The Problem of the Angle Bisectors
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At <^= — I, T = o is an inflexion <^'3= 54T' which has four-point contact with the curve /8= — T = 54 at this point. At <^ = o, t= — i is a conjugate point. The point A is represented by a cusp at <^=i, T=-V. At B (<^= -^MillLJl) ^ ^^_ (45+in i7) \ ^^^ ^^^^^ j^^g ^.^^jj^^^, . with D2 and also at C the conjugate of J5 in (abc). The point . Ff becomes the infinite point on <^— 4r=o, the axis of the parabolic branch. The locus D2 is ' • (-T) (<^-4t) (3, ^_4t)+<^^ = o (53) Its asymptotes are — T-j-| = o with intersection at <^=— 5, t=o <^—4T+§ = o with intersection at <^ = ^^, t=^ 3<^—4T— 2 = with intersection at<^=2, t=i At the origin is a cusp <^^= i6t3.
The contacts of the curve with D, have been noted. At <^=2, t=i, which is an infinite point in ia, b, c) and {y, z), D^ touches <^— t— 1 = 0, the line which also falls on D{a, fi) in the (o, /8) plane.
The locus r= o is a hyperbola t(6<^-i)-(6.^'-3<^+i) = o (54) the asjanptotes being THE TRANSFORMATIONS 29 The complete representatives of £>, and D^ are the irreducible factors above set out with the addition of <^ = o in both cases and also — t=o in the case of Di.
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To quickly assess the difficulty of the text, read a short excerpt:
At <^= — I, T = o is an inflexion <^'3= 54T' which has four-point contact with the curve /8= — T = 54 at this point. At <^ = o, t= — i is a conjugate point. The point A is represented by a cusp at <^=i, T=-V. At B (<^= -^MillLJl) ^ ^^_ (45+in i7) \ ^^^ ^^^^^ j^^g ^.^^jj^^^, . with D2 and also at C the conjugate of J5 in (abc). The point . Ff becomes the infinite point on <^— 4r=o, the axis of the parabolic branch. The locus D2 is ' • (
What to read after The Problem of the Angle Bisectors?
You can find similar books in the "Read Also" column, or choose other free books by Richard Philip Baker to read online
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