Theorems in Projective Geometry
The flavour of this chapter will be very different from the previous two. It is chiefly devoted to giving an account of some theorems which establish that there is a subject worthy of investigation, and which Poncelet was rediscovering. I shall state what they say, and indicate how they might be proved. Then I shall indicate a way of proving them by the tactic of establishing them in a special case (when the argument is easy) and then showing that the general case reduces to this special one. I shall prove them in the special case, and indicate how the reduction from general to special can be carried out. This method of reduction is the key idea in projective geometry, and in that way we shall begin our study of the subject. Towards the end of the section we shall work our way back to Poncelet and see what he required of projective geometry.
KeywordsProjective Geometry Conic Section Polar Line Outer Conic Closure Theorem
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