462
THE THEORY OF SCREWS.
[418
will be transformed to
o, PaXi, 0, PiX4.
The question may be illustrated by Figure 45.
Let 1, 2, 3, 4 be the four corners of the tetrahedron. Let the transfor-
mation convey P to P' and Q to Q'. Xs P varies along the ray, so will P'
vary, and the two will describe homographic systems, of which 2 and 4 are
the double points. In a similar way, Q and Q' will trace out homographic
systems on the ray 1 3. We shall write the points on 2 4, in the order,
2, 4, P, P'.
Through 2, the generator of the surface 2 3 can be drawn (12 is not a
generator), and through 4 the generator 4 1 can be drawn (4 3 is not a
generator); thus we have, for the corresponding order on 1 3.
The anharmonic ratio of the first set is that of 0, oo, ,
X2 ’ p2X2’
” » second „ oo, 0,
Xi Pi Xj
but since P1Psi = paPit
then the anharmonic ratios are equal.