 0 0 7.8001 137.6 120.79 Tm ('\)'} )Tj /T1_0 1 Tf 9.7011 0 0 9.5 151.03 120.79 Tm (be )Tj 0.0449 Tc 9.5 0 0 9.5 164.5 120.79 Tm (the )Tj 0.0453 Tc 1.744 0 Td (net )Tj 0.05 Tc 9.5989 0 0 9.5 197.55 120.79 Tm (of )Tj 0.0349 Tc 9.5 0 0 9.5 208.89 120.79 Tm (quadrics )Tj 0.05 Tc 9.7722 0 0 9.5 247.48 120.79 Tm (through )Tj 9.5625 0 0 9.5 284.92 120.79 Tm (the )Tj 0.0311 Tc 9.5 0 0 9.5 301.66 120.79 Tm (twisted )Tj 0.009 Tc 3.441 0 Td (cubic )Tj 0 Tc 2.557 0 Td (C )Tj 0.05 Tc 10.2223 0 0 9.5 22.4 109.44 Tm (and )Tj 0.0207 Tc 9.5 0 0 9.5 42.22 109.44 Tm (let )Tj /T1_1 1 Tf -0.035 Tc 7.3387 0 0 8.3 56.07 109.44 Tm ('!fa )Tj /T1_0 1 Tf 0.05 Tc 9.5181 0 0 9.5 69.49 109.44 Tm (be )Tj 0 Tc 9.5 0 0 9.5 82.88 109.44 Tm (a )Tj 0.0394 Tc 0.864 0 Td (plane )Tj 0.0298 Tc 2.725 0 Td (meeting )Tj 0 Tc 3.743 0 Td (C )Tj 0.0349 Tc 0.987 0 Td (in )Tj 0.0416 Tc 1.2 0 Td (three )Tj 0.0382 Tc 2.588 0 Td (conjugate )Tj 0.05 Tc 9.5232 0 0 9.5 241.75 109.44 Tm (points )Tj /T1_2 1 Tf 0.0482 Tc 8.8 0 0 8.8 271.5 109.44 Tm (Q1,Q2,Q3; )Tj /T1_0 1 Tf 0.05 Tc 9.9596 0 0 9.5 318.76 109.44 Tm (that )Tj -0.0236 Tc 9.5 0 0 9.5 339.22 109.44 Tm (is, )Tj 0.0354 Tc 1.314 0 Td (the )Tj 0.05 Tc 9.6682 0 0 9.5 22.33 98.11 Tm (parameters )Tj 0.04 Tc 9.5 0 0 9.5 73.17 98.11 Tm (of )Tj 0.05 Tc 9.6991 0 0 9.5 84.76 98.11 Tm (the )Tj 0.0416 Tc 9.5 0 0 9.5 101.86 98.11 Tm (three )Tj 0.0324 Tc 2.618 0 Td (points )Tj 0.0213 Tc 3.058 0 Td (are )Tj 0.0334 Tc 1.706 0 Td (conjugate )Tj 0.0148 Tc 4.585 0 Td (over )Tj -0.035 Tc 8.419 0 0 9.5 236.79 98.11 Tm ('\)' )Tj 0.05 Tc 9.5456 0 0 9.5 246.34 98.11 Tm (in )Tj 0 Tc 9.5 0 0 9.5 258.38 98.11 Tm (a )Tj 0.0327 Tc 0.911 0 Td (cubic )Tj 0.0184 Tc 2.727 0 Td (extension. )Tj 0.0232 Tc 4.951 0 Td (Let )Tj /T1_2 1 Tf 0 Tc 11 0 0 11 357.07 98.11 Tm (T )Tj /T1_0 1 Tf 0.05 Tc 9.8842 0 0 9.5 22.33 86.58 Tm (be )Tj 9.8357 0 0 9.5 36.34 86.58 Tm (the )Tj 0.0455 Tc 9.5 0 0 9.5 52.97 86.58 Tm (set )Tj 0.0211 Tc 1.615 0 Td (of )Tj 0.0243 Tc 1.137 0 Td (chords )Tj 0.0211 Tc 3.202 0 Td (of )Tj -0.035 Tc 8.5874 0 0 9.5 120.33 86.58 Tm (C. )Tj 0.0465 Tc 9.5 0 0 9.5 133.66 86.58 Tm (The )Tj 0.0299 Tc 2.018 0 Td (plane )Tj /T1_1 1 Tf -0.035 Tc 7.3387 0 0 8.3 178.29 86.58 Tm ('!fa )Tj /T1_0 1 Tf 0.0347 Tc 9.5 0 0 9.5 191.32 86.58 Tm (meets )Tj 0 Tc 2.872 0 Td (a )Tj 0.0487 Tc 0.873 0 Td (quadric )Tj /T1_2 1 Tf -0.035 Tc 7.9428 0 0 10.2 261.96 86.58 Tm (F,\\I-\243v )Tj /T1_0 1 Tf 0.0349 Tc 9.5 0 0 9.5 286.66 86.58 Tm (in )Tj 0 Tc 1.192 0 Td (a )Tj 0.0233 Tc 0.862 0 Td (nondegenerate )Tj 0.0327 Tc -29.869 -1.212 Td (conic )Tj 0.05 Tc 9.5081 0 0 9.5 48.58 75.07 Tm (through )Tj /T1_2 1 Tf 8.813 0 0 8.8 85.38 75.07 Tm (Q1,Q2,Q3. )Tj /T1_0 1 Tf 0.0232 Tc 9.5 0 0 9.5 135.31 75.07 Tm (Let )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 152.37 75.07 Tm (N )Tj /T1_0 1 Tf 0.0329 Tc 9.5 0 0 9.5 165.79 75.07 Tm (be )Tj 0.05 Tc 9.5625 0 0 9.5 179.44 75.07 Tm (the )Tj 9.5694 0 0 9.5 196.55 75.07 Tm (net )Tj 0.04 Tc 9.5 0 0 9.5 213.57 75.07 Tm (of )Tj 0.0128 Tc 1.251 0 Td (conics )Tj /T1_1 1 Tf -0.035 Tc 7.4916 0 0 8.3 254.78 75.07 Tm ('!fa )Tj /T1_0 1 Tf 0 Tc 12.5 0 0 12.5 267.64 75.07 Tm (n )Tj /T1_2 1 Tf -0.035 Tc 8.0409 0 0 10.2 277.08 75.07 Tm (F,\\I-\243v, )Tj /T1_0 1 Tf 0.05 Tc 9.6317 0 0 9.5 306.82 75.07 Tm (Then )Tj 0.0135 Tc 9.5 0 0 9.5 332.18 75.07 Tm (any )Tj -0.0189 Tc 1.922 0 Td (two )Tj 0.0279 Tc -34.529 -1.194 Td (conics )Tj 0.05 Tc 9.5456 0 0 9.5 51.4 63.73 Tm (in )Tj /T1_1 1 Tf 0 Tc 11 0 0 11 61.58 63.73 Tm (N )Tj /T1_0 1 Tf 0.0496 Tc 9.5 0 0 9.5 74.32 63.73 Tm (meet )Tj 0.0255 Tc 2.445 0 Td (residually )Tj 0.016 Tc 4.502 0 Td (in )Tj 0 Tc 1.097 0 Td (a )Tj 0.032 Tc 0.805 0 Td (real )Tj 0.043 Tc 1.916 0 Td (point )Tj /T1_2 1 Tf 0.0117 Tc 10 0 0 10 201.5 63.73 Tm (P. )Tj /T1_0 1 Tf 0.05 Tc 9.6149 0 0 9.5 215.2 63.73 Tm (This )Tj 0.007 Tc 9.5 0 0 9.5 237.16 63.73 Tm (gives )Tj 0 Tc 2.48 0 Td (a )Tj 0.05 Tc 9.5398 0 0 9.5 268.54 63.73 Tm (mapping )Tj 0.0154 Tc 9.5 0 0 9.5 307.88 63.73 Tm (from )Tj /T1_1 1 Tf 0 Tc 11 0 0 11 329.42 63.73 Tm (N )Tj /T1_0 1 Tf 0.0401 Tc 9.5 0 0 9.5 341.8 63.73 Tm (to )Tj /T1_1 1 Tf -0.035 Tc 7.7361 0 0 8.3 352.69 63.73 Tm ('!fa. )Tj /T1_0 1 Tf 0 Tc 9.5 0 0 9.5 22.66 52.21 Tm (A )Tj 0.0376 Tc 1.148 0 Td (chord )Tj 0.0211 Tc 2.823 0 Td (of )Tj 0 Tc 1.117 0 Td (C )Tj 0.05 Tc 9.5008 0 0 9.5 80.26 52.21 Tm (maps )Tj 9.6041 0 0 9.5 105.46 52.21 Tm (to )Tj 0 Tc 9.5 0 0 9.5 117.26 52.21 Tm (a )Tj 0.043 Tc 0.826 0 Td (point )Tj 0.04 Tc 2.604 0 Td (of )Tj /T1_1 1 Tf -0.035 Tc 7.3387 0 0 8.3 160.65 52.21 Tm ('!fa )Tj /T1_0 1 Tf 0.0295 Tc 9.5 0 0 9.5 173.57 52.21 Tm (simply )Tj -0.0252 Tc 3.243 0 Td (as )Tj 0.05 Tc 9.8357 0 0 9.5 215.98 52.21 Tm (the )Tj 0.043 Tc 9.5 0 0 9.5 232.84 52.21 Tm (intersection )Tj 0.0211 Tc 5.532 0 Td (of )Tj 0.05 Tc 9.6991 0 0 9.5 296.26 52.21 Tm (the )Tj -0.0013 Tc 9.5 0 0 9.5 312.94 52.21 Tm (line )Tj 0.0347 Tc 1.864 0 Td (with )Tj 0.0354 Tc 2.254 0 Td (the )Tj 0.0421 Tc -34.689 -1.194 Td (plane. )Tj 0.0092 Tc 3.178 0 Td (Hence )Tj -0.035 Tc 9.2755 0 0 9.5 80.99 40.87 Tm (we )Tj 0.0105 Tc 9.5 0 0 9.5 95.39 40.87 Tm (have )Tj 0 Tc 2.302 0 Td (a )Tj 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(completes )Tj 0.0354 Tc 4.631 0 Td (the )Tj 0.0302 Tc 1.689 0 Td (proof. )Tj 0 Tc 9.6 0 0 9.6 303.74 509.77 Tm (0 )Tj 0.05 Tc 10.6634 0 0 9.5 28.21 488.17 Tm (Remarks )Tj -0.005 Tc 9.5 0 0 9.5 28.33 476.47 Tm (\(a\) )Tj 0.0465 Tc 1.519 0 Td (The )Tj 0.05 Tc 9.5132 0 0 9.5 61.83 476.47 Tm (chords )Tj 9.5989 0 0 9.5 92.79 476.47 Tm (of )Tj 0 Tc 9.5 0 0 9.5 103.4 476.47 Tm (C )Tj 0.0217 Tc 0.947 0 Td (form )Tj 0 Tc 2.387 0 Td (a )Tj -0.035 Tc 9.7777 0 0 10.4 143.52 476.47 Tm (\(1, )Tj 0.0498 Tc 9.5 0 0 9.5 155.95 476.47 Tm (3\)-congruence, )Tj 0.0379 Tc 7.059 0 Td (namely )Tj 0 Tc 3.477 0 Td (a )Tj 0.0177 Tc 0.798 0 Td (line )Tj 0.0421 Tc 1.894 0 Td (congruence )Tj 0.04 Tc 5.362 0 Td (of )Tj 0.0321 Tc 1.118 0 Td (order )Tj 0 Tc 2.627 0 Td (1 )Tj 0.0318 Tc -35.749 -1.232 Td (\(the )Tj 0.0456 Tc 1.962 0 Td (number )Tj 0.05 Tc 10.0163 0 0 9.5 81.44 464.77 Tm (of )Tj 0.0319 Tc 9.5 0 0 9.5 92.25 464.77 Tm (chords )Tj 0.05 Tc 9.6665 0 0 9.5 122.02 464.77 Tm (through )Tj 0 Tc 9.5 0 0 9.5 157.76 464.77 Tm (a )Tj 0.0242 Tc 0.779 0 Td (general )Tj 0.0382 Tc 3.344 0 Td (point )Tj 0.0211 Tc 2.509 0 Td (of )Tj /T1_3 1 Tf 0.0478 Tc 9.7 0 0 9.7 231.01 464.77 Tm (PG\(3, )Tj /T1_1 1 Tf -0.035 Tc 9.3586 0 0 10 258.7 464.77 Tm (q\)\) )Tj /T1_0 1 Tf 0.05 Tc 9.9874 0 0 9.5 273.14 464.77 Tm (and )Tj 0.0313 Tc 9.5 0 0 9.5 291.69 464.77 Tm (class )Tj 0 Tc 2.385 0 Td (3 )Tj 0.05 Tc 9.5126 0 0 9.5 322.09 464.77 Tm (\(the )Tj 0.0381 Tc 9.5 0 0 9.5 341.27 464.77 Tm (number )Tj 0.0021 Tc -32.977 -1.213 Td (of )Tj 0.0167 Tc 1.099 0 Td (chords )Tj 0.05 Tc 9.5989 0 0 9.5 68.13 453.25 Tm (of )Tj 0 Tc 9.5 0 0 9.5 79.1 453.25 Tm (C )Tj -0.003 Tc 1.025 0 Td (in )Tj 0 Tc 1.173 0 Td (a )Tj 0.0305 Tc 0.836 0 Td (general )Tj 0.0365 Tc 3.477 0 Td (plane\). )Tj 0.0037 Tc 3.5 0 Td (Dually, )Tj 0.05 Tc 9.5625 0 0 9.5 206.44 453.25 Tm (the )Tj 0.0183 Tc 9.5 0 0 9.5 222.38 453.25 Tm (axes )Tj 0.05 Tc 9.5989 0 0 9.5 243.27 453.25 Tm (of )Tj /T1_2 1 Tf 0 Tc 9.1 0 0 9.1 254.32 453.25 Tm (f )Tj /T1_0 1 Tf 0.028 Tc 9.5 0 0 9.5 263.06 453.25 Tm (form )Tj 0 Tc 2.425 0 Td (a )Tj 0.008 Tc 0.908 0 Td (\(3, )Tj 0.05 Tc 9.7638 0 0 9.5 308.09 453.25 Tm (I\)-congruence. )Tj 0.0057 Tc 9.5 0 0 9.5 27.86 441.73 Tm (For )Tj 0.0245 Tc 1.764 0 Td (more )Tj 0.0453 Tc 2.513 0 Td (details, )Tj 0.0004 Tc 3.577 0 Td (see )Tj -0.035 Tc 8.838 0 0 9.5 118.77 441.73 Tm ([1, )Tj -0.002 Tc 9.5 0 0 9.5 131.59 441.73 Tm (p. )Tj -0.0299 Tc 1.321 0 Td (49]. )Tj 0.0416 Tc -11.065 -1.194 Td (From )Tj 0.05 Tc 9.6827 0 0 9.5 64.58 430.39 Tm (Proposition )Tj -0.0023 Tc 9.5 0 0 9.5 118.04 430.39 Tm (4.2, )Tj 0.05 Tc 9.7985 0 0 9.5 136.72 430.39 Tm (it )Tj -0.0134 Tc 9.5 0 0 9.5 146.96 430.39 Tm (follows )Tj 0.05 Tc 10.0691 0 0 9.5 179.08 430.39 Tm (that )Tj 0.0449 Tc 9.5 0 0 9.5 199.96 430.39 Tm (the )Tj 0.0167 Tc 1.755 0 Td (chords )Tj 0.0419 Tc 3.239 0 Td (and )Tj 0.031 Tc 1.952 0 Td (axes )Tj 0.05 Tc 9.8778 0 0 9.5 288.34 430.39 Tm (through )Tj 0 Tc 9.5 0 0 9.5 326.24 430.39 Tm (a )Tj 0.043 Tc 0.883 0 Td (point )Tj 0.0213 Tc 2.679 0 Td (are )Tj 0.0311 Tc -34.976 -1.194 Td (contained )Tj 0.0349 Tc 4.605 0 Td (in )Tj 0.05 Tc 10.4356 0 0 9.5 83.95 419.05 Tm (at )Tj 0.0439 Tc 9.5 0 0 9.5 96.4 419.05 Tm (least )Tj 0.0182 Tc 2.462 0 Td (one )Tj 0.05 Tc 9.6449 0 0 9.5 138.15 419.05 Tm (quadratic )Tj -0.0094 Tc 9.5 0 0 9.5 182.07 419.05 Tm (cone )Tj 0.05 Tc 9.6349 0 0 9.5 204.02 419.05 Tm (and )Tj 9.6991 0 0 9.5 222.82 419.05 Tm (the )Tj 0.0205 Tc 9.5 0 0 9.5 239.85 419.05 Tm (chords )Tj 0.05 Tc 10.1049 0 0 9.5 270.62 419.05 Tm (and )Tj 0.0373 Tc 9.5 0 0 9.5 290.6 419.05 Tm (axes )Tj 0.05 Tc 9.5456 0 0 9.5 313.12 419.05 Tm (in )Tj 0 Tc 9.5 0 0 9.5 325.16 419.05 Tm (a )Tj 0.0299 Tc 0.921 0 Td (plane )Tj 0.0213 Tc 2.736 0 Td (are )Tj 0.0287 Tc -34.938 -1.194 Td (contained )Tj 0.05 Tc 9.5456 0 0 9.5 71.02 407.71 Tm (in )Tj 10.9099 0 0 9.5 82.51 407.71 Tm (at )Tj 0.0439 Tc 9.5 0 0 9.5 94.42 407.71 Tm (least )Tj 0.0087 Tc 2.424 0 Td (one )Tj 0.05 Tc 9.6723 0 0 9.5 134.91 407.71 Tm (dual )Tj 0.0027 Tc 9.5 0 0 9.5 156.51 407.71 Tm (conic. )Tj -0.0241 Tc -13.455 -1.213 Td (\(b\) )Tj 0.0044 Tc 1.547 0 Td (Some )Tj 0.05 Tc 9.9461 0 0 9.5 68.56 396.19 Tm (tests )Tj 0.0422 Tc 9.5 0 0 9.5 91.63 396.19 Tm (performed )Tj 0.0042 Tc 4.82 0 Td (for )Tj -0.0219 Tc 1.556 0 Td (low )Tj 0.0099 Tc 1.787 0 Td (values )Tj 0.04 Tc 2.929 0 Td (of )Tj /T1_3 1 Tf 0 Tc 9.3 0 0 9.3 207.66 396.19 Tm (q )Tj /T1_0 1 Tf -0.0068 Tc 9.5 0 0 9.5 214.97 396.19 Tm (show )Tj 0.05 Tc 10.2879 0 0 9.5 238.29 396.19 Tm (that )Tj 0.0449 Tc 9.5 0 0 9.5 258.82 396.19 Tm (the )Tj 0.05 Tc 9.5436 0 0 9.5 274.77 396.19 Tm (caps )Tj 9.6285 0 0 9.5 296.55 396.19 Tm (constructed )Tj 0.0078 Tc 9.5 0 0 9.5 349.1 396.19 Tm (above )Tj 0.0118 Tc -33.802 -1.213 Td (are )Tj 0.0043 Tc 1.629 0 Td (far )Tj 0.0344 Tc 1.516 0 Td (from )Tj 0.049 Tc 2.456 0 Td (being )Tj 0.0277 Tc 2.794 0 Td (complete. )Tj 0.05 Tc 10.4816 0 0 9.5 28.33 367.39 Tm (Corollary )Tj 10.2405 0 0 9.5 76.82 367.39 Tm (4.3. )Tj /T1_3 1 Tf 9.7533 0 0 9.7 100.96 367.39 Tm (The )Tj -0.035 Tc 9.0001 0 0 9.3 120.78 367.39 Tm (\(2q2 )Tj /T1_2 1 Tf 0 Tc 13.2 0 0 13.2 140 367.39 Tm (+ )Tj /T1_3 1 Tf 9.3 0 0 9.3 149.7 367.39 Tm (q )Tj /T1_2 1 Tf 13.2 0 0 13.2 156.56 367.39 Tm (+ )Tj /T1_0 1 Tf 0.05 Tc 11.0599 0 0 9.5 166.78 367.39 Tm (I\)-cap )Tj /T1_3 1 Tf 0 Tc 9.7 0 0 9.7 199.52 367.39 Tm (K )Tj -0.0181 Tc 1.23 0 Td (has )Tj /T1_0 1 Tf 0 Tc 9.5 0 0 9.5 228.32 367.39 Tm (a )Tj /T1_3 1 Tf 0.0129 Tc 9.7 0 0 9.7 236.27 367.39 Tm (collineation )Tj 