Elements of Projective Geometry

Cover Elements of Projective Geometry
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6. 45, in space.
4. Ex. 3, in the bundle. 7. Ex. 6, in the bundle.
Solve the duals of each of the following : 8. Ex. 1, page 49, in space.
9. Ex. 3, page 49, in the plane.
10. Ex. 3, page 49, in space.
11. Ex. 1, page 49, in the plane, considering the case in which the ranges are coplanar.
12. If three ranges in a plane have concurrent bases and if two of the ranges are perspective with the third, these two ranges are perspective with each other.
13. Three fixed lines p l, p 2, p 3 radiate from
... A I} one of three fixed collinear points A^ A. 2, A 3 . A point P a moves on j^, and the lines Af^ A Z P 1 cut p^ p a respectively in P 2, P 3 . Show that P 2 P 3 has a fixed point.
54 PROJECTIVITIES OF PRIME FORMS 46. Special Case. In the construction described in 39 the only limitation upon the position of the points P and P^ was that P l should not be at A 1 and that P% should not be at A y The necessity for this limitation is due to the complete failure of the construction which would result from the coincidence of the lines PiA v ^-Bp P\C r We shall now consider a special case which is noteworthy because it puts in evidence a line that has important relations to all pairs of corresponding points of the ranges and furnishes a basis for several simple constructions.


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