Veblen, Oswald, 1880-1960, Young, John Wesley, 1879-1932 · Boston, New York [etc.] Ginn and Company · leaf 248
pairs AA andBB be representedby the points Ocoand la respectively (fig. 96). Let xx be any other pair of the invo-lution. We then have, clearly from the above, xx = a. Further, thecross ratios in question give R(0co, la) = -> B(0oo, xx) = —;-■ a x These are equal, if and only if x = ax, or if… … Fig. 96 EXERCISES 1. Show that an involution which has two harmonic conjugate pairs has.double points if and only if — 1 has a square root in the field. 2. Show that any involution may be represented by the equation xx = a. 234 ONE-DIMENSIONAL PEOJECTIVITIES [Chap, vm 3. The equation of Ex. 13, p.…
Geometry, Projective
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