0.0393 Tc 5.286 0 Td (group )Tj 0.0177 Tc 2.911 0 Td (isomorphic )Tj /T1_0 1 Tf 0.0401 Tc 9.5 0 0 9.5 364.66 367.39 Tm (to )Tj /T1_3 1 Tf 0.0495 Tc 9.7 0 0 9.7 28.15 355.87 Tm (PGL\(2, )Tj -0.035 Tc 9.4213 0 0 9.7 61.68 355.87 Tm (q\) )Tj /C0_0 1 Tf 0 Tc 4.8601 0 0 7.3801 73.45 355.87 Tm <007E0020>Tj /T1_3 1 Tf 9.7 0 0 9.7 82.07 355.87 Tm (C)Tj 6.7 0 0 6.7 89.61 354.43 Tm (2)Tj 0.681 0.215 Td (, )Tj 0.0215 Tc 9.7 0 0 9.7 99.67 355.87 Tm (namely, )Tj 0.05 Tc 9.727 0 0 9.7 135.43 355.87 Tm (the )Tj 0.0229 Tc 9.7 0 0 9.7 151.59 355.87 Tm (semidirect )Tj 0.0313 Tc 4.689 0 Td (product )Tj /T1_0 1 Tf 0.05 Tc 10.2249 0 0 9.5 232.64 355.87 Tm (of )Tj /T1_3 1 Tf 9.8599 0 0 9.7 243.44 355.87 Tm (PGL\(2, )Tj -0.035 Tc 9.4213 0 0 9.7 277.86 355.87 Tm (q\) )Tj /T1_0 1 Tf 0.05 Tc 9.3426 0 0 9.2 290.35 355.87 Tm (by )Tj 0 Tc 9.5 0 0 9.5 303.38 355.87 Tm (a )Tj /T1_3 1 Tf 0.0125 Tc 9.7 0 0 9.7 311.69 355.87 Tm (cyclic )Tj 0.0069 Tc 2.706 0 Td (group )Tj /T1_0 1 Tf 0.05 Tc 10.0163 0 0 9.5 364.94 355.87 Tm (of )Tj /T1_3 1 Tf -0.0028 Tc 9.7 0 0 9.7 28.18 344.35 Tm (order )Tj -0.0056 Tc 2.558 0 Td (two. )Tj -0.0211 Tc -2.542 -1.763 Td (Proof. )Tj /T1_0 1 Tf 0.05 Tc 10.0089 0 0 9.5 57.33 327.25 Tm (The )Tj 0.0366 Tc 9.5 0 0 9.5 76.59 327.25 Tm (collineation )Tj 0.0457 Tc 5.382 0 Td (group )Tj 0.05 Tc 9.8076 0 0 9.5 154.35 327.25 Tm (of )Tj 9.6994 0 0 9.5 164.6 327.25 Tm (Cis )Tj /T1_3 1 Tf 0.0384 Tc 9.7 0 0 9.7 181.69 327.25 Tm (PGL\(2, )Tj /T1_1 1 Tf -0.0244 Tc 9 0 0 9 214.79 327.25 Tm (q\); )Tj /T1_0 1 Tf 0.05 Tc 9.7985 0 0 9.5 228.34 327.25 Tm (it )Tj 0.0485 Tc 9.5 0 0 9.5 236.96 327.25 Tm (acts )Tj 0.05 Tc 10.1228 0 0 9.5 256.02 327.25 Tm (3-transitively )Tj 9.6154 0 0 9.5 318.87 327.25 Tm (on )Tj 9.6991 0 0 9.5 331.72 327.25 Tm (the )Tj 0.0361 Tc 9.5 0 0 9.5 347.05 327.25 Tm (points )Tj 0.0211 Tc -33.585 -1.194 Td (of )Tj 0 Tc 1.079 0 Td (C )Tj -0.035 Tc 8.6539 0 0 9.5 47.49 315.91 Tm ([5, )Tj -0.002 Tc 9.5 0 0 9.5 59.95 315.91 Tm (p. )Tj -0.0044 Tc 1.338 0 Td (234], )Tj 0.05 Tc 9.7524 0 0 9.5 96.02 315.91 Tm (and )Tj 9.6109 0 0 9.5 114.67 315.91 Tm (partitions )Tj 9.6991 0 0 9.5 158.74 315.91 Tm (the )Tj 0.0129 Tc 9.5 0 0 9.5 175.05 315.91 Tm (chords )Tj 0.0211 Tc 3.107 0 Td (of )Tj 0 Tc 1.098 0 Td (C )Tj 0.0369 Tc 0.893 0 Td [(into )-43(three )]TJ 0.05 Tc 9.6983 0 0 9.5 266.85 315.91 Tm (orbits )Tj -0.035 Tc 9.2063 0 0 9.5 295.16 315.91 Tm ([5, )Tj 0.05 Tc 9.6734 0 0 9.5 308.47 315.91 Tm (Lemma )Tj -0.0128 Tc 9.5 0 0 9.5 343.38 315.91 Tm (21.1.4], )Tj 0.0228 Tc -33.191 -1.194 Td (namely )Tj 0.05 Tc 9.6991 0 0 9.5 59.92 304.57 Tm (the )Tj 9.6251 0 0 9.5 75.59 304.57 Tm (real )Tj 0.0259 Tc 9.5 0 0 9.5 93.87 304.57 Tm (chords, )Tj 0.05 Tc 9.6991 0 0 9.5 126.34 304.57 Tm (the )Tj 0.0499 Tc 9.5 0 0 9.5 142.18 304.57 Tm (tangents )Tj 0.0419 Tc 3.989 0 Td (and )Tj 0.0449 Tc 1.808 0 Td (the )Tj 0.0358 Tc 1.623 0 Td (imaginary )Tj 0.0228 Tc 4.584 0 Td (chords. )Tj -0.0172 Tc 3.592 0 Td (So )Tj /T1_3 1 Tf 0.05 Tc 10.027 0 0 9.7 303.2 304.57 Tm (PGL\(2, )Tj /T1_1 1 Tf -0.035 Tc 8.3892 0 0 10 338.1 304.57 Tm (q\) )Tj /T1_0 1 Tf -0.0071 Tc 9.5 0 0 9.5 348.4 304.57 Tm (leaves )Tj /T1_3 1 Tf -0.035 Tc 14.0678 0 0 15.2 27.99 293.05 Tm (vi )Tj /T1_0 1 Tf 0.0343 Tc 9.5 0 0 9.5 42.4 293.05 Tm (invariant. )Tj 0.05 Tc 9.679 0 0 9.5 88.84 293.05 Tm (The )Tj 0.0263 Tc 9.5 0 0 9.5 109.07 293.05 Tm (null )Tj 0.05 Tc 9.5534 0 0 9.5 128.71 293.05 Tm (polarity )Tj 0.0043 Tc 9.5 0 0 9.5 165.69 293.05 Tm (defined )Tj 0.0138 Tc 3.459 0 Td (by )Tj 0.0354 Tc 1.456 0 Td (the )Tj 0.0242 Tc 1.756 0 Td (general )Tj 0.0449 Tc 3.505 0 Td (linear )Tj 0.0426 Tc 2.936 0 Td (complex )Tj 0.0284 Tc 4.131 0 Td (containing )Tj 0.0449 Tc -31.729 -1.213 Td (the )Tj 0.05 Tc 9.5468 0 0 9.5 43.36 281.53 Tm (tangents )Tj 10.2589 0 0 9.5 81.87 281.53 Tm (to )Tj 0 Tc 9.5 0 0 9.5 92.96 281.53 Tm (C )Tj 0.0277 Tc 0.912 0 Td (induces )Tj 0.05 Tc 9.8988 0 0 9.5 135.26 281.53 Tm (an )Tj 0.0318 Tc 9.5 0 0 9.5 148.06 281.53 Tm (involutory )Tj 0.0175 Tc 4.736 0 Td (collineation, )Tj 0.0064 Tc 5.541 0 Td (which )Tj 0.0455 Tc 2.778 0 Td (interchanges )Tj 0.0205 Tc 5.873 0 Td (chords )Tj 0.0419 Tc 3.087 0 Td (and )Tj -0.0006 Tc -34.636 -1.326 Td (axes )Tj -0.035 Tc 8.6539 0 0 9.5 49.11 268.93 Tm ([5, )Tj 0.05 Tc 9.7261 0 0 9.5 61.84 268.93 Tm (Th. )Tj 0.0035 Tc 9.5 0 0 9.5 81.84 268.93 Tm (21.1.2]. )Tj /T1_2 1 Tf 0.05 Tc 11.8001 0 0 9.4 116.13 268.93 Tm (It )Tj /T1_0 1 Tf -0.0102 Tc 9.5 0 0 9.5 126.8 268.93 Tm (follows )Tj 0.05 Tc 10.1785 0 0 9.5 158.74 268.93 Tm (that )Tj /T1_3 1 Tf 0.0458 Tc 9.7 0 0 9.7 179.53 268.93 Tm (PGL\(2, )Tj /T1_1 1 Tf -0.035 Tc 8.3892 0 0 10 213 268.93 Tm (q\) )Tj /T1_0 1 Tf 0.0042 Tc 9.5 0 0 9.5 224.18 268.93 Tm (also )Tj -0.0071 Tc 2.029 0 Td (leaves )Tj /T1_3 1 Tf -0.035 Tc 11.8808 0 0 15.9 270.46 268.93 Tm (Vi )Tj /T1_0 1 Tf 0.0448 Tc 9.5 0 0 9.5 285.22 268.93 Tm (invariant. )Tj 0 Tc 5.322 0 Td (0 )Tj 0.0197 Tc 9.3 0 0 9.3 61.43 240.49 Tm (5. )Tj 0 Tc 1.483 0 Td (A )Tj 0.05 Tc 7.8775 0 0 7.6 87.45 240.49 Tm (PLANE )Tj 7.8247 0 0 7.6 118.58 240.49 Tm (REPRESENTATION )Tj 7.8576 0 0 7.6 195.76 240.49 Tm (OF )Tj 7.909 0 0 7.6 210.35 240.49 Tm (THE )Tj 7.6079 0 0 7.6 230.5 240.49 Tm (CHORDS )Tj 8.2711 0 0 7.6 267.4 240.49 Tm (OF )Tj 0 Tc 9.3 0 0 9.3 282.32 240.49 Tm (C )Tj 0.05 Tc 8.3479 0 0 7.6 292.1 240.49 Tm (FOR )Tj /T1_3 1 Tf 0 Tc 9.3 0 0 9.3 313.14 240.49 Tm (q )Tj /T1_0 1 Tf 0.05 Tc 7.7014 0 0 7.6 321.4 240.49 Tm (ODD )Tj 0.0084 Tc 9.5 0 0 9.5 28.24 218.71 Tm (Again, )Tj 0.039 Tc 3.138 0 Td (consider )Tj 0 Tc 4.054 0 Td (a )Tj 0.0406 Tc 0.861 0 Td (twisted )Tj 0.0374 Tc 3.517 0 Td (cubic )Tj 0 Tc 2.652 0 Td (C )Tj 0.04 Tc 0.929 0 Td (of )Tj /T1_3 1 Tf 0.0339 Tc 9.7 0 0 9.7 183.31 218.71 Tm (PG\(3, )Tj /T1_1 1 Tf -0.035 Tc 8.3892 0 0 10 210.3 218.71 Tm (q\) )Tj /T1_0 1 Tf 0.0349 Tc 9.5 0 0 9.5 221.5 218.71 Tm (in )Tj 0.0482 Tc 1.175 0 Td (its )Tj 0.0335 Tc 1.42 0 Td (canonical )Tj 0.0181 Tc 4.452 0 Td (form: )Tj /T1_1 1 Tf 0.05 Tc 9.5089 0 0 6.3001 121.6 195.85 Tm (XO=t3, )Tj 12.6425 0 0 6.3001 166.09 195.85 Tm (XI=t)Tj 0 Tc 6.3001 0 0 6.3001 191.77 199.81 Tm (2)Tj 0.725 -0.629 Td (, )Tj 0.05 Tc 10.526 0 0 6.3001 209.63 195.85 Tm (X2=t, )Tj /T1_0 1 Tf 12.3942 0 0 9.5 249.08 195.85 Tm (x3=I, )Tj /T1_3 1 Tf 0 Tc 10.6 0 0 10.6 27.95 172.99 Tm (t )Tj /T1_0 1 Tf 8.7 0 0 8.7 35.77 172.99 Tm (E )Tj 0.05 Tc 8.0279 0 0 7.1 45.09 172.99 Tm ('\)'+. )Tj 0.0228 Tc 9.5 0 0 9.5 66.21 172.99 Tm (We )Tj 0.0305 Tc 1.916 0 Td (recall )Tj 0.05 Tc 10.3974 0 0 9.5 111.21 172.99 Tm (that )Tj 0 Tc 9.5 0 0 9.5 132.56 172.99 Tm (C )Tj -0.0246 Tc 1.063 0 Td (is )Tj 0.05 Tc 9.6991 0 0 9.5 153.16 172.99 Tm (the )Tj 0.0241 Tc 9.5 0 0 9.5 170.37 172.99 Tm (complete )Tj 0.0309 Tc 4.283 0 Td (intersection )Tj 0.05 Tc 9.5989 0 0 9.5 262.71 172.99 Tm (of )Tj 9.6825 0 0 9.5 274.66 172.99 Tm (three )Tj 0.043 Tc 9.5 0 0 9.5 300.69 172.99 Tm (quadrics )Tj 0 Tc 4.214 0 Td (Y)Tj /T1_2 1 Tf 6.3001 0 0 6.3001 346.15 171.37 Tm (I )Tj /T1_0 1 Tf 11.4 0 0 11.4 354.18 172.99 Tm (= )Tj -0.035 Tc 8.8261 0 0 9.6 365.31 172.99 Tm (0, )Tj 0 Tc 9.5 0 0 9.5 28.24 161.29 Tm (Y)Tj /T1_2 1 Tf 6.2 0 0 6.2 33.79 159.85 Tm (2 )Tj /T1_0 1 Tf 12.1 0 0 12.1 40.62 161.29 Tm (= )Tj -0.035 Tc 9.3453 0 0 9.5 50.12 161.29 Tm (0, )Tj 0 Tc 9.5 0 0 9.5 61 161.29 Tm (Y)Tj /T1_2 1 Tf 6.2 0 0 6.2 66.53 159.85 Tm (3 )Tj /T1_0 1 Tf 13 0 0 13 73.91 161.29 Tm (= )Tj 9.5 0 0 9.5 84.32 161.29 Tm (0 )Tj 0.05 Tc 9.5989 0 0 9.5 92.25 161.29 Tm (of )Tj /T1_3 1 Tf 9.7361 0 0 9.7 103.75 161.29 Tm (PG\(3, )Tj -0.0312 Tc 10.2 0 0 10.2 131.7 161.29 Tm (q\), )Tj 0 Tc 1.394 0 Td (q )Tj /T1_2 1 Tf -0.035 Tc 5.8501 0 0 10.4 153.85 161.29 Tm (2:: )Tj /T1_0 1 Tf 0 Tc 9.5 0 0 9.5 163.7 161.29 Tm (7 )Tj -0.035 Tc 8.838 0 0 9.5 171.87 161.29 Tm ([5, )Tj 0.0316 Tc 9.5 0 0 9.5 184.81 161.29 Tm (Lemma )Tj 0.004 Tc 3.504 0 Td (21.1.6 )Tj -0.035 Tc 10.0066 0 0 10.4 246.48 161.29 Tm (\(i\)], )Tj 0.0445 Tc 9.5 0 0 9.5 263.87 161.29 Tm (where )Tj 0.0222 Tc -24.784 -4.813 Td (Associate )Tj 0.05 Tc 10.0407 0 0 9.5 71.62 115.57 Tm (to )Tj 0 Tc 9.5 0 0 9.5 84.86 115.57 Tm (a )Tj 0.05 Tc 9.7016 0 0 9.5 93.61 115.57 Tm (point )Tj /T1_2 1 Tf 10.7387 0 0 9.8 120 115.57 Tm (P\(X\) )Tj /T1_0 1 Tf 0.04 Tc 9.5 0 0 9.5 148.05 115.57 Tm (of )Tj /T1_3 1 Tf 0.0432 Tc 9.7 0 0 9.7 160.09 115.57 Tm (PG\(3, )Tj /T1_1 1 Tf -0.035 Tc 9.0101 0 0 10 187.61 115.57 Tm (q\), )Tj /T1_0 1 Tf 0 Tc 9.5 0 0 9.5 202.66 115.57 Tm (X )Tj /T1_3 1 Tf -0.035 Tc 10.1745 0 0 10.2 226.96 115.57 Tm (\(xo, )Tj /T1_1 1 Tf 0.05 Tc 8.8257 0 0 6.3001 244.35 115.57 Tm (Xl, )Tj 7.0275 0 0 6.3001 258.19 115.57 Tm (X2, )Tj 7.8328 0 0 6.3001 272.24 115.57 Tm (X3\), )Tj /T1_0 1 Tf 9.9723 0 0 9.5 293.2 115.57 Tm (the )Tj 0.0477 Tc 9.5 0 0 9.5 311.23 115.57 Tm (point )Tj 0.05 Tc 9.5548 0 0 9.5 337.13 115.57 Tm (with )Tj -0.0109 Tc 9.5 0 0 9.5 359.63 115.57 Tm (ho\255)Tj 0.0166 Tc -34.883 -1.175 Td (mogeneous )Tj 0.0493 Tc 5.052 0 Td (coordinates )Tj /T1_3 1 Tf 0.0135 Tc 9.8 0 0 9.8 128.68 104.41 Tm (\(YI, )Tj 0 Tc 1.794 0 Td (Y)Tj 6.5001 0 0 6.5001 152.07 102.96 Tm (2)Tj 0.729 0.223 Td (, )Tj 9.8 0 0 9.8 160.48 104.41 Tm (Y)Tj 6.5001 0 0 6.5001 166.26 102.96 Tm (3)Tj 0.708 0.223 Td (\) )Tj /T1_0 1 Tf 0.04 Tc 9.5 0 0 9.5 177.03 104.41 Tm (of )Tj 0 Tc 1.117 0 Td (a )Tj 0.0289 Tc 0.769 0 Td (projective )Tj 0.0347 Tc 4.623 0 Td (plane )Tj 0.0415 Tc 6.5001 0 0 6.5001 263.84 104.41 Tm (1r )Tj 0.0412 Tc 9.5 0 0 9.5 273.16 104.41 Tm (isomorphic )Tj 0.05 Tc 9.8224 0 0 9.5 322.72 104.41 Tm (to )Tj /T1_3 1 Tf 0.0385 Tc 9.7 0 0 9.7 334.51 104.41 Tm (PG\(2, )Tj /T1_1 1 Tf -0.035 Tc 9.1769 0 0 9.8 361.84 104.41 Tm (q\). )Tj /T1_0 1 Tf -0.0002 Tc 9.5 0 0 9.5 28.4 92.89 Tm (Hence )Tj 0 Tc 2.931 0 Td (a )Tj 0.05 Tc 9.9422 0 0 9.5 64.28 92.89 Tm (point )Tj /T1_3 1 Tf 9.8105 0 0 9.8 90.7 92.89 Tm (\(AI, )Tj 0 Tc 9.8 0 0 9.8 110.13 92.89 Tm (A)Tj /T1_1 1 Tf 5.9001 0 0 5.9001 117.44 91.45 Tm (2)Tj 0.773 0.244 Td (, )Tj /T1_3 1 Tf 9.8 0 0 9.8 126.15 92.89 Tm (A)Tj /T1_1 1 Tf 5.9001 0 0 5.9001 133.29 91.45 Tm (3)Tj 0.764 0.244 Td (\) )Tj /T1_0 1 Tf 8.6 0 0 8.6 144.31 92.89 Tm (E )Tj 0.0415 Tc 6.5001 0 0 6.5001 152.96 92.89 Tm (1r )Tj 0.023 Tc 9.5 0 0 9.5 162.27 92.89 Tm (corresponds )Tj 0.0211 Tc 5.445 0 Td (to )Tj 0.037 Tc 1.213 0 Td (those )Tj 0.0399 Tc 2.637 0 Td (points )Tj 0.05 Tc 9.8076 0 0 9.5 279.27 92.89 Tm (of )Tj /T1_3 1 Tf 10.0104 0 0 9.7 290.96 92.89 Tm (PG\(3, )Tj -0.035 Tc 9.4213 0 0 9.7 319.44 92.89 Tm (q\) )Tj /T1_0 1 Tf 0.023 Tc 9.5 0 0 9.5 330.89 92.89 Tm (such )Tj 0.05 Tc 10.1785 0 0 9.5 352.42 92.89 Tm (that )Tj -0.035 Tc 9.5256 0 0 10.2 361.33 69.67 Tm (\(6\) )Tj 0.0492 Tc 9.5 0 0 9.5 28.4 46.99 Tm (But, )Tj -0.035 Tc 9.2755 0 0 9.5 50.75 46.99 Tm (we )Tj 0.0317 Tc 9.5 0 0 9.5 65.97 46.99 Tm (observe )Tj 0.05 Tc 10.3974 0 0 9.5 102.21 46.99 Tm (that )Tj 9.6991 0 0 9.5 124.18 46.99 Tm (the )Tj 0.0376 Tc 9.5 0 0 9.5 141.93 46.99 Tm (quadrics )Tj /T1_1 1 Tf 0.05 Tc 13.6885 0 0 11.5 181.21 46.99 Tm (Ii )Tj /T1_0 1 Tf 0 Tc 11.4 0 0 11.4 194.16 46.99 Tm (= )Tj 9.6 0 0 9.6 205.64 46.99 Tm (0 )Tj 0.0213 Tc 9.5 0 0 9.5 214.46 46.99 Tm (are )Tj 0.0266 Tc 1.745 0 Td (linearly )Tj 0.05 Tc 9.6593 0 0 9.5 266.14 46.99 Tm (independent )Tj 9.6349 0 0 9.5 323.18 46.99 Tm (and )Tj 0.0344 Tc 9.5 0 0 9.5 342.81 46.99 Tm (contain )Tj -0.035 Tc 8.378 0 0 9.5 28.35 35.47 Tm (C. )Tj 0.0451 Tc 9.5 0 0 9.5 40.78 35.47 Tm (This )Tj 0.05 Tc 9.6304 0 0 9.5 62.62 35.47 Tm (means )Tj 10.3974 0 0 9.5 92.85 35.47 Tm (that )Tj 9.6991 0 0 9.5 114.1 35.47 Tm (the )Tj 9.5232 0 0 9.5 130.69 35.47 Tm (points )Tj -0.0241 Tc 9.5 0 0 9.5 160.63 35.47 Tm (\(6\) )Tj 0.0308 Tc 1.555 0 Td (are )Tj 0.0246 Tc 1.668 0 Td (on )Tj 0.0449 Tc 1.372 0 Td (the )Tj 0.0309 Tc 1.699 0 Td (intersection )Tj 0.05 Tc 9.5989 0 0 9.5 271.71 35.47 Tm (of )Tj 0.0285 Tc 9.5 0 0 9.5 283.12 35.47 Tm (two )Tj 0.043 Tc 1.963 0 Td (quadrics )Tj 0.041 Tc 4.1 0 Td (through )Tj -0.035 Tc 9.6718 0 0 10.1 194.06 12.61 Tm (105 )Tj ET endstream endobj 196 0 obj <>/Filter/CCITTFaxDecode/Height 1872/Length 60853/Name/Im0/Subtype/Image/Type/XObject/Width 2240>>stream *. *R *.GQ(QQ)QQ# A dJTdJdEH2ˆA dEH2$uQu:F@T]Dm JlD *. *R1)PEDr莢9QtGQF@T]F@TBc *R1)P A dJT 2*CR!