Repository: UIHistories Project: Mathematical Models by Arnold Emch - Series 3 (1925) [PAGE 9]

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s is the same as before, T h e quartic of N o * 28 degenerates into the z-plane and the cubic: x2 ~j-jy2

2z2 2z2 1

which reduces to

X z z 1

y z

=

0,

(x2+y2) (z -- 1) - *(2z2 - 1) + 2z2 - z = 0. The jy-plane touches the cubic along h. The intersection k of the planes x = \,z = \ lies on the cubic, and the plane z = 1 touches the cubic along s, the infinite line of the z-plane* T h u s the cubic has 7 real lines, of which 4 are absorbed by h and s.

Fig. 4

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