Quadratic Involutions On the Plane Rational Quartic
Quadratic Involutions On the Plane Rational Quartic
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To quickly assess the difficulty of the text, read a short excerpt:
We shall now study the four-point more in detail. The one point ob- tained was that determined by the fines L(o, i), L(o, 2) and L(o, 3)- Thus the point is paired off with the double line o. In the same way each of the four points is paired with a double line. Now there is reason to believe from other considerations, that these points are in some way related to the Stahl conic N, which is the locus of the flex lines of cubic osculants of the rational quartic. We shall show that the four points ...are the polar points of the four double lines as to the conic N.
If the quartic is written (21) X, = a, - 1* + ^ bi /3 + 6 Ci f + 4 ^, - f + e. -, [i = I, 2, 3], it is known that N takes the form (22) — 36( bcx) (cdx) +12 {ad x) (c d x) +12 {b e x)(b c x) +4 (b d x)' + {aexY + 4 {ab x) {dex) — 8 (adx) (b ex) =0, where (b c x) Cq Ci C2 and so on.
bo b.
b.
Co Ci Ci Xq Xi X2 i6 T. B. Ashcraft: Quadratic Involutions on the Plane Rational Quartic. Taking the quartic as given by (i) N is (23 )xo'[ — 4|oiii(a2C2+2&/) I |62C2(a, c, +2fe, *) | +4|62C2(aiC, +25, ") | {ai't^c^l + 4 I o, ft, (flj C2 + 2 b^') 1 1 a, 6, C2' I +4 |a, ft, ^2 C2 1' + I a, ' ^2' 1' + 4 I a, " ^2 ^2 II by CyCi' I — 8 I a, " ^2^2 I I o, ft, C2' | ] + Xi' [i6a2b2'c2] + x' [ i6aift, 'Ci] + x, ^2 [ — i6ft, ft2(a^iC2 + Oz^i)] + Xo Xj [ — 8 6, c, I a, 6, (02 C2 + 2 62') I + 8 a, 6, I ^2 C2 (
What to read after Quadratic Involutions On the Plane Rational Quartic?
You can find similar books in the "Read Also" column, or choose other free books by Thomas Bryce Ashcraft to read online
To quickly assess the difficulty of the text, read a short excerpt:
We shall now study the four-point more in detail. The one point ob- tained was that determined by the fines L(o, i), L(o, 2) and L(o, 3)- Thus the point is paired off with the double line o. In the same way each of the four points is paired with a double line. Now there is reason to believe from other considerations, that these points are in some way related to the Stahl conic N, which is the locus of the flex lines of cubic osculants of the rational quartic. We shall show that the four points ...are the polar points of the four double lines as to the conic N.
If the quartic is written (21) X, = a, - 1* + ^ bi /3 + 6 Ci f + 4 ^, - f + e. -, [i = I, 2, 3], it is known that N takes the form (22) — 36( bcx) (cdx) +12 {ad x) (c d x) +12 {b e x)(b c x) +4 (b d x)' + {aexY + 4 {ab x) {dex) — 8 (adx) (b ex) =0, where (b c x) Cq Ci C2 and so on.
bo b.
b.
Co Ci Ci Xq Xi X2 i6 T. B. Ashcraft: Quadratic Involutions on the Plane Rational Quartic. Taking the quartic as given by (i) N is (23 )xo'[ — 4|oiii(a2C2+2&/) I |62C2(a, c, +2fe, *) | +4|62C2(aiC, +25, ") | {ai't^c^l + 4 I o, ft, (flj C2 + 2 b^') 1 1 a, 6, C2' I +4 |a, ft, ^2 C2 1' + I a, ' ^2' 1' + 4 I a, " ^2 ^2 II by CyCi' I — 8 I a, " ^2^2 I I o, ft, C2' | ] + Xi' [i6a2b2'c2] + x' [ i6aift, 'Ci] + x, ^2 [ — i6ft, ft2(a^iC2 + Oz^i)] + Xo Xj [ — 8 6, c, I a, 6, (02 C2 + 2 62') I + 8 a, 6, I ^2 C2 (
What to read after Quadratic Involutions On the Plane Rational Quartic?
You can find similar books in the "Read Also" column, or choose other free books by Thomas Bryce Ashcraft to read online
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