@T]G *R1Q)P A dJT 2*CR!F@T]D *.#DuQ. *.GQQ# lBGP1B9$YJh2(My6-GG2>HrY莈#fdtG() frЈAr(pÙ,BwA#Ě% "V8nB!fDD$:BF]chD<&9pv*.;t"RCH*,bqi|C+3tGG3!a5àAN2>@%wKtGS%8 D?BA:ޮ D$:mYGܯ65(l-+q_}רI7X"=aESh":>_֗Ť4+Fx_ur/{tGES3#<#i3 N20Q#aSoZ0a#@ds^21D݌qw̴_I]Z"]VZ,r4\0/O+Otkh ِүoޫ2:":>萍y"(㤩&!B#]!a] BX%r0&JĎGZGbGGfSdb!k.~3 h!-إw0"GIAJI1 鱉M&L$M˲(KZMЊFqR !f4^?Ѵg &_#Ed. 7 ^c L":#:#:.莈.nqӤ޾v %ʂ G!d1,q4"Ћn%F4OzX6t V/WDDDDDEZWW%{Ld4GEѢ#EA""9 5F#7681|JǤ iCv)R:v*IB#q&GDt]٤GDxGDy3`"E(Plh'Z(0paҶZ 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1.192 0 Td (a )Tj 0.0382 Tc 0.826 0 Td (point )Tj /T1_1 1 Tf 0 Tc 10 0 0 10 99.97 521.29 Tm (R )Tj /T1_0 1 Tf 11.4 0 0 11.4 109.92 521.29 Tm (= )Tj 9.7 0 0 9.7 119.66 521.29 Tm [(P )-189(\( )]TJ -0.035 Tc 9.5091 0 0 9.7 134.13 521.29 Tm (1, )Tj /T1_2 1 Tf 6.157 0 0 8.4 150.42 521.29 Tm (J-l, )Tj 6.6994 0 0 8.4 168.42 521.29 Tm (J-lv )Tj /T1_3 1 Tf 0 Tc 8.4 0 0 8.4 181.55 521.29 Tm (-)Tj /T1_1 1 Tf 0.05 Tc 7.8099 0 0 6.5001 190.34 521.29 Tm (W, )Tj /T1_2 1 Tf 0.0039 Tc 8.4 0 0 8.4 210.39 521.29 Tm (\(v)Tj 0 Tc 0.951 0.45 Td (2 )Tj /T1_3 1 Tf 0.823 -0.45 Td (-)Tj /T1_2 1 Tf 0.05 Tc 8.8485 0 0 8.4 234.34 521.29 Tm (w\) )Tj -0.035 Tc 5.4773 0 0 8.4 245.47 521.29 Tm (J-l )Tj /T1_3 1 Tf 0 Tc 8.4 0 0 8.4 254.09 521.29 Tm (-)Tj /T1_2 1 Tf 0.05 Tc 9.099 0 0 8.4 263.31 521.29 Tm (vw )Tj /T1_3 1 Tf 0 Tc 8.4 0 0 8.4 277.77 521.29 Tm [(\) )-45(. )]TJ /T1_0 1 Tf 0.0438 Tc 9.5 0 0 9.5 20.15 500.41 Tm (Using )Tj 0.05 Tc 9.6991 0 0 9.5 48.04 500.41 Tm (the )Tj 0.0434 Tc 9.5 0 0 9.5 64.43 500.41 Tm (relation )Tj 0.0017 Tc 3.779 0 Td (\(5\), )Tj -0.035 Tc 9.2755 0 0 9.5 117.53 500.41 Tm (we )Tj -0.0062 Tc 9.5 0 0 9.5 131.48 500.41 Tm (find )Tj 0.05 Tc 10.1785 0 0 9.5 150.28 500.41 Tm (that )Tj /T1_1 1 Tf 0 Tc 10 0 0 10 139.03 472.69 Tm (R )Tj /T1_0 1 Tf 11.4 0 0 11.4 148.62 472.69 Tm (= )Tj /T1_3 1 Tf 9.3 0 0 9.3 158.37 472.69 Tm (P )Tj 0.0219 Tc 1.031 0 Td (\(1, )Tj /T1_2 1 Tf -0.035 Tc 6.0104 0 0 8.4 189.49 472.69 Tm (J-l, )Tj 6.3812 0 0 8.4 207.66 472.69 Tm (J-l2, )Tj 7.8787 0 0 8.4 229.61 472.69 Tm (J-l3\) )Tj /T1_0 1 Tf 0.05 Tc 10.0232 0 0 9.5 20.15 455.59 Tm (with )Tj /T1_2 1 Tf -0.035 Tc 5.2948 0 0 8.4 44.23 455.59 Tm (J-l )Tj /T1_0 1 Tf 0 Tc 8.7 0 0 8.7 55.03 455.59 Tm (E )Tj -0.035 Tc 6.8076 0 0 9 65.26 455.59 Tm ('Y. )Tj 0.0451 Tc 9.5 0 0 9.5 81.46 455.59 Tm (This )Tj 0.0263 Tc 2.413 0 Td (means )Tj 0.05 Tc 9.9596 0 0 9.5 134.44 455.59 Tm (that )Tj /T1_1 1 Tf -0.035 Tc 14.3332 0 0 15.6 155.97 455.59 Tm (vi )Tj /T1_0 1 Tf 0.03 Tc 9.5 0 0 9.5 170.81 455.59 Tm (represents )Tj 0.05 Tc 9.6991 0 0 9.5 216.7 455.59 Tm (the )Tj 0.0358 Tc 9.5 0 0 9.5 234.45 455.59 Tm (congruence )Tj 0.04 Tc 5.457 0 Td (of )Tj 0.05 Tc 9.5625 0 0 9.5 298.24 455.59 Tm (the )Tj 0.0091 Tc 9.5 0 0 9.5 315.81 455.59 Tm (chords )Tj 0.0021 Tc 3.202 0 Td (of )Tj 0 Tc 1.231 0 Td (a )Tj 0.05 Tc 9.6147 0 0 9.5 20.32 444.07 Tm (twisted )Tj 0.0185 Tc 9.5 0 0 9.5 54.27 444.07 Tm (cubic )Tj -0.035 Tc 8.7969 0 0 9.5 78.75 444.07 Tm (C, )Tj 0.0161 Tc 9.5 0 0 9.5 90.35 444.07 Tm (where )Tj 0 Tc 2.833 0 Td (C )Tj -0.035 Tc 9.3682 0 0 9.5 126.1 444.07 Tm (is )Tj 0.0449 Tc 9.5 0 0 9.5 135.34 444.07 Tm (the )Tj 0.0455 Tc 1.637 0 Td (set )Tj 0.04 Tc 1.539 0 Td (of )Tj 0.05 Tc 9.5625 0 0 9.5 176.2 444.07 Tm (the )Tj 0.003 Tc 9.5 0 0 9.5 192.14 444.07 Tm (focal )Tj 0.0437 Tc 2.361 0 Td (points )Tj 0.05 Tc 9.8076 0 0 9.5 243.09 444.07 Tm (of )Tj 0.0483 Tc 9.5 0 0 9.5 254.03 444.07 Tm (such )Tj 0 Tc 2.334 0 Td (a )Tj 0.0121 Tc 0.816 0 Td (congruence; )Tj -0.0186 Tc 5.396 0 Td (see )Tj -0.035 Tc 8.6078 0 0 9.5 350.61 444.07 Tm ([7]. )Tj 0.0008 Tc 9.3 0 0 9.3 133.88 411.13 Tm (4. )Tj 0 Tc 1.434 0 Td (A )Tj 0.05 Tc 7.6546 0 0 7.4001 158.62 411.13 Tm (NEW )Tj 0.03 Tc 7.4001 0 0 7.4001 180.87 411.13 Tm (FAMILY )Tj 0.05 Tc 7.8576 0 0 7.4001 214.3 411.13 Tm (OF )Tj 7.8756 0 0 7.4001 229.06 411.13 Tm (CAPS )Tj 9.9506 0 0 9.5 20.27 389.17 Tm (In )Tj /T1_3 1 Tf -0.035 Tc 9.309 0 0 10.3 33.48 389.17 Tm ([3], )Tj /T1_0 1 Tf 0.05 Tc 9.7985 0 0 9.5 49.42 389.17 Tm (it )Tj 0.0275 Tc 9.5 0 0 9.5 59.39 389.17 Tm (has )Tj 0.044 Tc 1.802 0 Td (been )Tj 0.0167 Tc 2.392 0 Td (shown )Tj 0.05 Tc 10.0691 0 0 9.5 128.5 389.17 Tm (that )Tj 0.0138 Tc 9.5 0 0 9.5 148.87 389.17 Tm (by )Tj 0.05 Tc 9.6485 0 0 9.5 162.04 389.17 Tm (starting )Tj 0.0091 Tc 9.5 0 0 9.5 197.72 389.17 Tm (from )Tj 0.05 Tc 9.6991 0 0 9.5 220.3 389.17 Tm (the )Tj 0.0455 Tc 9.5 0 0 9.5 237.11 389.17 Tm (set )Tj 0.05 Tc 9.5989 0 0 9.5 252.45 389.17 Tm (of )Tj 0.0281 Tc 9.5 0 0 9.5 263.96 389.17 Tm (all )Tj 0.009 Tc 1.46 0 Td (conics )Tj 0.0211 Tc 2.994 0 Td (of )Tj /T1_1 1 Tf 0.0447 Tc 9.4 0 0 9.4 317.41 389.17 Tm (PG\(2, )Tj -0.035 Tc 9.9166 0 0 10.4 344.28 389.17 Tm (q\), )Tj 0 Tc 10.4 0 0 10.4 358.32 389.17 Tm (q )Tj /T1_0 1 Tf 0.05 Tc 9.8638 0 0 9.5 20.25 377.65 Tm (odd, )Tj 0.0111 Tc 9.5 0 0 9.5 42.83 377.65 Tm (which )Tj 0.0308 Tc 2.871 0 Td (are )Tj 0.0274 Tc 1.669 0 Td (inscribed )Tj 0.0349 Tc 4.263 0 Td (in )Tj 0 Tc 1.173 0 Td (a )Tj 0.026 Tc 0.804 0 Td (triangle, )Tj 0.05 Tc 9.7985 0 0 9.5 182.44 377.65 Tm (it )Tj -0.035 Tc 9.3682 0 0 9.5 191.8 377.65 Tm (is )Tj 0.0179 Tc 9.5 0 0 9.5 201.25 377.65 Tm (possible )Tj 0.05 Tc 9.8224 0 0 9.5 237.22 377.65 Tm (to )Tj 9.6637 0 0 9.5 249.03 377.65 Tm (construct )Tj 0 Tc 9.5 0 0 9.5 292.04 377.65 Tm (a )Tj 0.0276 Tc 0.816 0 Td (cap )Tj 0.0211 Tc 1.819 0 Td (of )Tj /T1_1 1 Tf 0.04 Tc 9.4 0 0 9.4 328.03 377.65 Tm (PG\(5, )Tj /T1_2 1 Tf -0.035 Tc 8.1741 0 0 10 354.66 377.65 Tm (q\) )Tj /T1_0 1 Tf 0.05 Tc 9.8076 0 0 9.5 20.25 366.13 Tm (of )Tj 0.0153 Tc 9.5 0 0 9.5 31.01 366.13 Tm (size )Tj /T1_2 1 Tf -0.035 Tc 7.9644 0 0 8.4 49.37 366.13 Tm (2q2 )Tj /T1_3 1 Tf 0 Tc 8.4 0 0 8.4 64.91 366.13 Tm (-)Tj /T1_2 1 Tf 0.958 0 Td (q )Tj /T1_3 1 Tf 12.9 0 0 12.9 78.81 366.13 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 9.0505 0 0 9.5 87.61 366.13 Tm (2. )Tj 0.0147 Tc 9.5 0 0 9.5 99.19 366.13 Tm (Such )Tj 0 Tc 2.357 0 Td (a )Tj 0.037 Tc 0.778 0 Td (cap )Tj 0.05 Tc 9.5054 0 0 9.5 145.96 366.13 Tm (turns )Tj 9.686 0 0 9.5 170.01 366.13 Tm (out )Tj 9.6041 0 0 9.5 186.46 366.13 Tm (to )Tj 9.5181 0 0 9.5 197.65 366.13 Tm (be )Tj 9.5625 0 0 9.5 210.22 366.13 Tm (the )Tj 0.042 Tc 9.5 0 0 9.5 226.08 366.13 Tm (union )Tj 0.05 Tc 9.8076 0 0 9.5 252.45 366.13 Tm (of )Tj 0.038 Tc 9.5 0 0 9.5 263.32 366.13 Tm (two )Tj 0.006 Tc 1.895 0 Td (Veronese )Tj 0.007 Tc 4.119 0 Td (surfaces )Tj 0.0211 Tc 3.661 0 Td (of )Tj /T1_1 1 Tf 0.05 Tc 9.9418 0 0 9.4 20.6 354.61 Tm (PG\(5, )Tj /T1_2 1 Tf -0.035 Tc 8.3892 0 0 10 49.2 354.61 Tm (q\) )Tj /T1_0 1 Tf 0.0206 Tc 9.5 0 0 9.5 60.11 354.61 Tm (which )Tj 0.0369 Tc 2.841 0 Td (meet )Tj -0.003 Tc 2.419 0 Td (in )Tj 0.05 Tc 9.6991 0 0 9.5 120.4 354.61 Tm (the )Tj 0.0277 Tc 9.5 0 0 9.5 136.26 354.61 Tm (union )Tj 0.0211 Tc 2.681 0 Td (of )Tj 0.0416 Tc 1.087 0 Td (three )Tj 0.0014 Tc 2.494 0 Td (conics )Tj 0.0349 Tc 2.891 0 Td (pairwise )Tj 0.0378 Tc 3.951 0 Td (intersecting )Tj 0.016 Tc 5.4 0 Td (in )Tj -0.0102 Tc 1.098 0 Td (one )Tj 0.0223 Tc 1.735 0 Td (point. )Tj 0.0202 Tc -33.515 -1.213 Td (Now, )Tj -0.035 Tc 9.2755 0 0 9.5 45.71 343.09 Tm (we )Tj 0.0105 Tc 9.5 0 0 9.5 59.75 343.09 Tm (have )Tj 0.0231 Tc 2.299 0 Td (seen )Tj 0.05 Tc 10.1785 0 0 9.5 102.22 343.09 Tm (that )Tj 0.0328 Tc 9.5 0 0 9.5 122.59 343.09 Tm (by )Tj 0.05 Tc 9.5401 0 0 9.5 135.59 343.09 Tm (starting )Tj 0.0091 Tc 9.5 0 0 9.5 170.54 343.09 Tm (from )Tj 0.05 Tc 9.6991 0 0 9.5 192.94 343.09 Tm (the )Tj 0.0205 Tc 9.5 0 0 9.5 209.25 343.09 Tm (chords )Tj 0.05 Tc 9.8699 0 0 9.5 239.12 343.09 Tm (and )Tj 0.0373 Tc 9.5 0 0 9.5 258.02 343.09 Tm (axes )Tj 0.05 Tc 9.5989 0 0 9.5 279.27 343.09 Tm (of )Tj 0 Tc 9.5 0 0 9.5 290.42 343.09 Tm (a )Tj 0.0343 Tc 0.785 0 Td (twisted )Tj 0.0043 Tc 3.441 0 Td (cubic )Tj -0.035 Tc 8.5874 0 0 9.5 354.51 343.09 Tm (C, )Tj 0.05 Tc 9.7985 0 0 9.5 20.62 331.75 Tm (it )Tj 0.0133 Tc 9.5 0 0 9.5 30.52 331.75 Tm (is )Tj 0.0179 Tc 1.071 0 Td (possible )Tj 0.05 Tc 9.8224 0 0 9.5 76.66 331.75 Tm (to )Tj 0.0421 Tc 9.5 0 0 9.5 88.47 331.75 Tm (construct )Tj 0.0001 Tc 4.384 0 Td (two )Tj 0.0006 Tc 1.857 0 Td (Veronese )Tj 0.0124 Tc 4.157 0 Td (surfaces )Tj 0.04 Tc 3.756 0 Td (of )Tj /T1_1 1 Tf 0.05 Tc 9.8733 0 0 9.4 234.08 331.75 Tm (PG\(5, )Tj /T1_2 1 Tf -0.035 Tc 9.5106 0 0 10 262.3 331.75 Tm (q\), )Tj /T1_0 1 Tf 0.0159 Tc 9.5 0 0 9.5 276.83 331.75 Tm (which )Tj -0.035 Tc 9.1156 0 0 9.5 304.19 331.75 Tm (we )Tj -0.0021 Tc 9.5 0 0 9.5 318.05 331.75 Tm (have )Tj 0.0087 Tc 2.265 0 Td (called )Tj /T1_1 1 Tf -0.035 Tc 14.8641 0 0 15.6 20.79 317.71 Tm (vi )Tj /T1_0 1 Tf 0.05 Tc 9.7524 0 0 9.5 35.72 317.71 Tm (and )Tj /T1_1 1 Tf -0.035 Tc 11.5099 0 0 15.6 54.29 317.71 Tm (Vi\267 )Tj /T1_0 1 Tf 0.05 Tc 9.9219 0 0 9.5 32.84 307.45 Tm (Our )Tj 9.5338 0 0 9.5 52.82 307.45 Tm (aim )Tj 0.0349 Tc 9.5 0 0 9.5 71.02 307.45 Tm (in )Tj 0.05 Tc 9.5056 0 0 9.5 81.88 307.45 Tm (this )Tj 0.0253 Tc 9.5 0 0 9.5 100.31 307.45 Tm (section )Tj -0.035 Tc 9.3682 0 0 9.5 131.86 307.45 Tm (is )Tj 0.0211 Tc 9.5 0 0 9.5 141.1 307.45 Tm (to )Tj 0.0398 Tc 1.148 0 Td (construct )Tj 0 Tc 4.376 0 Td (a )Tj -0.0066 Tc 0.805 0 Td (new )Tj 0.0242 Tc 1.999 0 Td (family )Tj 0.05 Tc 9.8076 0 0 9.5 249.57 307.45 Tm (of )Tj 0.0466 Tc 9.5 0 0 9.5 260.55 307.45 Tm (caps )Tj 0.04 Tc 2.274 0 Td (of )Tj /T1_1 1 Tf 0.05 Tc 9.4619 0 0 9.4 293.11 307.45 Tm (PG\(5, )Tj -0.0019 Tc 9.3 0 0 9.3 320.52 307.45 Tm (q\), )Tj 0 Tc 1.452 0 Td (q )Tj /T1_0 1 Tf 13 0 0 13 341.21 307.45 Tm (= )Tj /T1_1 1 Tf -0.0085 Tc 9.3 0 0 9.3 350.59 307.45 Tm (ph, )Tj 0 Tc 15.6 0 0 15.6 20.28 294.31 Tm (P )Tj /T1_3 1 Tf -0.035 Tc 5.5908 0 0 10.6 29.55 294.31 Tm (::/= )Tj /T1_0 1 Tf -0.0163 Tc 9.3 0 0 9.3 41.47 294.31 Tm (3, )Tj 0.0415 Tc 9.5 0 0 9.5 52.64 294.31 Tm (embedded )Tj 0.0349 Tc 4.853 0 Td (in )Tj 0.05 Tc 9.5625 0 0 9.5 110.5 294.31 Tm (the )Tj 0.0047 Tc 9.5 0 0 9.5 127.4 294.31 Tm (Klein )Tj 0.0361 Tc 2.666 0 Td (quadric )Tj /T1_1 1 Tf -0.035 Tc 7.4023 0 0 9.5 187.25 294.31 Tm (1-l)Tj 0 Tc 7 0 0 7 195.77 297.91 Tm (5)Tj 0.657 -0.514 Td (, )Tj /T1_0 1 Tf -0.0051 Tc 9.5 0 0 9.5 206.65 294.31 Tm (by )Tj 0.024 Tc 1.412 0 Td (glueing )Tj /T1_1 1 Tf -0.035 Tc 14.8641 0 0 15.6 254.25 294.31 Tm (vi )Tj /T1_0 1 Tf 0.05 Tc 10.1049 0 0 9.5 269.18 294.31 Tm (and )Tj /T1_1 1 Tf -0.035 Tc 14.3332 0 0 15.6 289.17 294.31 Tm (vi )Tj /T1_0 1 Tf 0.0335 Tc 9.5 0 0 9.5 303.64 294.31 Tm (together )Tj 0.0114 Tc 3.952 0 Td (along )Tj 0.05 Tc 10.0314 0 0 9.5 20.68 282.97 Tm (their )Tj 0.0296 Tc 9.5 0 0 9.5 44.56 282.97 Tm (intersection. )Tj 0.05 Tc 11.0633 0 0 9.3 20.82 266.23 Tm (Lemma )Tj 9.8 0 0 9.3 60.44 266.23 Tm (4.1. )Tj /T1_1 1 Tf 9.6412 0 0 9.5 83.86 266.23 Tm (The )Tj 0 Tc 9.5 0 0 9.5 103.33 266.23 Tm (Veronese )Tj 0.0041 Tc 4.076 0 Td (surfaces )Tj -0.035 Tc 14.3332 0 0 15.6 177.21 266.23 Tm (vi )Tj 0.05 Tc 9.5024 0 0 9.5 191.1 266.23 Tm (and )Tj -0.035 Tc 11.2443 0 0 15.6 209.1 266.23 Tm (Vi )Tj 0.05 Tc 9.992 0 0 9.5 222.97 266.23 Tm (meet )Tj 0.0168 Tc 9.5 0 0 9.5 246.66 266.23 Tm (in )Tj 0 Tc 1.162 0 Td (q )Tj /T1_3 1 Tf 12.9 0 0 12.9 264.21 266.23 Tm (+ )Tj /T1_0 1 Tf 9.3 0 0 9.3 273.82 266.23 Tm (1 )Tj /T1_1 1 Tf 0.0301 Tc 9.5 0 0 9.5 281.48 266.23 Tm (points, )Tj 0.0122 Tc 3.351 0 Td (belonging )Tj /T1_0 1 Tf 0.0211 Tc 4.42 0 Td (to )Tj 0 Tc -35.194 -1.213 Td (a )Tj /T1_1 1 Tf 0.0298 Tc 0.859 0 Td (parabolic )Tj 0.0243 Tc 4.469 0 Td (quadric )Tj -0.035 Tc 9.5518 0 0 10.5 105.91 254.71 Tm (P4, )Tj 0.0139 Tc 9.5 0 0 9.5 122.53 254.71 Tm (namely, )Tj 0.0373 Tc 3.688 0 Td (the )Tj 0.0242 Tc 1.647 0 Td (intersection )Tj 0.0117 Tc 5.385 0 Td (of1-l)Tj 0 Tc 6.2 0 0 6.2 243.66 258.12 Tm (5 )Tj /T1_0 1 Tf 0.05 Tc 9.5157 0 0 9.2 251.83 254.71 Tm (by )Tj 0 Tc 9.5 0 0 9.5 264.86 254.71 Tm (a )Tj /T1_1 1 Tf 0.05 Tc 10.1285 0 0 9.5 273.01 254.71 Tm (non-tangent )Tj 0.0093 Tc 9.5 0 0 9.5 330.44 254.71 Tm (prime. )Tj 0.0195 Tc -32.559 -1.857 Td (Proof. )Tj /T1_0 1 Tf 0.05 Tc 9.569 0 0 9.5 51.76 237.07 Tm (The )Tj 0.0205 Tc 9.5 0 0 9.5 71.69 237.07 Tm (surfaces )Tj /T1_1 1 Tf -0.035 Tc 14.3332 0 0 15.6 108.63 237.07 Tm (vi )Tj /T1_0 1 Tf 0.05 Tc 9.5174 0 0 9.5 123.02 237.07 Tm (and )Tj /T1_1 1 Tf -0.035 Tc 11.2443 0 0 15.6 141.78 237.07 Tm (Vi )Tj /T1_0 1 Tf 0.0306 Tc 9.5 0 0 9.5 156.4 237.07 Tm (meet )Tj 0.016 Tc 2.476 0 Td (in )Tj /T1_1 1 Tf 0 Tc 1.215 0 Td (q )Tj /T1_3 1 Tf 12.9 0 0 12.9 198.69 237.07 Tm (+ )Tj /T1_0 1 Tf 9.3 0 0 9.3 208.66 237.07 Tm (1 )Tj 0.0358 Tc 9.5 0 0 9.5 216.73 237.07 Tm (points, )Tj 0.0191 Tc 3.396 0 Td (since )Tj 0.05 Tc 9.9723 0 0 9.5 273.76 237.07 Tm (the )Tj 0.0445 Tc 9.5 0 0 9.5 291.04 237.07 Tm (tangents )Tj 0.0211 Tc 4.074 0 Td (to )Tj 0.05 Tc 10.46 0 0 9.5 341.35 237.07 Tm (Care )Tj 10.2798 0 0 9.5 20.37 225.73 Tm (self-dual )Tj 9.5548 0 0 9.5 64.79 225.73 Tm (with )Tj 0.0308 Tc 9.5 0 0 9.5 87.83 225.73 Tm (respect )Tj 0.05 Tc 9.6041 0 0 9.5 121.3 225.73 Tm (to )Tj 0.0449 Tc 9.5 0 0 9.5 133.9 225.73 Tm (the )Tj 0.0136 Tc 1.801 0 Td (null )Tj 0.0446 Tc 2.048 0 Td (polarity )Tj 0.0106 Tc 3.874 0 Td (defined )Tj 0.05 Tc 9.5157 0 0 9.5 241.21 225.73 Tm (by )Tj /T1_1 1 Tf 0.0278 Tc 10.6 0 0 10.6 256.12 225.73 Tm (A. )Tj /T1_0 1 Tf 0.0095 Tc 9.5 0 0 9.5 273.79 225.73 Tm (Since, )Tj -0.0242 Tc 3.058 0 Td (for )Tj /T1_1 1 Tf 0 Tc 9.3 0 0 9.3 318.01 225.73 Tm (p )Tj /T1_2 1 Tf 11.7 0 0 11.7 327.45 225.73 Tm (f )Tj /T1_0 1 Tf -0.0088 Tc 9.2 0 0 9.2 338.47 225.73 Tm (3, )Tj 0.0449 Tc 9.5 0 0 9.5 350.08 225.73 Tm (the )Tj 0.05 Tc 9.7426 0 0 9.5 20.5 214.21 Tm (tangents )Tj 9.6041 0 0 9.5 60.1 214.21 Tm (to )Tj 0 Tc 9.5 0 0 9.5 71.54 214.21 Tm (C )Tj -0.0077 Tc 0.949 0 Td (lie )Tj 0.016 Tc 1.345 0 Td (in )Tj 0 Tc 1.173 0 Td (a )Tj 0.021 Tc 0.836 0 Td (general )Tj 0.0259 Tc 3.411 0 Td (linear )Tj 0.0269 Tc 2.746 0 Td (complex )Tj -0.0244 Tc 3.996 0 Td (\(see )Tj -0.035 Tc 8.838 0 0 10.6 227.67 214.21 Tm ([5, )Tj 0.05 Tc 9.8508 0 0 9.5 240.58 214.21 Tm (Th. )Tj 0.0154 Tc 9.5 0 0 9.5 260.4 214.21 Tm (21.1.2 )Tj -0.0058 Tc 3.007 0 Td (\(ii\)\)\) )Tj 0 Tc 2.004 0 Td (, )Tj 0.0405 Tc 0.544 0 Td (their )Tj 0.0096 Tc 2.343 0 Td (images )Tj 0.05 Tc 9.7439 0 0 9.5 20.7 202.87 Tm (under )Tj 9.6991 0 0 9.5 48.4 202.87 Tm (the )Tj 0.037 Tc 9.5 0 0 9.5 64.76 202.87 Tm (Plucker )Tj 0.0301 Tc 3.613 0 Td (embedding )Tj 0.0213 Tc 5.04 0 Td (are )Tj /T1_2 1 Tf 0 Tc 8.1 0 0 8.1 162.24 202.87 Tm (q )Tj /T1_3 1 Tf 12.4 0 0 12.4 168.82 202.87 Tm (+ )Tj /T1_0 1 Tf 9.3 0 0 9.3 177.88 202.87 Tm (1 )Tj 0.0361 Tc 9.5 0 0 9.5 185.59 202.87 Tm (points )Tj 0.0246 Tc 2.964 0 Td (on )Tj 0 Tc 1.401 0 Td (a )Tj 0.05 Tc 9.5107 0 0 9.5 234.73 202.87 Tm (parabolic )Tj 0.0361 Tc 9.5 0 0 9.5 277.47 202.87 Tm (quadric )Tj /T1_1 1 Tf 0 Tc 10 0 0 10 311.48 202.87 Tm (P)Tj 6.7 0 0 6.7 318 201.25 Tm (4)Tj 0.739 0.242 Td (, )Tj /T1_0 1 Tf 0.0312 Tc 9.5 0 0 9.5 327.87 202.87 Tm (obtained )Tj 0.05 Tc 9.5157 0 0 9.5 20.53 191.35 Tm (by )Tj 9.6662 0 0 9.5 34.65 191.35 Tm (cutting )Tj /T1_1 1 Tf -0.035 Tc 7.4023 0 0 9.5 67.55 191.35 Tm (1-l)Tj 0 Tc 6.2 0 0 6.2 76.08 194.77 Tm (5 )Tj /T1_0 1 Tf 0.0138 Tc 9.5 0 0 9.5 83.53 191.35 Tm (by )Tj 0 Tc 1.428 0 Td (a )Tj 0.05 Tc 10.0765 0 0 9.5 104.75 191.35 Tm (non-tangent )Tj 0.0201 Tc 9.5 0 0 9.5 161.65 191.35 Tm (prime. )Tj 0 Tc 9.6 0 0 9.6 197.54 191.35 Tm (0 )Tj 0.05 Tc 11.0255 0 0 9.5 20.65 155.35 Tm (Proposition )Tj 10.0202 0 0 9.5 80.96 155.35 Tm (4.2. )Tj /T1_1 1 Tf 9.5291 0 0 9.5 104.39 155.35 Tm (The )Tj 9.567 0 0 9.5 123.15 155.35 Tm (set )Tj 0 Tc 15.6 0 0 15.6 138.19 155.35 Tm (K )Tj /T1_3 1 Tf 8.1 0 0 8.1 149.27 155.35 Tm (= )Tj /T1_1 1 Tf -0.035 Tc 14.3332 0 0 15.6 159.39 155.35 Tm (vi )Tj /T1_3 1 Tf 0 Tc 11.2 0 0 11.2 172.05 155.35 Tm (u )Tj /T1_1 1 Tf -0.035 Tc 14.5986 0 0 15.6 180.45 155.35 Tm (vi )Tj 0.0141 Tc 9.5 0 0 9.5 194.46 155.35 Tm (is )Tj /T1_0 1 Tf 0 Tc 1.044 0 Td (a )Tj /T1_2 1 Tf -0.035 Tc 8.3598 0 0 8.4 212.37 155.35 Tm (\(2q2 )Tj /T1_3 1 Tf 0 Tc 12.4 0 0 12.4 231.64 155.35 Tm (+ )Tj /T1_2 1 Tf 8.4 0 0 8.4 241.08 155.35 Tm (q )Tj /T1_0 1 Tf 11.9 0 0 11.9 248.34 155.35 Tm (+ )Tj /T1_1 1 Tf 0.05 Tc 11.0372 0 0 9.5 258.77 155.35 Tm (I\)-cap )Tj 0.0376 Tc 9.5 0 0 9.5 292.24 155.35 Tm (embedded )Tj 0.0168 Tc 4.676 0 Td (in )Tj /T1_2 1 Tf 0.0089 Tc 9.6 0 0 9.6 347.22 155.35 Tm (?i)Tj 0 Tc 8.4 0 0 8.4 355.33 158.59 Tm (5)Tj 0.561 -0.386 Td (. )Tj 0.0176 Tc 9.1 0 0 9.1 20.77 138.43 Tm (Proof. )Tj /T1_0 1 Tf 0.0416 Tc 9.5 0 0 9.5 51.62 138.43 Tm (From )Tj 0.05 Tc 9.5067 0 0 9.5 76.45 138.43 Tm (Lemma )Tj -0.0046 Tc 9.3 0 0 9.3 110.48 138.43 Tm (4.1, )Tj /T1_2 1 Tf -0.035 Tc 10.5777 0 0 13.2 128.7 138.43 Tm (IKI )Tj /T1_0 1 Tf 0 Tc 12.1 0 0 12.1 144.84 138.43 Tm (= )Tj /T1_2 1 Tf -0.035 Tc 7.7368 0 0 8.4 154.67 138.43 Tm (2q2 )Tj /T1_3 1 Tf 0 Tc 12.4 0 0 12.4 169.72 138.43 Tm (+ )Tj /T1_2 1 Tf 8.4 0 0 8.4 178.26 138.43 Tm (q )Tj /T1_3 1 Tf 12.4 0 0 12.4 184.66 138.43 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 9.2294 0 0 9.5 193.54 138.43 Tm (1. )Tj 0.0114 Tc 9.5 0 0 9.5 205.34 138.43 Tm (By )Tj 0.0224 Tc 1.481 0 Td (way )Tj 0.05 Tc 9.5989 0 0 9.5 238.77 138.43 Tm (of )Tj 0.0419 Tc 9.5 0 0 9.5 249.75 138.43 Tm (contradiction, )Tj 0.02 Tc 6.438 0 Td (suppose )Tj 0.05 Tc 10.0691 0 0 9.5 345.94 138.43 Tm (that )Tj 9.8466 0 0 9.5 20.68 127.08 Tm (there )Tj 0.0261 Tc 9.5 0 0 9.5 46.7 127.08 Tm (exist )Tj 0.05 Tc 9.5184 0 0 9.5 70 127.08 Tm (three )Tj 0.0183 Tc 9.5 0 0 9.5 95.49 127.08 Tm (collinear )Tj 0.0324 Tc 4.046 0 Td (points )Tj /T1_2 1 Tf 0.0496 Tc 9.1 0 0 9.1 162.97 127.08 Tm (PI )Tj 0.05 Tc 9.423 0 0 9.1 173.82 127.08 Tm (,P)Tj 0 Tc 6.2 0 0 6.2 182.24 125.83 Tm (2 )Tj 0.05 Tc 9.423 0 0 9.1 186.78 127.08 Tm (,P)Tj 0 Tc 6.2 0 0 6.2 195.02 125.65 Tm (3 )Tj /T1_0 1 Tf 0.0057 Tc 9.5 0 0 9.5 203.31 127.08 Tm (on )Tj /T1_2 1 Tf 0 Tc 9.1 0 0 9.1 216.78 127.08 Tm (K )Tj /T1_0 1 Tf 0.05 Tc 9.7524 0 0 9.5 229.76 127.08 Tm (and )Tj 0.0491 Tc 9.5 0 0 9.5 249.22 127.08 Tm (let )Tj /T1_2 1 Tf 0 Tc 9.1 0 0 9.1 264.17 127.08 Tm (l )Tj /T1_0 1 Tf 0.05 Tc 9.8842 0 0 9.5 271.09 127.08 Tm (be )Tj 9.6991 0 0 9.5 285.28 127.08 Tm (the )Tj 0.005 Tc 9.5 0 0 9.5 302.32 127.08 Tm (line )Tj 0.0242 Tc 1.951 0 Td (containing )Tj 0.05 Tc 9.7192 0 0 9.5 20.68 115.75 Tm (them. )Tj 0.0493 Tc 9.5 0 0 9.5 50.36 115.75 Tm (By )Tj 0.0455 Tc 1.592 0 Td (Bezout's )Tj 0.033 Tc 4.095 0 Td (theorem, )Tj /T1_1 1 Tf 0 Tc 4.198 0 Td (l )Tj /T1_0 1 Tf -0.0246 Tc 0.646 0 Td (is )Tj 0.0311 Tc 1.041 0 Td (contained )Tj 0.016 Tc 4.548 0 Td (in )Tj /T1_1 1 Tf -0.035 Tc 7.4023 0 0 9.5 214.25 115.75 Tm (1-l)Tj 0 Tc 6.2 0 0 6.2 222.78 119.17 Tm (5)Tj 0.755 -0.552 Td (. )Tj /T1_0 1 Tf 0.05 Tc 9.7889 0 0 9.5 234.64 115.75 Tm (The )Tj 9.6825 0 0 9.5 254.86 115.75 Tm (three )Tj 0.0399 Tc 9.5 0 0 9.5 280.09 115.75 Tm (points )Tj 0.0078 Tc 3.039 0 Td (above )Tj 0.036 Tc 2.805 0 Td (cannot )Tj 0.0453 Tc -33.147 -1.307 Td (belong )Tj 0.05 Tc 9.6041 0 0 9.5 51.82 103.33 Tm (to )Tj /T1_1 1 Tf -0.035 Tc 14.3332 0 0 15.6 63.45 103.33 Tm (vi )Tj /T1_0 1 Tf 0.04 Tc 9.5 0 0 9.5 77.13 103.33 Tm (or )Tj /T1_1 1 Tf -0.035 Tc 11.6792 0 0 15.6 88.67 103.33 Tm (Vi, )Tj /T1_0 1 Tf 0.0049 Tc 9.5 0 0 9.5 105.17 103.33 Tm (since )Tj 0.05 Tc 9.7633 0 0 9.5 128.35 103.33 Tm (both )Tj /T1_1 1 Tf -0.035 Tc 14.5986 0 0 15.6 150.21 103.33 Tm (vi )Tj /T1_0 1 Tf 0.05 Tc 9.5174 0 0 9.5 164.06 103.33 Tm (and )Tj /T1_1 1 Tf -0.035 Tc 14.5986 0 0 15.6 182.07 103.33 Tm (vi )Tj /T1_0 1 Tf 0.0308 Tc 9.5 0 0 9.5 195.92 103.33 Tm (are )Tj 0.0276 Tc 1.631 0 Td (caps )Tj -0.035 Tc 9.0221 0 0 9.5 232.88 103.33 Tm ([6, )Tj 0.05 Tc 9.7846 0 0 9.5 245.83 103.33 Tm (Lemma )Tj -0.0074 Tc 9.5 0 0 9.5 280.74 103.33 Tm (25.2.5]. )Tj 0.0303 Tc 3.545 0 Td (By )Tj 0.0315 Tc 1.499 0 Td (virtue )Tj 0.0211 Tc 2.835 0 Td (of )Tj 0.05 Tc 10.1089 0 0 9.5 20.86 91.99 Tm (the )Tj 0.0307 Tc 9.5 0 0 9.5 38.3 91.99 Tm (Plucker )Tj 0.0306 Tc 3.594 0 Td (embedding, )Tj 0.05 Tc 9.6991 0 0 9.5 123.46 91.99 Tm (the )Tj 0.0208 Tc 9.5 0 0 9.5 139.95 91.99 Tm (collinearity )Tj 0.04 Tc 5.116 0 Td (of )Tj 0.05 Tc 9.5625 0 0 9.5 199.6 91.99 Tm (the )Tj 0.0475 Tc 