Projective Geometry

Cover Projective Geometry
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A further development of the properties of the conies and their reciprocals, the envelopes of second class, requires the aid of two important and historic theorems which are reciprocals of each other. These theorems will be the subject of the next chapter.
Exercises 1. If the axes of two protectively related sheaves of planes are parallel to each other, what elementary form is generated by them?
2. If from a given point perpendicular lines are dropped upon the planes of a sheaf of first class,
...what is the locus of the feet of these perpendiculars?
3. If from a given point perpendicular lines are dropped upon the planes of a sheaf of second class, show that these lines lie upon a cone of second order.
4. If from a point outside the plane of a sheaf of rays of first class, perpendicular planes are drawn to the rays of the sheaf, these planes will form a sheaf of planes of first class. What line is the axis of the sheaf?
5. Construct a hyperbola having given the two asymptotes and one point.


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