Solution Exercise 4.28.
I studied the lives of great men
and famous women, and I found that the men and women who got to the top were
those who did the jobs they had in hand, with everything they had of energy and
enthusiasm.
—
Henry Truman
Phelps (1871–1944)
Exercise 4.28. Symbolize each perspectivity forming the projectivity in each of the above diagrams.
Figure 1.
Define A'
= AP
· A"O, B' = BP
· B"O, and C' = CP
· C"O. The perspectivities and
determine the projectivity
Figure 2.
Let o be
the line determined by the points of intersection of lines a, b, c with lines a', b', c',
respectively. Let p be the line determined by the
intersections of the lines a', b', c'
with lines a", b", c",
respectively. The perspectivities and
determine the projectivity
Figure 3.
Let lines a,
b, and c be concurrent at point P. Let A, B, and C be the
respective points of intersection lines a,
b, and c with line o. Let a' = AA", b = BB', and c
= CC" be concurrent at the point Q.
The elementary correspondence and the perspectivity
determined the projectivity
Or, the perspectivity
and elementary correspondence
determine the projectivity