9.5 0 0 9.5 215.65 91.99 Tm (points )Tj /T1_2 1 Tf 0.05 Tc 9.5716 0 0 9.1 244.86 91.99 Tm (PI, )Tj 0 Tc 9.1 0 0 9.1 259.99 91.99 Tm (P)Tj 6.2 0 0 6.2 266.48 90.54 Tm (2)Tj 0.735 0.234 Td (, )Tj 9.1 0 0 9.1 275.11 91.99 Tm (P)Tj 6.2 0 0 6.2 281.42 90.36 Tm (3 )Tj /T1_0 1 Tf 0.0246 Tc 9.5 0 0 9.5 288.99 91.99 Tm (on )Tj /T1_2 1 Tf 0.0089 Tc 9.6 0 0 9.6 301.86 91.99 Tm (?i)Tj 0 Tc 6.2 0 0 6.2 310.2 95.22 Tm (5 )Tj /T1_0 1 Tf 0.0168 Tc 9.5 0 0 9.5 317.68 91.99 Tm (means )Tj 0.05 Tc 10.0691 0 0 9.5 346.12 91.99 Tm (that )Tj 10.3822 0 0 9.5 20.67 80.29 Tm (the )Tj 0.0336 Tc 9.5 0 0 9.5 38.43 80.29 Tm (corresponding )Tj 0.006 Tc 6.5 0 Td (lines )Tj 0.0349 Tc 2.312 0 Td (in )Tj /T1_1 1 Tf 0.05 Tc 9.5304 0 0 9.4 133.45 80.29 Tm (PG\(3, )Tj /T1_2 1 Tf -0.035 Tc 8.3892 0 0 10 160.8 80.29 Tm (q\) )Tj /T1_0 1 Tf 0.0226 Tc 9.5 0 0 9.5 172.27 80.29 Tm (belong )Tj 0.05 Tc 9.6041 0 0 9.5 203.02 80.29 Tm (to )Tj 9.6991 0 0 9.5 214.72 80.29 Tm (the )Tj 9.5096 0 0 9.5 231.35 80.29 Tm (same )Tj 0.0269 Tc 9.5 0 0 9.5 256.15 80.29 Tm (pencil. )Tj -0.0105 Tc 3.448 0 Td (So, )Tj 0.05 Tc 9.5456 0 0 9.5 305.02 80.29 Tm (in )Tj 0.0353 Tc 9.5 0 0 9.5 316.35 80.29 Tm (our )Tj 0.0314 Tc 1.758 0 Td (setting, )Tj 0.05 Tc 9.8466 0 0 9.5 20.86 68.94 Tm (there )Tj 0.0158 Tc 9.5 0 0 9.5 46.43 68.94 Tm (would )Tj 0.05 Tc 9.8842 0 0 9.5 74.35 68.94 Tm (be )Tj 0.019 Tc 9.5 0 0 9.5 87.82 68.94 Tm (two )Tj 0.0205 Tc 1.925 0 Td (chords )Tj 0.0211 Tc 3.164 0 Td (of )Tj 0 Tc 1.117 0 Td (C )Tj 0.05 Tc 9.5174 0 0 9.5 155.96 68.94 Tm (and )Tj 0.0087 Tc 9.5 0 0 9.5 174.33 68.94 Tm (one )Tj 0.0168 Tc 1.875 0 Td (axis )Tj 0.0211 Tc 2.047 0 Td (of )Tj /T1_3 1 Tf 0 Tc 12.4 0 0 12.4 222.24 68.94 Tm (r )Tj /T1_0 1 Tf 0.04 Tc 9.5 0 0 9.5 232.11 68.94 Tm (or )Tj 0.038 Tc 1.258 0 Td (two )Tj 0.031 Tc 1.981 0 Td (axes )Tj 0.05 Tc 9.5989 0 0 9.5 284.49 68.94 Tm 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482.59 Tm (2)Tj 0.05 Tc 7.8141 0 0 6.5001 189.8 478.81 Tm (\), )Tj /T1_0 1 Tf -0.0242 Tc 9.5 0 0 9.5 199.34 478.81 Tm (for )Tj /T1_2 1 Tf -0.0046 Tc 9.6 0 0 9.6 214.48 478.81 Tm (u, )Tj 0.0264 Tc 0.996 0 Td (v, )Tj /T1_0 1 Tf 0.05 Tc 14.0231 0 0 9.4 233.44 478.81 Tm (wE" )Tj -0.0246 Tc 9.5 0 0 9.5 266.14 478.81 Tm (is )Tj 0 Tc 1.135 0 Td (a )Tj 0.05 Tc 9.862 0 0 9.5 285.68 478.81 Tm (point )Tj 9.5989 0 0 9.5 312.39 478.81 Tm (of )Tj 0 Tc 9.5 0 0 9.5 324.26 478.81 Tm (a )Tj 0.0033 Tc 0.899 0 Td (Veronese )Tj 0.013 Tc -32.431 -1.269 Td (surface )Tj /T1_2 1 Tf -0.035 Tc 14.5986 0 0 15.6 56.43 466.75 Tm (vi )Tj /T1_0 1 Tf 0.05 Tc 9.6163 0 0 9.5 70.28 466.75 Tm (embedded )Tj 0.0349 Tc 9.5 0 0 9.5 116.92 466.75 Tm (in )Tj 0.05 Tc 6.7065 0 0 6.7 127.75 466.75 Tm (1-[5 )Tj 0 Tc 6.7 0 0 6.7 143.83 466.75 Tm (: )Tj /T1_2 1 Tf -0.035 Tc 9.6163 0 0 9.8 149.24 466.75 Tm (XOX5 )Tj /T1_0 1 Tf 0 Tc 9.8 0 0 9.8 175.57 466.75 Tm (-)Tj 9.5 0 0 9.5 184.3 466.75 Tm (X)Tj 6.7 0 0 6.7 192.55 465.31 Tm (1)Tj 9.5 0 0 9.5 196.36 466.75 Tm (X)Tj 6.7 0 0 6.7 204.27 465.31 Tm (4 )Tj /T1_1 1 Tf 12.3 0 0 12.3 210.22 466.75 Tm (+ )Tj /T1_2 1 Tf 9.8 0 0 9.8 219.8 466.75 Tm (X)Tj 6.5001 0 0 6.5001 227.49 465.31 Tm (2)Tj 9.8 0 0 9.8 231.86 466.75 Tm (X)Tj 6.5001 0 0 6.5001 239.52 465.31 Tm (3 )Tj /T1_0 1 Tf 11.2 0 0 11.2 246.72 466.75 Tm (= )Tj -0.035 Tc 6.8872 0 0 9.5 256.43 466.75 Tm (O. )Tj 0.05 Tc 10.1579 0 0 9.5 267.77 466.75 Tm (In )Tj 9.9723 0 0 9.5 280.06 466.75 Tm (the )Tj 9.9006 0 0 9.5 296.9 466.75 Tm (open )Tj 0.0455 Tc 9.5 0 0 9.5 320.81 466.75 Tm (set )Tj /T1_2 1 Tf 0 Tc 6.5001 0 0 6.5001 335.68 466.75 Tm (U )Tj /T1_0 1 Tf 11.2 0 0 11.2 344.28 466.75 Tm (= )Tj 9.5 0 0 9.5 354.27 466.75 Tm (1 )Tj 0.0211 Tc 0.783 0 Td (of )Tj /T1_2 1 Tf 0.05 Tc 9.4619 0 0 9.3 25.09 455.41 Tm (PG\(5, )Tj /T1_0 1 Tf -0.035 Tc 10.105 0 0 10.2 51.85 455.41 Tm (1'\), )Tj 0.05 Tc 9.8357 0 0 9.5 67.12 455.41 Tm (the )Tj 9.8405 0 0 9.5 84.04 455.41 Tm (tangent )Tj 0.0441 Tc 9.5 0 0 9.5 119.89 455.41 Tm (plane )Tj 0.05 Tc 9.8224 0 0 9.5 145.78 455.41 Tm (to )Tj /T1_2 1 Tf -0.035 Tc 14.3332 0 0 15.6 157.59 455.41 Tm (vi )Tj /T1_0 1 Tf 0.05 Tc 10.1984 0 0 9.5 171.44 455.41 Tm (at )Tj /T1_2 1 Tf 0 Tc 9.3 0 0 9.3 183.43 455.41 Tm (Z )Tj /T1_0 1 Tf -0.035 Tc 9.0754 0 0 9.5 193.43 455.41 Tm (is )Tj 0 Tc 6.7 0 0 6.7 155.49 432.37 Tm (4 )Tj /T1_2 1 Tf 0.05 Tc 19.547 0 0 10 198.86 432.37 Tm (\(8Z )Tj 12.5755 0 0 10 235.48 432.37 Tm (8Z\) )Tj 10.7404 0 0 9.7 132.98 426.97 Tm (Tz\(V)Tj 0 Tc 6.1 0 0 6.1 155.14 426.97 Tm [(2)-362(\) )]TJ /T1_0 1 Tf 11.2 0 0 11.2 166.44 426.97 Tm (= )Tj /T1_2 1 Tf 0.0214 Tc 9.7 0 0 9.7 176.61 426.97 Tm (span )Tj 0.0119 Tc 2.893 0 Td (Z, )Tj 0.05 Tc 9.7516 0 0 9.7 217.51 426.97 Tm (8v )Tj 11.762 0 0 9.7 230.3 426.97 Tm ('8w )Tj 0 Tc 9.7 0 0 9.7 258.1 426.97 Tm (' )Tj /T1_0 1 Tf 0.0114 Tc 9.5 0 0 9.5 24.65 403.93 Tm (where )Tj /T1_2 1 Tf 0 Tc 2.901 0 Td (Z )Tj /T1_1 1 Tf 8.1 0 0 8.1 61.97 403.93 Tm (= )Tj /T1_0 1 Tf -0.011 Tc 9.5 0 0 9.5 72.61 403.93 Tm (\(1, )Tj /T1_2 1 Tf 0.05 Tc 7.5461 0 0 6.5001 85.22 403.93 Tm (V, )Tj 0 Tc 9.3 0 0 9.3 94.99 403.93 Tm (v)Tj 6.7 0 0 6.7 100.23 407.71 Tm (2 )Tj /T1_0 1 Tf 0.987 -0.564 Td (-)Tj /T1_2 1 Tf 0.05 Tc 7.8099 0 0 6.5001 116 403.93 Tm (W, )Tj 7.9693 0 0 6.5001 127.51 403.93 Tm (W, )Tj 7.8461 0 0 6.5001 139.21 403.93 Tm (VW, )Tj /T1_3 1 Tf 0 Tc 8.4 0 0 8.4 155.87 403.93 Tm (w)Tj /T1_2 1 Tf 6.7 0 0 6.7 163.23 407.53 Tm (2)Tj 0.05 Tc 8.0932 0 0 6.7 167.49 403.93 Tm (\). )Tj /T1_1 1 Tf 11.8001 0 0 9.1 177.33 403.93 Tm (It )Tj /T1_0 1 Tf -0.026 Tc 9.5 0 0 9.5 187.82 403.93 Tm (follows )Tj 0.05 Tc 10.1785 0 0 9.5 218.68 403.93 Tm (that )Tj /T1_2 1 Tf 11.216 0 0 10 147.3 384.31 Tm (8Z )Tj 10.1196 0 0 9.7 148.39 376.93 Tm (8v )Tj /T1_0 1 Tf 0 Tc 12.1 0 0 12.1 164.1 376.93 Tm (= )Tj 0.0344 Tc 9.5 0 0 9.5 174.49 376.93 Tm (\(0,1, )Tj /T1_2 1 Tf -0.0142 Tc 9.7 0 0 9.7 195.62 376.93 Tm (2v, )Tj /T1_0 1 Tf -0.035 Tc 9.3453 0 0 9.5 209.24 376.93 Tm (0, )Tj /T1_2 1 Tf 0.039 Tc 9.3 0 0 9.3 218.12 376.93 Tm (w, )Tj /T1_3 1 Tf -0.035 Tc 9.3563 0 0 10 229.49 376.93 Tm (0\), )Tj /T1_2 1 Tf 0.05 Tc 11.381 0 0 10 147.29 360.73 Tm (8Z )Tj 9.8893 0 0 9.7 147.31 353.53 Tm (8w )Tj /T1_0 1 Tf 0 Tc 11.2 0 0 11.2 163.92 353.53 Tm (= )Tj 0.0344 Tc 9.5 0 0 9.5 174.31 353.53 Tm (\(0,0, )Tj 0.05 Tc 11.3374 0 0 9.3 195.71 353.53 Tm (-1, )Tj -0.0205 Tc 9.3 0 0 9.3 211.72 353.53 Tm (1, )Tj /T1_2 1 Tf 0.05 Tc 9.2917 0 0 9.2 220.45 353.53 Tm (v, )Tj 0.0155 Tc 9.7 0 0 9.7 229.82 353.53 Tm (2w\). )Tj /T1_0 1 Tf 0.05 Tc 9.569 0 0 9.5 24.76 328.51 Tm (The )Tj 0.0147 Tc 9.5 0 0 9.5 42.76 328.51 Tm (generic )Tj 0.05 Tc 9.8961 0 0 9.5 74.32 328.51 Tm (tangent )Tj 0.0113 Tc 9.5 0 0 9.5 109.18 328.51 Tm (line )Tj 0.05 Tc 10.0407 0 0 9.5 126.34 328.51 Tm (to )Tj /T1_2 1 Tf -0.035 Tc 14.8641 0 0 15.6 137.25 328.51 Tm (vi )Tj /T1_0 1 Tf 0.05 Tc 10.1984 0 0 9.5 150.56 328.51 Tm (at )Tj /T1_3 1 Tf 0 Tc 9.3 0 0 9.3 161.4 328.51 Tm (Z )Tj /T1_0 1 Tf -0.035 Tc 9.3682 0 0 9.5 170.38 328.51 Tm (is )Tj 0.05 Tc 9.9167 0 0 9.5 178.82 328.51 Tm (ofthe )Tj 0.0028 Tc 9.5 0 0 9.5 203.66 328.51 Tm (form )Tj /T1_3 1 Tf 0.05 Tc 9.9883 0 0 9.3 224.88 328.51 Tm (P\(Z\)P\(V\), )Tj /T1_0 1 Tf 0.0398 Tc 9.5 0 0 9.5 274.49 328.51 Tm (where )Tj /T1_3 1 Tf 0 Tc 9.3 0 0 9.3 302.06 328.51 Tm (V )Tj /T1_1 1 Tf 8.1 0 0 8.1 313.07 328.51 Tm (= )Tj /T1_3 1 Tf 9.3 0 0 9.3 323.34 328.51 Tm (A )Tj /C0_0 1 Tf 4.5901 0 0 8.64 330.13 328.51 Tm <007E007E0020>Tj /T1_0 1 Tf 0.05 Tc 10.2993 0 0 8.9 341.41 328.51 Tm (+/l )Tj /C0_0 1 Tf 0 Tc 4.2601 0 0 8.64 355.51 328.51 Tm <007E007E002C0020>Tj /T1_0 1 Tf 0.0411 Tc 9.5 0 0 9.5 24.65 316.45 Tm (with )Tj /T1_3 1 Tf -0.035 Tc 7.6077 0 0 10 46.49 316.45 Tm (A, )Tj /T1_0 1 Tf 0.0119 Tc 8.9 0 0 8.9 55.98 316.45 Tm (/l )Tj -0.035 Tc 14.101 0 0 21.3 64.72 316.45 Tm (E" )Tj /T1_3 1 Tf 8.516 0 0 10 87.63 316.45 Tm (\(A, )Tj /T1_0 1 Tf 0.0316 Tc 8.9 0 0 8.9 100.8 316.45 Tm (/l\) )Tj /T1_2 1 Tf -0.035 Tc 4.7577 0 0 8 113.37 316.45 Tm (-=J )Tj /T1_0 1 Tf 0.05 Tc 9.6133 0 0 9.5 123.73 316.45 Tm (\(0,0\) )Tj 9.6349 0 0 9.5 148.22 316.45 Tm (and )Tj /T1_3 1 Tf 10.0693 0 0 9.3 166.49 316.45 Tm (VQV)Tj /T1_2 1 Tf 0 Tc 7.6 0 0 7.6 189.45 320.23 Tm (t )Tj /T1_1 1 Tf 8.1 0 0 8.1 195.35 316.45 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 9.0857 0 0 9.5 205.29 316.45 Tm (0, )Tj 0.0161 Tc 9.5 0 0 9.5 215.63 316.45 Tm (where )Tj 0 Tc -5.675 -2.122 Td (0 )Tj 1.895 0.019 Td (0 )Tj 1.857 -0.019 Td (0 )Tj 1.478 -0.019 Td (0 )Tj 1.895 0.019 Td [(0 )-1196(1 )]TJ -7.125 -1.213 Td (0 )Tj 1.876 0.019 Td (0 )Tj 1.857 -0.019 Td (0 )Tj 1.497 -0.019 Td (0 )Tj 0.05 Tc 12.1537 0 0 9.5 226.12 285.13 Tm (-1 )Tj 0 Tc 9.5 0 0 9.5 247.58 284.59 Tm (0 )Tj /T1_2 1 Tf 0.0219 Tc 12.2 0 0 12.2 131.23 267.13 Tm (Q= )Tj /T1_0 1 Tf 0 Tc 9.5 0 0 9.5 161.9 273.43 Tm [(0 )-1126(0 )]TJ 3.733 -0.019 Td (0 )Tj 1.511 0.019 Td (1 )Tj 1.862 -0.019 Td [(0 )-1164(0 )]TJ -7.124 -1.194 Td [(0 )-1126(0 )]TJ 3.765 0.019 Td (1 )Tj 1.464 -0.038 Td (0 )Tj 1.876 0.019 Td (0 )Tj 1.933 -0.019 Td (0 )Tj -9.019 -1.175 Td (0 )Tj 0.05 Tc 12.1537 0 0 9.5 176.44 250.93 Tm (-1 )Tj 0 Tc 9.5 0 0 9.5 197.36 250.39 Tm [(0 )-747(0 )-1126(0 )-1164(0 )]TJ -3.718 -1.175 Td [(1 )-1112(0 )]TJ 3.719 -0.019 Td (0 )Tj 8.9 0 0 8.9 211.59 239.05 Tm (0 )Tj 9.5 0 0 9.5 229.4 239.05 Tm (0 )Tj 8.9 0 0 8.9 247.77 238.87 Tm (0 )Tj -0.035 Tc 9.3682 0 0 9.5 24.58 217.45 Tm (is )Tj 0.05 Tc 9.5625 0 0 9.5 34.18 217.45 Tm (the )Tj 9.5671 0 0 9.5 50.08 217.45 Tm (symmetric )Tj 9.907 0 0 9.5 97.72 217.45 Tm (matrix )Tj 0.0358 Tc 9.5 0 0 9.5 129.5 217.45 Tm (associated )Tj 0.05 Tc 9.6041 0 0 9.5 175.12 217.45 Tm (to )Tj -0.035 Tc 8.9223 0 0 10.1 186.35 217.45 Tm (1\2435. )Tj /T1_1 1 Tf 0.05 Tc 11.8001 0 0 9.1 205.23 217.45 Tm (It )Tj /T1_0 1 Tf -0.0166 Tc 9.5 0 0 9.5 215.9 217.45 Tm (follows )Tj 0.05 Tc 9.9596 0 0 9.5 247.48 217.45 Tm (that )Tj /T1_3 1 Tf 0 Tc 9.3 0 0 9.3 121.16 195.31 Tm (V )Tj /T1_1 1 Tf 8.1 0 0 8.1 132.17 195.31 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 9.7777 0 0 10.2 142.8 195.31 Tm (\(0, )Tj /T1_2 1 Tf 8.778 0 0 9.8 155.47 195.31 Tm (A, )Tj 8.8025 0 0 9.8 165.2 195.31 Tm (2VA )Tj /T1_0 1 Tf 0 Tc 9.8 0 0 9.8 182.59 195.31 Tm (-)Tj 0.0023 Tc 8.9 0 0 8.9 191.7 195.31 Tm [(/l, )-68(/l, )]TJ /T1_2 1 Tf -0.035 Tc 8.0814 0 0 9.8 211.8 195.31 Tm (AW )Tj /T1_1 1 Tf 0 Tc 12.3 0 0 12.3 226.06 195.31 Tm (+ )Tj /T1_2 1 Tf -0.035 Tc 9.3303 0 0 9.8 235.72 195.31 Tm (/lV, )Tj 0 Tc 9.8 0 0 9.8 250.7 195.31 Tm (2/lw\) )Tj /T1_0 1 Tf 0.0474 Tc 9.5 0 0 9.5 24.47 174.25 Tm (with )Tj /T1_2 1 Tf -0.035 Tc 9.094 0 0 9.8 46.58 174.25 Tm (A\(AW )Tj /T1_1 1 Tf 0 Tc 13.2 0 0 13.2 70.16 174.25 Tm (+ )Tj /T1_2 1 Tf -0.035 Tc 7.4209 0 0 9.7 80 174.25 Tm (/-Lv\) )Tj /T1_0 1 Tf 0 Tc 13 0 0 13 97.85 174.25 Tm (= )Tj /T1_2 1 Tf -0.0338 Tc 9.8 0 0 9.8 108.1 174.25 Tm (/l\(2AV )Tj /T1_0 1 Tf 0 Tc 2.844 0 Td (-)Tj /T1_2 1 Tf -0.035 Tc 9.6503 0 0 9.8 145.36 174.25 Tm (/l\); )Tj /T1_0 1 Tf 0.05 Tc 10.1785 0 0 9.5 160.54 174.25 Tm (that )Tj -0.0331 Tc 9.5 0 0 9.5 181.18 174.25 Tm (is, )Tj /T1_2 1 Tf 0 Tc 9.8 0 0 9.8 154.41 152.83 Tm (A)Tj 6.7 0 0 6.7 159.81 156.97 Tm (2)Tj 9.8 0 0 9.8 163.45 152.83 Tm (W )Tj -0.035 Tc 8.9771 0 0 9.8 182.84 152.83 Tm (A/lV )Tj /T1_1 1 Tf 0 Tc 12.3 0 0 12.3 200.68 152.83 Tm (+ )Tj /T1_0 1 Tf -0.0317 Tc 8.9 0 0 8.9 210.06 152.83 Tm (/l2 )Tj /T1_1 1 Tf 0 Tc 8.1 0 0 8.1 222.53 152.83 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 6.8872 0 0 9.3 232.67 152.83 Tm (O. )Tj 9.6928 0 0 10.2 357.55 152.83 Tm (\(5\) )Tj -0.0014 Tc 9.5 0 0 9.5 24.67 131.95 Tm (Since )Tj 0.05 Tc 9.6991 0 0 9.5 50.02 131.95 Tm (the )Tj 0.0482 Tc 9.5 0 0 9.5 67.41 131.95 Tm (discriminant )Tj 0.05 Tc 9.5989 0 0 9.5 124.65 131.95 Tm (of )Tj 9.5056 0 0 9.5 136.6 131.95 Tm (this )Tj 0.0436 Tc 9.5 0 0 9.5 156.51 131.95 Tm (quadratic )Tj 0.0091 Tc 4.546 0 Td (form )Tj -0.035 Tc 9.3682 0 0 9.5 222.76 131.95 Tm (is )Tj 0.05 Tc 9.5655 0 0 9.5 233.45 131.95 Tm (not )Tj 0.0031 Tc 9.5 0 0 9.5 251.05 131.95 Tm (zero, )Tj 0.05 Tc 9.6825 0 0 9.5 275.2 131.95 Tm (there )Tj 0.0497 Tc 9.5 0 0 9.5 301.58 131.95 Tm (are )Tj 0.0001 Tc 1.808 0 Td (two )Tj 0.0472 Tc 1.989 0 Td (tangent )Tj -0.0035 Tc -32.937 -1.213 Td (lines )Tj 0.0212 Tc 2.46 0 Td (\(real )Tj 0.05 Tc 9.5989 0 0 9.5 70.83 120.43 Tm (or )Tj 0.0332 Tc 9.5 0 0 9.5 84.51 120.43 Tm (complex )Tj 0.0369 Tc 4.112 0 Td (conjugate\) )Tj 0.05 Tc 10.1984 0 0 9.5 172.34 120.43 Tm (at )Tj 0.0354 Tc 9.5 0 0 9.5 185.2 120.43 Tm (the )Tj 0.0084 Tc 1.813 0 Td (generic )Tj 0.0477 Tc 3.496 0 Td (point )Tj 0.05 Tc 9.5989 0 0 9.5 261.63 120.43 Tm (of )Tj /T1_2 1 Tf -0.035 Tc 14.5105 0 0 15.6 274.05 120.43 Tm (vi. )Tj /T1_0 1 Tf 0.05 Tc 9.6017 0 0 9.5 296.02 120.43 Tm (To )Tj 0.0323 Tc 9.5 0 0 9.5 312.1 120.43 Tm (these )Tj 0.05 Tc 9.5069 0 0 9.5 337.66 120.43 Tm (tangent )Tj 0.0013 Tc 9.5 0 0 9.5 24.58 108.91 Tm (lines )Tj 0.05 Tc 9.6137 0 0 9.5 47.68 108.91 Tm (through )Tj /T1_2 1 Tf 0 Tc 9.5 0 0 9.5 86.41 108.91 Tm (Z )Tj /T1_0 1 Tf 0.0456 Tc 1.221 0 Td (correspond )Tj 0.0001 Tc 5.388 0 Td (two )Tj 0.0163 Tc 2.031 0 Td (pencils )Tj 0.016 Tc 3.477 0 Td (in )Tj /T1_2 1 Tf 0.05 Tc 9.599 0 0 9.3 214.09 108.91 Tm (PG\(3, )Tj /T1_3 1 Tf -0.035 Tc 8.3892 0 0 9.8 241.8 108.91 Tm (q\) )Tj /T1_0 1 Tf 0.0222 Tc 9.5 0 0 9.5 254.42 108.91 Tm (each )Tj 0.0495 Tc 2.445 0 Td (containing )Tj 0.05 Tc 9.6991 0 0 9.5 327.04 108.91 Tm (the )Tj 0.005 Tc 9.5 0 0 9.5 344.8 108.91 Tm (line )Tj /T1_3 1 Tf 0 Tc 8.4 0 0 8.4 364.46 108.91 Tm (z )Tj /T1_0 1 Tf 0.0336 Tc 9.5 0 0 9.5 24.75 97.21 Tm (corresponding )Tj 0.05 Tc 9.6041 0 0 9.5 86.74 97.21 Tm (to )Tj /T1_2 1 Tf 0 Tc 9.8 0 0 9.8 98.65 97.21 Tm (Z )Tj /T1_0 1 Tf 0.05 Tc 9.7524 0 0 9.5 108.98 97.21 Tm (and )Tj 9.6988 0 0 9.5 127.88 97.21 Tm (another )Tj 0.005 Tc 9.5 0 0 9.5 163.18 97.21 Tm (line )Tj 0.0349 Tc 1.895 0 Td (in )Tj 0.05 Tc 9.6991 0 0 9.5 191.86 97.21 Tm (the )Tj 0.0343 Tc 9.5 0 0 9.5 208.25 97.21 Tm (neighbourhood )Tj 0.05 Tc 9.5989 0 0 9.5 273.33 97.21 Tm (of )Tj /T1_2 1 Tf -0.0073 Tc 10.1 0 0 10.1 284.85 97.21 Tm (z. )Tj /T1_0 1 Tf 0.05 Tc 9.9464 0 0 9.5 296.78 97.21 Tm (By )Tj 9.8015 0 0 9.5 312.32 97.21 Tm (putting )Tj /T1_2 1 Tf 0 Tc 9.8 0 0 9.8 346.83 97.21 Tm (A )Tj /T1_0 1 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8.3181 0 0 7.4001 237.94 541.45 Tm (VERONESE )Tj 7.5954 0 0 7.4001 91.84 530.11 Tm (SURFACE )Tj 7.8576 0 0 7.4001 132.22 530.11 Tm (OF )Tj /T1_1 1 Tf 0.0339 Tc 9.7 0 0 9.7 146.41 530.11 Tm (PG\(5, )Tj /T1_2 1 Tf -0.035 Tc 8.6043 0 0 9.8 173.57 530.11 Tm (q\) )Tj /T1_0 1 Tf 0.05 Tc 7.7685 0 0 7.4001 185.73 530.11 Tm (FROM )Tj 8.0868 0 0 7.4001 212.87 530.11 Tm (THE )Tj 7.7761 0 0 7.4001 233.38 530.11 Tm (CHORDS )Tj 8.2711 0 0 7.4001 271.18 530.11 Tm (OF )Tj /T1_3 1 Tf 0 Tc 9.2 0 0 9.2 286.07 530.11 Tm (C )Tj /T1_0 1 Tf 0.0357 Tc 9.4 0 0 9.4 143.35 497.35 Tm (3.1. )Tj 0.05 Tc 7.99 0 0 7.4001 164.98 497.35 Tm (CONSTRUCTION )Tj 0 Tc 9.4 0 0 9.4 235.19 497.35 Tm (I )Tj 0.05 Tc 9.4103 0 0 9.4 31.33 475.57 Tm (Suppose )Tj 10.2879 0 0 9.4 69.63 475.57 Tm (that )Tj /T1_1 1 Tf 0 Tc 9.3 0 0 9.3 90.13 475.57 Tm (p )Tj /T1_0 1 Tf -0.035 Tc 5.0875 0 0 9 98.15 475.57 Tm (::/= )Tj 0 Tc 9 0 0 9 107.9 475.57 Tm (3 )Tj 0.05 Tc 9.5174 0 0 9.4 115.82 475.57 Tm (and )Tj 0.0172 Tc 9.4 0 0 9.4 134.19 475.57 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512.47 Tm (l\(tI, )Tj -0.0082 Tc 9.6 0 0 9.6 240.37 512.47 Tm (t2\) )Tj /T1_1 1 Tf -0.035 Tc 9.3682 0 0 9.5 255.16 512.47 Tm (is )Tj 0.05 Tc 10.0821 0 0 9.5 264.5 512.47 Tm (an )Tj /T1_0 1 Tf 0.0464 Tc 9.6 0 0 9.6 278.7 512.47 Tm (imaginary )Tj -0.0031 Tc 4.918 0 Td (chord )Tj /T1_1 1 Tf 0.04 Tc 9.5 0 0 9.5 350.91 512.47 Tm (of )Tj -0.035 Tc 8.378 0 0 9.8 361.71 512.47 Tm (C. )Tj 0.0221 Tc 9.5 0 0 9.5 25.24 500.95 Tm (Note )Tj 0.05 Tc 10.2879 0 0 9.5 47.67 500.95 Tm (that )Tj 9.5809 0 0 9.5 68.68 500.95 Tm (imaginary )Tj 0.0281 Tc 9.5 0 0 9.5 114.75 500.95 Tm (chords )Tj 0.0308 Tc 3.239 0 Td (are )Tj 0.0074 Tc 1.668 0 Td (defined )Tj -0.0105 Tc 3.429 0 Td (over )Tj -0.035 Tc 8.1611 0 0 9.5 213.69 500.95 Tm ("\(. )Tj /T1_2 1 Tf 0.05 Tc 12.4556 0 0 9.1 225.92 500.95 Tm (If )Tj /T1_0 1 Tf 11.4405 0 0 9.6 235.48 500.95 Tm (tl )Tj /T1_2 1 Tf 0 Tc 8.1 0 0 8.1 246.65 500.95 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 9.0504 0 0 9.6 256.21 500.95 Tm (t2 )Tj /T1_2 1 Tf 0 Tc 8.1 0 0 8.1 266.63 500.95 Tm (= )Tj /T1_0 1 Tf 0.0229 Tc 9.6 0 0 9.6 276.91 500.95 Tm (t, )Tj /T1_1 1 Tf 0.05 Tc 10.1197 0 0 9.5 286.54 500.95 Tm (then )Tj -0.035 Tc 9.0754 0 0 9.5 25.13 455.41 Tm (is )Tj 0.05 Tc 9.6991 0 0 9.5 34.36 455.41 Tm (the )Tj 9.6737 0 0 9.5 50.74 455.41 Tm (tangent )Tj 10.2589 0 0 9.5 86.19 455.41 Tm (to )Tj /T1_2 1 Tf 0 Tc 9.2 0 0 9.2 98.15 455.41 Tm (C )Tj /T1_1 1 Tf 0.05 Tc 10.1984 0 0 9.5 107.36 455.41 Tm (at )Tj 9.8357 0 0 9.5 118.96 455.41 Tm (the )Tj 9.6215 0 0 9.5 135.73 455.41 Tm (point )Tj /T1_0 1 Tf 9.9241 0 0 9.6 161.36 455.41 Tm (P\(t\). )Tj /T1_1 1 Tf 0.03 Tc 9.5 0 0 9.5 36.52 443.89 Tm (At )Tj 0.0348 Tc 1.413 0 Td (each )Tj 0.05 Tc 9.862 0 0 9.5 71.66 443.89 Tm (point )Tj /T1_0 1 Tf 10.191 0 0 9.6 97.82 443.89 Tm (P\(t\) )Tj /T1_1 1 Tf 9.5989 0 0 9.5 119.25 443.89 Tm (of )Tj -0.035 Tc 9.0063 0 0 9.8 130.05 443.89 Tm (C, )Tj 0.05 Tc 9.6005 0 0 9.5 142.18 443.89 Tm (there )Tj -0.035 Tc 9.3682 0 0 9.5 166.78 443.89 Tm (is )Tj 0.05 Tc 9.7155 0 0 9.5 176.48 443.89 Tm (an )Tj /T1_0 1 Tf 0.0022 Tc 9.6 0 0 9.6 190.36 443.89 Tm (osculating )Tj 0.0106 Tc 4.542 0 Td (plane )Tj /T1_1 1 Tf 0.0111 Tc 9.5 0 0 9.5 25.01 397.63 Tm (which )Tj 0.0394 Tc 2.822 0 Td (meets )Tj /T1_2 1 Tf 0 Tc 9.2 0 0 9.2 78.35 397.63 Tm (C )Tj /T1_1 1 Tf 0.0334 Tc 9.5 0 0 9.5 87.39 397.63 Tm (only )Tj 0.0349 Tc 2.199 0 Td (in )Tj /T1_0 1 Tf 0.05 Tc 10.1923 0 0 9.6 119.06 397.63 Tm (P\(t\). )Tj /T1_1 1 Tf 0.0273 Tc 9.5 0 0 9.5 144.55 397.63 Tm (Such )Tj 0.0239 Tc 2.396 0 Td (osculating )Tj 0.0257 Tc 4.615 0 Td (planes )Tj 0.0154 Tc 3.02 0 Td (form )Tj 0.05 Tc 9.8357 0 0 9.5 261.88 397.63 Tm (the )Tj /T1_0 1 Tf 0.0272 Tc 9.6 0 0 9.6 278.92 397.63 Tm (osculating )Tj -0.0155 Tc 4.766 0 Td (developable )Tj /T1_2 1 Tf 0 Tc 12.1 0 0 12.1 24.79 386.11 Tm (r )Tj /T1_1 1 Tf 0.05 Tc 9.8224 0 0 9.5 33.82 386.11 Tm (to )Tj -0.035 Tc 8.7969 0 0 9.8 45.09 386.11 Tm (C. )Tj 0.05 Tc 9.7433 0 0 9.5 57.89 386.11 Tm (In )Tj 9.7868 0 0 9.5 70.04 386.11 Tm (particular )Tj /T1_2 1 Tf 0 Tc 12.1 0 0 12.1 115.15 386.11 Tm (r )Tj /T1_1 1 Tf -0.0246 Tc 9.5 0 0 9.5 124.48 386.11 Tm (is )Tj 0.05 Tc 9.8357 0 0 9.5 134.26 386.11 Tm (the )Tj 9.5755 0 0 9.5 150.93 386.11 Tm (dual )Tj 0.04 Tc 9.5 0 0 9.5 172.17 386.11 Tm (of )Tj -0.035 Tc 8.5874 0 0 9.8 182.79 386.11 Tm (C. )Tj 0.0151 Tc 9.5 0 0 9.5 195.08 386.11 Tm (For )Tj /T1_3 1 Tf 0 Tc 8.1 0 0 8.1 211.35 386.11 Tm (p )Tj /T1_2 1 Tf -0.035 Tc 5.783 0 0 10.9 219.51 386.11 Tm (=I-)Tj /T1_1 1 Tf 9.5562 0 0 9.8 229.39 386.11 Tm (3, )Tj 0.0486 Tc 9.5 0 0 9.5 240.03 386.11 Tm (dual )Tj 0.05 Tc 9.6041 0 0 9.5 261.16 386.11 Tm (to )Tj 9.9723 0 0 9.5 272.86 386.11 Tm (the )Tj 0.0432 Tc 9.5 0 0 9.5 290.07 386.11 Tm (chords )Tj 0.04 Tc 3.259 0 Td (of )Tj 0 Tc 9.8 0 0 9.8 331.64 386.11 Tm (C )Tj 0.0213 Tc 9.5 0 0 9.5 340.82 386.11 Tm (are )Tj 0.0449 Tc 1.657 0 Td (the )Tj /T1_0 1 Tf -0.0137 Tc 9.6 0 0 9.6 25.86 374.77 Tm (axes )Tj /T1_1 1 Tf 0.04 Tc 9.5 0 0 9.5 45.63 374.77 Tm (of )Tj /T1_2 1 Tf 0.0301 Tc 12.1 0 0 12.1 56.65 374.77 Tm (r. )Tj /T1_1 1 Tf 0.05 Tc 9.809 0 0 9.5 70.36 374.77 Tm (An )Tj /T1_0 1 Tf 0.0104 Tc 9.6 0 0 9.6 87.6 374.77 Tm (axis )Tj /T1_1 1 Tf 0.04 Tc 9.5 0 0 9.5 106.65 374.77 Tm (of )Tj /T1_2 1 Tf 0 Tc 12.1 0 0 12.1 117.67 374.77 Tm (r )Tj /T1_1 1 Tf -0.0246 Tc 9.5 0 0 9.5 127.36 374.77 Tm (is )Tj 0 Tc 1.04 0 Td (a )Tj 0.0113 Tc 0.874 0 Td (line )Tj 0.04 Tc 1.932 0 Td (of )Tj /T1_0 1 Tf 0.0359 Tc 9.6 0 0 9.6 175.03 374.77 Tm (PG\(3, )Tj -0.0185 Tc 2.818 0 Td (q\), )Tj /T1_1 1 Tf 0.0159 Tc 9.5 0 0 9.5 216.17 374.77 Tm (which )Tj -0.0246 Tc 2.911 0 Td (is )Tj 0.0354 Tc 1.029 0 Td (the )Tj 0.0499 Tc 1.718 0 Td (intersection )Tj 0.05 Tc 9.5989 0 0 9.5 323.01 374.77 Tm (of )Tj 0 Tc 9.5 0 0 9.5 334.34 374.77 Tm (a )Tj 0.0411 Tc 0.864 0 Td (pair )Tj 0.04 Tc 2.036 0 Td (of )Tj 0.0256 Tc -35.48 -1.194 Td (real )Tj 0.0295 Tc 1.935 0 Td (planes )Tj 0.04 Tc 3.097 0 Td (of )Tj /T1_2 1 Tf 0.05 Tc 12.8433 0 0 12.1 83.63 363.43 Tm (r, )Tj /T1_1 1 Tf 0.0287 Tc 9.5 0 0 9.5 95.95 363.43 Tm (possibly )Tj 0.0271 Tc 3.912 0 Td (coincident, )Tj 0.0211 Tc 5.097 0 Td (or )Tj 0.0021 Tc 1.194 0 Td (of )Tj 0 Tc 1.117 0 Td (a )Tj 0.0474 Tc 0.807 0 Td (pair )Tj 0.0211 Tc 2.055 0 Td (of )Tj 0.03 Tc 1.137 0 Td (complex )Tj 0.05 Tc 9.6272 0 0 9.5 279.09 363.43 Tm (conjugate )Tj 0.0295 Tc 9.5 0 0 9.5 323.65 363.43 Tm (planes )Tj 0.04 Tc 3.078 0 Td (of )Tj /T1_2 1 Tf 0 Tc 12.1 0 0 12.1 363.37 363.43 Tm (r )Tj /T1_1 1 Tf -0.0024 Tc 9.5 0 0 9.5 25.63 352.09 Tm (\(also )Tj 0.0238 Tc 2.295 0 Td (called )Tj 0.05 Tc 11.9799 0 0 10.1 75.64 352.09 Tm (\(2-)Tj 0 Tc 10.1 0 0 10.1 91.92 352.09 Tm (\) )Tj 0.0332 Tc 9.5 0 0 9.5 95.31 352.09 Tm (complex )Tj 0.0406 Tc 3.998 0 Td (conjugate )Tj 0.0163 Tc 4.596 0 Td (planes\). )Tj 0.0232 Tc -14.804 -1.269 Td (Let )Tj /T1_0 1 Tf 0.05 Tc 9.7091 0 0 9.6 53.17 340.03 Tm (l'\(vI, )Tj -0.035 Tc 8.8066 0 0 9.6 75.99 340.03 Tm (V2\) )Tj /T1_1 1 Tf 0 Tc 11.4 0 0 11.4 92.46 340.03 Tm (= )Tj -0.035 Tc 8.945 0 0 9.8 102.33 340.03 Tm (7r\(VI\) )Tj /T1_2 1 Tf 0 Tc 10.8 0 0 10.8 126.87 340.03 Tm (n )Tj /T1_0 1 Tf -0.035 Tc 9.2011 0 0 9.6 135.23 340.03 Tm (7r\(V2\)' )Tj /T1_1 1 Tf 0.05 Tc 9.6317 0 0 9.5 164.98 340.03 Tm (Then )Tj /T1_0 1 Tf 0.0459 Tc 8.8 0 0 8.8 36.44 316.81 Tm (l' )Tj -0.035 Tc 9.4209 0 0 9.6 42.65 316.81 Tm (\(VI, )Tj 8.5437 0 0 9.6 58.54 316.81 Tm (V2\) )Tj /T1_1 1 Tf 0 Tc 13 0 0 13 74.63 316.81 Tm (= )Tj /T1_2 1 Tf 0.0271 Tc 10 0 0 10 84.88 316.81 Tm (J\( )Tj /T1_0 1 Tf -0.035 Tc 7.224 0 0 9.6 93.87 316.81 Tm (V1)Tj 0 Tc 9.6 0 0 9.6 103.28 321.31 Tm (2)Tj -0.035 Tc 7.392 0 0 9.6 107.01 316.81 Tm (V2)Tj 0 Tc 9.6 0 0 9.6 116.6 321.13 Tm (2)Tj 0.495 -0.45 Td (, )Tj /T1_1 1 Tf -0.035 Tc 7.6378 0 0 9.8 125.08 316.81 Tm (VI )Tj /T1_0 1 Tf 7.392 0 0 9.6 133.83 316.81 Tm (V2 )Tj /T1_1 1 Tf 8.3135 0 0 9.8 143.9 316.81 Tm (\(VI )Tj /T1_2 1 Tf 0 Tc 12.5 0 0 12.5 158.2 316.81 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 9.0885 0 0 9.6 167.42 316.81 Tm (V2\), )Tj 8.9161 0 0 9.6 184.78 316.81 Tm (3VIV2, )Tj /T1_1 1 Tf 7.8298 0 0 9.8 211.23 316.81 Tm (\(V12 )Tj /T1_2 1 Tf 0 Tc 12.2 0 0 12.2 229.66 316.81 Tm (+ )Tj /T1_1 1 Tf -0.035 Tc 7.8154 0 0 9.8 239.2 316.81 Tm (VI )Tj /T1_0 1 Tf 7.224 0 0 9.6 247.95 316.81 Tm (V2 )Tj /T1_2 1 Tf 0 Tc 12.2 0 0 12.2 259.18 316.81 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 8.8311 0 0 9.6 268.23 316.81 Tm (V22\) )Tj /T1_1 1 Tf 0.05 Tc 10.2185 0 0 9.4 286.2 316.81 Tm (/3, )Tj 10.1354 0 0 9.8 301.02 316.81 Tm (-\(VI )Tj /T1_2 1 Tf 0 Tc 12.5 0 0 12.5 323.08 316.81 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 9.0885 0 0 9.6 332.48 316.81 Tm (V2\), )Tj /T1_1 1 Tf -0.0339 Tc 9.4 0 0 9.4 349.77 316.81 Tm (1\) )Tj /T1_2 1 Tf 0 Tc 8.1 0 0 8.1 74.75 301.33 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 8.5893 0 0 9.8 85.23 301.33 Tm (J\({32)Tj 0 Tc 6.7 0 0 6.7 104.19 305.83 Tm (2 )Tj /T1_1 1 Tf 0.661 -0.672 Td (, )Tj /T1_0 1 Tf -0.035 Tc 8.62 0 0 9.8 112.33 301.33 Tm ({3d3)Tj 0 Tc 9.8 0 0 9.8 127.94 300.07 Tm (2 )Tj /T1_1 1 Tf 0.466 0.129 Td (, )Tj -0.035 Tc 7.9821 0 0 9.8 136.71 301.33 Tm (3{32, )Tj 7.3569 0 0 9.8 156.15 301.33 Tm (\({312 )Tj 9.4678 0 0 9.8 184.29 301.33 Tm ({32\)/3, )Tj 0.0465 Tc 9.8 0 0 9.8 211.75 301.33 Tm (-i3I, )Tj -0.0117 Tc 10.2 0 0 10.2 232.75 301.33 Tm (1\), )Tj 0.0114 Tc 9.5 0 0 9.5 25.01 278.29 Tm (where )Tj -0.035 Tc 7.1042 0 0 9.8 52.14 278.29 Tm (i31 )Tj 0 Tc 11.4 0 0 11.4 64.74 278.29 Tm (= )Tj -0.035 Tc 7.9931 0 0 9.8 74.86 278.29 Tm (VI )Tj /T1_0 1 Tf 0.0114 Tc 9.6 0 0 9.6 86.14 278.29 Tm (+V2 )Tj /T1_1 1 Tf 0.05 Tc 9.8699 0 0 9.5 107.36 278.29 Tm (and )Tj /T1_0 1 Tf -0.035 Tc 7.2603 0 0 9.6 126.09 278.29 Tm (i32 )Tj /T1_1 1 Tf 0 Tc 11.4 0 0 11.4 138.72 278.29 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 9.0024 0 0 9.6 148.71 278.29 Tm (VIV2. )Tj /T1_1 1 Tf -0.0341 Tc 9.5 0 0 9.5 173.49 278.29 Tm (We )Tj -0.0236 Tc 1.707 0 Td (will )Tj /T1_0 1 Tf 0.0319 Tc 9.6 0 0 9.6 206.93 278.29 Tm (call1'\(vl,V2\) )Tj /T1_1 1 Tf 0 Tc 9.5 0 0 9.5 262.16 278.29 Tm (a )Tj /T1_0 1 Tf -0.0172 Tc 9.6 0 0 9.6 270.67 278.29 Tm (real )Tj 0.0015 Tc 1.949 0 Td (axis, )Tj /T1_1 1 Tf 0 Tc 9.5 0 0 9.5 311.3 278.29 Tm (a )Tj /T1_0 1 Tf 0.0165 Tc 9.6 0 0 9.6 319.58 278.29 Tm (generator )Tj /T1_1 1 Tf 0.0211 Tc 9.5 0 0 9.5 360.99 278.29 Tm (or )Tj 0.05 Tc 9.7155 0 0 9.5 25.1 267.13 Tm (an )Tj /T1_0 1 Tf 0.0324 Tc 9.6 0 0 9.6 38.4 267.13 Tm (imaginary )Tj 0.0104 Tc 4.787 0 Td (axis )Tj /T1_1 1 Tf 0.04 Tc 9.5 0 0 9.5 103.23 267.13 Tm (of )Tj /T1_2 1 Tf 0.0389 Tc 12.5 0 0 12.5 113.7 267.13 Tm (r, )Tj /T1_1 1 Tf 0.0324 Tc 9.5 0 0 9.5 125.9 267.13 Tm (according )Tj 0.0127 Tc 4.547 0 Td (as )Tj /T1_0 1 Tf -0.035 Tc 7.4608 0 0 9.6 180.69 267.13 Tm (X2 )Tj /T1_1 1 Tf 0 Tc 9.6 0 0 9.6 192.13 267.13 Tm (-)Tj /T1_0 1 Tf 0.0004 Tc 0.861 0 Td (i3lx )Tj /T1_2 1 Tf 0 Tc 12.2 0 0 12.2 217.24 267.13 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.1091 0 0 9.6 226.17 267.13 Tm (i32 )Tj /T1_1 1 Tf 0.037 Tc 9.5 0 0 9.5 238.85 267.13 Tm (has )Tj 0.0052 Tc 1.78 0 Td (two, )Tj 0.0371 Tc 2.172 0 Td (one )Tj 0.05 Tc 9.8076 0 0 9.5 294.21 267.13 Tm (or )Tj 0.0116 Tc 9.5 0 0 9.5 306.31 267.13 Tm (zero )Tj 0.0451 Tc 2.107 0 Td (roots )Tj 0.0349 Tc 2.551 0 Td (in )Tj -0.035 Tc 8.3651 0 0 9.5 360.92 267.13 Tm ("\(. )Tj 0.0284 Tc 9.5 0 0 9.5 25.06 255.97 Tm (Note )Tj 0.05 Tc 10.2879 0 0 9.5 47.85 255.97 Tm (that )Tj 9.9723 0 0 9.5 68.74 255.97 Tm (the )Tj 0.049 Tc 9.5 0 0 9.5 85.96 255.97 Tm (generator )Tj 0.05 Tc 9.5989 0 0 9.5 128.97 255.97 Tm (of )Tj /T1_2 1 Tf 0 Tc 12.5 0 0 12.5 139.98 255.97 Tm (r )Tj /T1_1 1 Tf 0.0349 Tc 9.5 0 0 9.5 149.5 255.97 Tm (in )Tj -0.035 Tc 9.4949 0 0 9.8 160.82 255.97 Tm (7r\(t\) )Tj -0.0246 Tc 9.5 0 0 9.5 180.46 255.97 Tm (is )Tj 0.05 Tc 10.1785 0 0 9.5 25 209.71 Tm (that )Tj -0.0236 Tc 9.5 0 0 9.5 46 209.71 Tm (is, )Tj 0 Tc 1.343 0 Td (a )Tj 0.05 Tc 9.6121 0 0 9.5 67.24 209.71 Tm (generator )Tj 0.0211 Tc 9.5 0 0 9.5 111.51 209.71 Tm (of )Tj /T1_2 1 Tf 0 Tc 12.5 0 0 12.5 122.7 209.71 Tm (r )Tj /T1_1 1 Tf -0.0056 Tc 9.5 0 0 9.5 132.58 209.71 Tm (is )Tj 0.05 Tc 9.9542 0 0 9.5 142.96 209.71 Tm (self-dual )Tj 0.0284 Tc 9.5 0 0 9.5 185.75 209.71 Tm (with )Tj 0.034 Tc 2.255 0 Td (respect )Tj 0.05 Tc 9.8224 0 0 9.5 240.46 209.71 Tm (to )Tj 0.0449 Tc 9.5 0 0 9.5 252.52 209.71 Tm (the )Tj 0.0326 Tc 1.763 0 Td (null )Tj 0.05 Tc 9.6578 0 0 9.5 289.09 209.71 Tm (polarity )Tj 0.0106 Tc 9.5 0 0 9.5 326.43 209.71 Tm (defined )Tj 0.0138 Tc 3.497 0 Td (by )Tj 0.05 Tc 9.5625 0 0 9.5 25 198.19 Tm (the )Tj 0.0297 Tc 9.5 0 0 9.5 41.32 198.19 Tm (linear )Tj 0.0426 Tc 2.803 0 Td (complex )Tj /T1_0 1 Tf 0 Tc 10.8 0 0 10.8 106.54 198.19 Tm (A )Tj /T1_1 1 Tf 0.05 Tc 9.8224 0 0 9.5 117.34 198.19 Tm (to )Tj 0.0253 Tc 9.5 0 0 9.5 129.23 198.19 Tm (which )Tj 0.05 Tc 9.6991 0 0 9.5 156.94 198.19 Tm (the )Tj 0.0363 Tc 9.5 0 0 9.5 173.32 198.19 Tm (tangents )Tj 0.05 Tc 9.6041 0 0 9.5 211.12 198.19 Tm (to )Tj /T1_2 1 Tf 0 Tc 8.5 0 0 8.5 222.54 198.19 Tm (C )Tj /T1_1 1 Tf 0.0263 Tc 9.5 0 0 9.5 231.49 198.19 Tm (belong )Tj 0.0008 Tc 3.246 0 Td (\(see )Tj /T1_2 1 Tf -0.013 Tc 8.5 0 0 8.5 281.89 198.19 Tm ([5, )Tj /T1_1 1 Tf 0.05 Tc 9.6721 0 0 9.5 295.12 198.19 Tm (Theorem )Tj /T1_2 1 Tf 0.0188 Tc 8.5 0 0 8.5 336.53 198.19 Tm (21.1.2]\). )Tj 0.05 Tc 12.1279 0 0 9.1 36.03 186.67 Tm (If )Tj /T1_0 1 Tf 0 Tc 9.3 0 0 9.3 45.67 186.67 Tm (p )Tj /T1_2 1 Tf -0.035 Tc 5.9483 0 0 10.9 53.55 186.67 Tm (=I-)Tj /T1_1 1 Tf 9.8216 0 0 10.5 63.61 186.67 Tm (3, )Tj 0.0407 Tc 9.5 0 0 9.5 74.42 186.67 Tm (from )Tj -0.035 Tc 8.838 0 0 10.5 98.25 186.67 Tm ([5, )Tj 0.05 Tc 9.6734 0 0 9.5 111.19 186.67 Tm (Lemma )Tj /T1_2 1 Tf 0.0032 Tc 8.5 0 0 8.5 146.09 186.67 Tm (21.1.4] )Tj /T1_1 1 Tf -0.035 Tc 9.1156 0 0 9.5 176.21 186.67 Tm (we )Tj -0.0021 Tc 9.5 0 0 9.5 190.07 186.67 Tm (have )Tj 0.05 Tc 10.2879 0 0 9.5 211.47 186.67 Tm (that )Tj -0.035 Tc 7.7713 0 0 9.8 37.21 172.81 Tm (IJCII )Tj /T1_2 1 Tf 0 Tc 8.7 0 0 8.7 56.02 172.81 Tm (= )Tj /T1_0 1 Tf -0.0029 Tc 9.6 0 0 9.6 66 172.81 Tm (q\(q )Tj /T1_2 1 Tf 0 Tc 12.9 0 0 12.9 81.51 172.81 Tm (+ )Tj /T1_1 1 Tf 0.05 Tc 9.8663 0 0 9.7 91.82 172.81 Tm (1\)/2, )Tj 0.0303 Tc 9.5 0 0 9.5 115.73 172.81 Tm (where )Tj -0.035 Tc 6.7599 0 0 9.8 143.96 172.81 Tm (JC)Tj 0 Tc 9.8 0 0 9.8 151.67 171.73 Tm (I )Tj -0.035 Tc 9.3682 0 0 9.5 158.86 172.81 Tm (is )Tj 0.05 Tc 9.6991 0 0 9.5 168.28 172.81 Tm (the )Tj 0.0076 Tc 9.5 0 0 9.5 184.73 172.81 Tm (set )Tj 0.0021 Tc 1.52 0 Td (of )Tj 0.0091 Tc 1.136 0 Td (all )Tj 0.0383 Tc 1.374 0 Td (real )Tj 0.0167 Tc 1.981 0 Td (chords )Tj 0.04 Tc 3.145 0 Td (of )Tj -0.035 Tc 8.732 0 0 9.7 282.69 172.81 Tm (C; )Tj 6.6294 0 0 9.8 37.22 161.47 Tm (IJC)Tj /T1_2 1 Tf 0 Tc 5.8001 0 0 5.8001 46.57 160.21 Tm (2)Tj /T1_1 1 Tf 5.2 0 0 5.2 51.3 161.47 Tm (1 )Tj /T1_2 1 Tf 8.1 0 0 8.1 56.03 161.47 Tm (= )Tj /T1_3 1 Tf 1.246 0 Td (q )Tj /T1_1 1 Tf 11.9 0 0 11.9 73.2 161.47 Tm (+ )Tj /T1_2 1 Tf -0.0294 Tc 8.8 0 0 8.8 83.24 161.47 Tm (1, )Tj /T1_1 1 Tf 0.0256 Tc 9.5 0 0 9.5 93.95 161.47 Tm (where )Tj -0.035 Tc 6.582 0 0 9.8 122.18 161.47 Tm (JC)Tj 0 Tc 9.8 0 0 9.8 129.54 160.21 Tm (2 )Tj -0.0246 Tc 9.5 0 0 9.5 137.08 161.47 Tm (is )Tj 0.05 Tc 9.8357 0 0 9.5 146.86 161.47 Tm (the )Tj 0.036 Tc 9.5 0 0 9.5 163.31 161.47 Tm (set )Tj 0.0211 Tc 1.577 0 Td (of )Tj -0.0098 Tc 1.136 0 Td (all )Tj 0.0418 Tc 1.354 0 Td (tangents )Tj 0.05 Tc 9.8224 0 0 9.5 240.1 161.47 Tm (to )Tj -0.035 Tc 8.3258 0 0 10 251.55 161.47 Tm (C; )Tj 6.4913 0 0 9.8 37.22 150.13 Tm (IJC)Tj 0 Tc 6.7 0 0 6.7 46.36 148.69 Tm (3)Tj /T1_2 1 Tf 5.2 0 0 5.2 51.14 150.13 Tm (1 )Tj /T1_1 1 Tf 13 0 0 13 55.91 150.13 Tm (= )Tj /T1_0 1 Tf 0.0065 Tc 9.6 0 0 9.6 66 150.13 Tm (q\(q )Tj /T1_1 1 Tf 0 Tc 1.664 0 Td (-)Tj 0.05 Tc 10.0473 0 0 9.7 91.63 150.13 Tm (1\)/2, )Tj 0.0351 Tc 9.5 0 0 9.5 115.73 150.13 Tm (where )Tj -0.035 Tc 6.7599 0 0 9.8 143.96 150.13 Tm (JC)Tj 0 Tc 6.7 0 0 6.7 151.3 148.69 Tm (3 )Tj -0.0246 Tc 9.5 0 0 9.5 158.86 150.13 Tm (is )Tj 0.05 Tc 9.5625 0 0 9.5 168.46 150.13 Tm (the )Tj 0.0171 Tc 9.5 0 0 9.5 184.55 150.13 Tm (set )Tj 0.0211 Tc 1.539 0 Td (of )Tj 0.0091 Tc 1.136 0 Td (all )Tj 0.0381 Tc 1.385 0 Td (imaginary )Tj 0.0394 Tc 4.698 0 Td (chords )Tj 0.05 Tc 9.5989 0 0 9.5 298.89 150.13 Tm (of )Tj -0.035 Tc 8.7969 0 0 9.7 310.05 150.13 Tm (C. )Tj 9.3061 0 0 9.5 25.21 136.27 Tm (So )Tj 0.05 Tc 9.5625 0 0 9.5 38.14 136.27 Tm (the )Tj 10.1337 0 0 9.5 54.52 136.27 Tm (total )Tj 9.6555 0 0 9.5 77.93 136.27 Tm (number )Tj 9.8076 0 0 9.5 113.49 136.27 Tm (of )Tj 0.0319 Tc 9.5 0 0 9.5 124.65 136.27 Tm (chords )Tj 0.05 Tc 9.5989 0 0 9.5 155.25 136.27 Tm (of )Tj /T1_2 1 Tf 0 Tc 9.4 0 0 9.4 166.18 136.27 Tm (C )Tj /T1_1 1 Tf -0.035 Tc 9.3682 0 0 9.5 175.24 136.27 Tm (is )Tj /T1_0 1 Tf 7.9552 0 0 9.3 184.63 136.27 Tm (q2 )Tj /T1_2 1 Tf 0 Tc 12.5 0 0 12.5 195.28 136.27 Tm (+ )Tj /T1_0 1 Tf 9.3 0 0 9.3 204.78 136.27 Tm (q )Tj /T1_2 1 Tf 12.5 0 0 12.5 211.48 136.27 Tm (+ )Tj -0.035 Tc 8.1087 0 0 8.5 221.14 136.27 Tm (1. )Tj /T1_1 1 Tf 0.0069 Tc 9.5 0 0 9.5 232.7 136.27 Tm (Dually, )Tj 0.05 Tc 9.8357 0 0 9.5 265.3 136.27 Tm (the )Tj 10.3163 0 0 9.5 282.21 136.27 Tm (total )Tj 9.5464 0 0 9.5 306.17 136.27 Tm (number )Tj 0.0211 Tc 9.5 0 0 9.5 341.37 136.27 Tm (of )Tj 0.0057 Tc 1.155 0 Td (axes )Tj 0.0211 Tc -34.445 -1.213 Td (of )Tj /T1_2 1 Tf 0 Tc 12.1 0 0 12.1 35.77 124.75 Tm (r )Tj /T1_1 1 Tf -0.035 Tc 9.3682 0 0 9.5 45.1 124.75 Tm (is )Tj /T1_0 1 Tf 8.1446 0 0 9.3 54.67 124.75 Tm (q2 )Tj /T1_2 1 Tf 0 Tc 12.9 0 0 12.9 65.85 124.75 Tm (+ )Tj /T1_0 1 Tf 9.3 0 0 9.3 75.54 124.75 Tm (q )Tj /T1_2 1 Tf 12.9 0 0 12.9 82.59 124.75 Tm (+ )Tj /T1_1 1 Tf -0.0061 Tc 9.1 0 0 9.1 92.57 124.75 Tm (1. )Tj -0.0345 Tc 9.4 0 0 9.4 191.01 15.48 Tm (101 )Tj ET endstream endobj 166 0 obj <>/Filter/CCITTFaxDecode/Height 1872/Length 42813/Name/Im0/Subtype/Image/Type/XObject/Width 2240>>stream *T1 ":JDr2 $uReR:BF@TD *P *P@TG *P#(Du+P@29RGDuRB#BF@TD1(Q# (dJHCRc *P"GQ(Q# ( 9RGQ:(CR!B0@TF@TF@TH !F@TD1# (dJdJDr2OnTh#C2-E&*bavmi7QҶvT(rC;N2,FHJ Za:#+vZCC" X茎m&EÝ_UrAv aNJ㥧I#P]$GMoޒDt߫*M1n2WlbU`'wO4IdQIMgwҸK߭kB͢:*2 )h4t]=mGUוH2K2:5A 0AD4#7-k=SL H#)3b J8q<4NG8vqKxK@a.q!9Cʨ1a4ѡNE؇8MOLRp&&Ah\E-DtGd"8Laa>E63Z +-.GU֒Isȏ(3GD#vb#ȎU.GXE_$> P䞖FDtM/^Jt2UZ_" "D"D! 7 *\Ehsc}h8jش?֓AuI$*WqZDB,r5":!#7hRCmGO&:=a &?[LaWdUڝ#"( cA[Ba`eIoiO#PzxtDtA0pѺGP+ _jk[FG(":Eu&VU_*:U"| O9G  V]6^~wqh PdP?]~*x~F?I-&I)GzK߯oK]=~u K3o"Y:~}/K#K 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Tm (-)Tj /T1_1 1 Tf -0.035 Tc 9.7671 0 0 9.9 229.52 306.55 Tm (XjYi; )Tj /T1_3 1 Tf 0 Tc 9.1 0 0 9.1 19.77 295.93 Tm (U )Tj /T1_0 1 Tf 0.05 Tc 8.3248 0 0 6.7 28.53 295.93 Tm (0, )Tj /T1_3 1 Tf 0 Tc 9.1 0 0 9.1 37.59 295.93 Tm (U )Tj /T1_0 1 Tf 0.05 Tc 7.6586 0 0 6.7 46.72 295.93 Tm (1, )Tj /T1_3 1 Tf 0 Tc 9.1 0 0 9.1 54.69 295.93 Tm (U )Tj /T1_0 1 Tf 0.05 Tc 7.3743 0 0 6.7 63.68 295.93 Tm (2, )Tj /T1_3 1 Tf 0 Tc 9.1 0 0 9.1 71.61 295.93 Tm (U )Tj /T1_0 1 Tf 6.7 0 0 6.7 80.38 295.93 Tm (3 )Tj 0.0308 Tc 9.5 0 0 9.5 87.74 295.93 Tm (are )Tj 0.05 Tc 9.5625 0 0 9.5 103.66 295.93 Tm (the )Tj 0.0174 Tc 9.5 0 0 9.5 119.86 295.93 Tm (vertices )Tj 0.0211 Tc 3.612 0 Td (of )Tj 0.0449 Tc 1.144 0 Td (the )Tj 0.05 Tc 9.5589 0 0 9.5 181.06 295.93 Tm (tetrahedron )Tj 9.5989 0 0 9.5 233.01 295.93 Tm (of )Tj 0.0213 Tc 9.5 0 0 9.5 244.07 295.93 Tm (reference )Tj 0.0349 Tc 4.313 0 Td (in )Tj /T1_1 1 Tf 0.05 Tc 10.2135 0 0 9.9 296.36 295.93 Tm (PG )Tj /T1_0 1 Tf -0.0299 Tc 9.5 0 0 9.5 311.65 295.93 Tm (\(3, )Tj /T1_1 1 Tf -0.035 Tc 8.989 0 0 9.9 323.77 295.93 Tm (q\); )Tj /T1_3 1 Tf 0 Tc 9.1 0 0 9.1 19.95 284.77 Tm (U )Tj /T1_0 1 Tf 0.0323 Tc 9.5 0 0 9.5 31.78 284.77 Tm (is )Tj 0.05 Tc 9.5625 0 0 9.5 42.28 284.77 Tm (the )Tj 0.038 Tc 9.5 0 0 9.5 58.86 284.77 Tm (unit )Tj 0.0358 Tc 2.066 0 Td (point; )Tj 0.05 Tc 7.6413 0 0 6.7 19.72 273.43 Tm (1{5 )Tj -0.0056 Tc 9.5 0 0 9.5 36.28 273.43 Tm (is )Tj 0.05 Tc 9.6991 0 0 9.5 46.06 273.43 Tm (the )Tj 0.0142 Tc 9.5 0 0 9.5 62.6 273.43 Tm (Klein )Tj 0.0361 Tc 2.647 0 Td (quadric )Tj 0.04 Tc 3.6 0 Td (of )Tj /T1_1 1 Tf 0.021 Tc 9.9 0 0 9.9 133.1 273.43 Tm (PG\(5, )Tj -0.035 Tc 8.9618 0 0 9.9 160.33 273.43 Tm (q\) )Tj /T1_0 1 Tf 0.0411 Tc 9.5 0 0 9.5 171.53 273.43 Tm (with )Tj 0.0473 Tc 2.245 0 Td (equation )Tj /T1_1 1 Tf -0.0316 Tc 9.8 0 0 9.8 232.4 273.43 Tm (XOX5 )Tj /T1_3 1 Tf 0 Tc 12.3 0 0 12.3 259.18 273.43 Tm (+ )Tj /T1_0 1 Tf 9.5 0 0 9.5 268.9 273.43 Tm (X)Tj 6.7 0 0 6.7 277.51 271.99 Tm (l)Tj 9.5 0 0 9.5 281.32 273.43 Tm (X)Tj 6.7 0 0 6.7 289.23 271.99 Tm (4 )Tj /T1_3 1 Tf 12.3 0 0 12.3 295.72 273.43 Tm (+ )Tj /T1_1 1 Tf 9.8 0 0 9.8 305.3 273.43 Tm (X)Tj 9.9 0 0 9.9 313.34 271.81 Tm (2)Tj 9.8 0 0 9.8 317.54 273.43 Tm (X)Tj 9.9 0 0 9.9 325.17 271.81 Tm (3 )Tj /T1_3 1 Tf 8.1 0 0 8.1 331.79 273.43 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 8.7452 0 0 9.5 341.55 273.43 Tm (0; )Tj /T1_1 1 Tf 14.8641 0 0 15.2 19.89 261.91 Tm (vi )Tj /T1_0 1 Tf 0.0133 Tc 9.5 0 0 9.5 34.48 261.91 Tm (is )Tj 0.05 Tc 9.6991 0 0 9.5 44.44 261.91 Tm (the )Tj 0.0033 Tc 9.5 0 0 9.5 61 261.91 Tm (Veronese )Tj 0.0193 Tc 4.176 0 Td (surface )Tj 0.0211 Tc 3.377 0 Td (of )Tj /T1_1 1 Tf 0.021 Tc 9.9 0 0 9.9 143.72 261.91 Tm (PG\(5, )Tj -0.035 Tc 9.7363 0 0 9.9 170.94 261.91 Tm (q\). )Tj /T1_0 1 Tf -0.0072 Tc 9.2 0 0 9.2 151.87 227.71 Tm (2. )Tj 0.05 Tc 7.9115 0 0 7.6 165.21 227.71 Tm (PRELIMINARIES )Tj 0.0371 Tc 9.5 0 0 9.5 31.4 205.93 Tm (Consider )Tj 0 Tc 4.244 0 Td (a )Tj 0.0406 Tc 0.823 0 Td (twisted )Tj 0.0137 Tc 3.517 0 Td (cubic )Tj 0.0211 Tc 2.615 0 Td (of )Tj /T1_1 1 Tf 0.0255 Tc 9.9 0 0 9.9 148.58 205.93 Tm (PG\(3, )Tj -0.035 Tc 8.9618 0 0 9.9 175.99 205.93 Tm (q\) )Tj /T1_0 1 Tf 0.016 Tc 9.5 0 0 9.5 187.12 205.93 Tm (in )Tj 0.0482 Tc 1.156 0 Td (its )Tj 0.0358 Tc 1.382 0 Td (canonical )Tj 0.0134 Tc 4.489 0 Td (form: )Tj 0.0445 Tc -24.66 -4.756 Td (where )Tj /T1_1 1 Tf 0 Tc 9.9 0 0 9.9 47.76 160.75 Tm (t )Tj /T1_3 1 Tf 0.05 Tc 7.4541 0 0 6 64.17 160.75 Tm (00 )Tj /T1_0 1 Tf -0.0025 Tc 9.5 0 0 9.5 76.42 160.75 Tm (gives )Tj 0.05 Tc 9.6991 0 0 9.5 99.7 160.75 Tm (the )Tj 0.0382 Tc 9.5 0 0 9.5 115.93 160.75 Tm (point )Tj -0.0079 Tc 9.8 0 0 9.8 140.57 160.75 Tm (Uo. )Tj 0 Tc 9.5 0 0 9.5 159.82 160.75 Tm (A )Tj /T1_1 1 Tf -0.0251 Tc 9.9 0 0 9.9 170.38 160.75 Tm (chord )Tj /T1_0 1 Tf 0.05 Tc 9.5989 0 0 9.5 195.03 160.75 Tm (of )Tj 0 Tc 9.8 0 0 9.8 205.46 160.75 Tm (C )Tj -0.0246 Tc 9.5 0 0 9.5 213.94 160.75 Tm (is )Tj 0 Tc 1.021 0 Td (a )Tj 0.0113 Tc 0.817 0 Td (line )Tj 0.05 Tc 9.8076 0 0 9.5 249.39 160.75 Tm (of )Tj /T1_1 1 Tf 0.0482 Tc 9.9 0 0 9.9 260.54 160.75 Tm (PG\(3, )Tj -0.035 Tc 9.1915 0 0 9.9 288.66 160.75 Tm (q\) )Tj /T1_0 1 Tf 0.0306 Tc 9.5 0 0 9.5 299.38 160.75 Tm (joining )Tj 0.0344 Tc 3.301 0 Td (either )Tj 0 Tc 2.785 0 Td (a )Tj 0.05 Tc 9.882 0 0 9.5 19.64 149.41 Tm (pair )Tj 0.0211 Tc 9.5 0 0 9.5 40.41 149.41 Tm (of )Tj 0.032 Tc 1.145 0 Td (real )Tj 0.0399 Tc 1.954 0 Td (points )Tj 0.0211 Tc 3.04 0 Td (of )Tj -0.035 Tc 8.5874 0 0 9.8 109.35 149.41 Tm (C, )Tj 0.0206 Tc 9.5 0 0 9.5 120.97 149.41 Tm (possibly )Tj 0.0176 Tc 3.836 0 Td (coincident, )Tj -0.0168 Tc 5.04 0 Td (or )Tj 0 Tc 1.212 0 Td (a )Tj 0.05 Tc 9.5632 0 0 9.5 225.01 149.41 Tm (pair )Tj 9.5989 0 0 9.5 244.89 149.41 Tm (of )Tj 0.0332 Tc 9.5 0 0 9.5 256.23 149.41 Tm (complex )Tj 0.0287 Tc 3.998 0 Td (conjugate )Tj 0.0248 Tc 4.501 0 Td (points )Tj 0.0211 Tc -33.396 -1.232 Td (of )Tj -0.035 Tc 9.4252 0 0 9.8 31.04 137.71 Tm (C. )Tj 0.0303 Tc 9.5 0 0 9.5 46.58 137.71 Tm (By )Tj 0 Tc 1.623 0 Td (a )Tj /T1_1 1 Tf -0.035 Tc 9.7022 0 0 9.9 71.05 137.71 Tm (real )Tj 0.012 Tc 9.9 0 0 9.9 89.43 137.71 Tm (point )Tj /T1_0 1 Tf 0.0211 Tc 9.5 0 0 9.5 113.67 137.71 Tm (of )Tj 0 Tc 9.8 0 0 9.8 124.82 137.71 Tm (C )Tj -0.035 Tc 9.1156 0 0 9.5 134.45 137.71 Tm (we )Tj 0.0447 Tc 9.5 0 0 9.5 149.02 137.71 Tm (mean )Tj 0 Tc 2.72 0 Td (a )Tj 0.043 Tc 0.883 0 Td (point )Tj 0.0021 Tc 2.68 0 Td (of )Tj 0 Tc 9.8 0 0 9.8 219.68 137.71 Tm (C )Tj 0.0232 Tc 9.5 0 0 9.5 229.41 137.71 Tm (defined )Tj 0.0085 Tc 3.619 0 Td (over )Tj -0.035 Tc 7.7947 0 0 9.5 285 137.71 Tm (,,\(, )Tj 0.05 Tc 9.6349 0 0 9.5 297.26 137.71 Tm (and )Tj 0.0138 Tc 9.5 0 0 9.5 316.27 137.71 Tm (by )Tj /T1_1 1 Tf -0.0252 Tc 9.9 0 0 9.9 330.76 137.71 Tm (complex )Tj 0.0024 Tc -31.345 -1.165 Td (conjugate )Tj 0.0046 Tc 4.332 0 Td (points )Tj /T1_0 1 Tf 0.04 Tc 9.5 0 0 9.5 90.99 126.18 Tm (of )Tj -0.035 Tc 8.7969 0 0 9.8 101.79 126.18 Tm (C, )Tj 9.1156 0 0 9.5 113.57 126.18 Tm (we )Tj 0.0447 Tc 9.5 0 0 9.5 127.78 126.18 Tm (mean )Tj 0.0324 Tc 2.675 0 Td (points )Tj /T1_1 1 Tf 0.05 Tc 11.0625 0 0 9.9 181.7 126.18 Tm (P\(h\) )Tj /T1_0 1 Tf 9.5174 0 0 9.5 207.44 126.18 Tm (and )Tj /T1_1 1 Tf 10.8248 0 0 9.9 226.16 126.18 Tm (P\(t)Tj 0 Tc 9.9 0 0 9.9 241.16 124.75 Tm (2)Tj -0.035 Tc 9.643 0 0 9.9 245.66 126.18 Tm (\), )Tj /T1_0 1 Tf 0.0356 Tc 9.5 0 0 9.5 255.11 126.18 Tm (such )Tj 0.05 Tc 10.1785 0 0 9.5 277.54 126.18 Tm (that )Tj 10.7704 0 0 9.3 298.23 126.18 Tm (tl )Tj 9.5174 0 0 9.5 309.32 126.18 Tm (and )Tj /T1_1 1 Tf -0.035 Tc 8.5612 0 0 9.9 327.68 126.18 Tm (t2 )Tj /T1_0 1 Tf 0.0213 Tc 9.5 0 0 9.5 338.48 126.18 Tm (are )Tj -0.003 Tc 1.669 0 Td (in )Tj -0.035 Tc 9.3076 0 0 9.5 19.26 114.49 Tm ("\(' )Tj 0.0453 Tc 9.5 0 0 9.5 31.05 114.49 Tm (conjugate )Tj 0.0148 Tc 4.604 0 Td (over )Tj -0.035 Tc 8.3651 0 0 9.5 95.24 114.49 Tm ("\(. )Tj 0.0327 Tc 9.5 0 0 9.5 107.77 114.49 Tm (Let )Tj /T1_1 1 Tf 0.05 Tc 10.4135 0 0 9.9 124.8 114.49 Tm (l\(tl' )Tj 0 Tc 9.9 0 0 9.9 143.52 114.49 Tm (t)Tj 0.354 -0.11 Td (2)Tj 0.474 0.11 Td (\) )Tj /T1_0 1 Tf 11.4 0 0 11.4 157.62 114.49 Tm (= )Tj /T1_1 1 Tf 0.05 Tc 10.1911 0 0 9.9 167.66 114.49 Tm (P\(h\)P\(t2\). )Tj /T1_0 1 Tf 9.961 0 0 9.5 218.97 114.49 Tm (Then )Tj /T1_1 1 Tf 10.2991 0 0 9.9 53.89 91.63 Tm (l\(tl' )Tj -0.0338 Tc 9.9 0 0 9.9 72.6 91.63 Tm (t2\) )Tj -0.0081 Tc 2.495 0 Td (I\(t12t22, )Tj 0.05 Tc 9.9686 0 0 9.9 133.8 91.63 Tm (tlt2\(t)Tj 0 Tc 9.9 0 0 9.9 156.67 90.72 Tm (l )Tj /T1_3 1 Tf 12.9 0 0 12.9 162.51 91.63 Tm (+ )Tj /T1_1 1 Tf -0.0089 Tc 9.9 0 0 9.9 171.6 91.63 Tm (t2\), )Tj /T1_0 1 Tf 0.0268 Tc 9.3 0 0 9.3 187.36 91.63 Tm (tI2 )Tj /T1_3 1 Tf 0 Tc 12.9 0 0 12.9 201.57 91.63 Tm (+ )Tj /T1_0 1 Tf 0.05 Tc 9.5006 0 0 9.3 210.76 91.63 Tm (tIt2 )Tj /T1_3 1 Tf 0 Tc 12.9 0 0 12.9 228.75 91.63 Tm (+ )Tj /T1_1 1 Tf -0.035 Tc 9.295 0 0 9.9 238.03 91.63 Tm (t2)Tj 0 Tc 9.9 0 0 9.9 246.2 95.95 Tm (2)Tj 0.499 -0.436 Td (, )Tj /T1_0 1 Tf 0.05 Tc 9.8165 0 0 9.3 255.04 91.63 Tm (tlt2, )Tj /T1_1 1 Tf 12.6479 0 0 9.9 275.66 91.63 Tm (-\(tl )Tj /T1_3 1 Tf 0 Tc 12.9 0 0 12.9 296.25 91.63 Tm (+ )Tj /T1_1 1 Tf 9.9 0 0 9.9 305.52 91.63 Tm (t)Tj 0.372 -0.128 Td (2)Tj -0.035 Tc 9.0002 0 0 9.9 314.04 91.63 Tm (\), )Tj /T1_3 1 Tf 8.6905 0 0 10 321.56 91.63 Tm (1\) )Tj /T1_2 1 Tf 0 Tc 8.1 0 0 8.1 86.73 76.68 Tm (= )Tj /T1_1 1 Tf -0.035 Tc 7.8256 0 0 9.9 97.28 76.68 Tm (I\(CX22,CXICX2,CXI2 )Tj /T1_0 1 Tf 0 Tc 9.9 0 0 9.9 166.38 76.68 Tm (-)Tj /T1_1 1 Tf -0.035 Tc 6.9674 0 0 9.9 175.18 76.68 Tm (CX2,CX2, )Tj /T1_0 1 Tf 0.05 Tc 7.7971 0 0 6.3001 204.93 76.68 Tm (-CXl, )Tj /T1_3 1 Tf -0.035 Tc 8.9254 0 0 10 226.69 76.68 Tm (1\) )Tj /T1_0 1 Tf 0.0445 Tc 9.5 0 0 9.5 19.79 54.19 Tm (where )Tj -0.035 Tc 5.8345 0 0 6.3001 48.54 54.19 Tm (CXl )Tj /T1_1 1 Tf 0.05 Tc 10.8384 0 0 9.9 71.33 54.19 Tm (tl )Tj /T1_3 1 Tf 0 Tc 12.3 0 0 12.3 81.52 54.19 Tm (+ )Tj /T1_1 1 Tf -0.035 Tc 9.295 0 0 9.9 90.79 54.19 Tm (t2 )Tj /T1_0 1 Tf 0.05 Tc 9.6349 0 0 9.5 101.96 54.19 Tm (and )Tj /T1_1 1 Tf -0.035 Tc 5.5166 0 0 9.9 120.31 54.19 Tm (CX2 )Tj /T1_0 1 Tf 0 Tc 11.4 0 0 11.4 133.68 54.19 Tm (= )Tj /T1_1 1 Tf 0.0333 Tc 9.9 0 0 9.9 143.16 54.19 Tm (tIt2' )Tj /T1_0 1 Tf 0.05 Tc 10.0089 0 0 9.5 31.59 43.21 Tm (The )Tj 0.0431 Tc 9.5 0 0 9.5 51.57 43.21 Tm (criteria )Tj -0.0147 Tc 3.447 0 Td (for )Tj 0.05 Tc 9.6991 0 0 9.5 98.8 43.21 Tm (the )Tj 0.0416 Tc 9.5 0 0 9.5 115 43.21 Tm (three )Tj 0.0323 Tc 2.52 0 Td (types )Tj 0.0021 Tc 2.607 0 Td (of )Tj 0.0167 Tc 1.08 0 Td (chords )Tj 0.0118 Tc 3.144 0 Td (are )Tj 0.05 Tc 10.3974 0 0 9.5 219.21 43.21 Tm (that )Tj 9.8357 0 0 9.5 239.92 43.21 Tm (the )Tj 0.0406 Tc 9.5 0 0 9.5 256.51 43.21 Tm (polynomial )Tj /T1_1 1 Tf -0.035 Tc 7.6195 0 0 9.9 306.34 43.21 Tm (X2 )Tj /T1_0 1 Tf 0 Tc 9.9 0 0 9.9 317.76 43.21 Tm (-)Tj /T1_1 1 Tf -0.035 Tc 7.0984 0 0 9.9 326.2 43.21 Tm (CXIX )Tj /T1_3 1 Tf 0 Tc 12.3 0 0 12.3 343.42 43.21 Tm (+ )Tj /T1_1 1 Tf -0.035 Tc 5.1984 0 0 9.9 352.34 43.21 Tm (CX2 )Tj /T1_0 1 Tf 0.05 Tc 9.5792 0 0 9.5 19.97 31.51 Tm (has )Tj -0.035 Tc 9.3091 0 0 9.5 38.83 31.51 Tm (2, )Tj 0 Tc 9.5 0 0 9.5 50.79 31.51 Tm (1 )Tj 0.04 Tc 0.897 0 Td (or )Tj 0 Tc 1.344 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