Common Contracts
1 similar null contracts
SEALSJanuary 25th, 2010
Proof. Take three translates K x , K2K 2 and K3K 3 of K that satisfy the conditions for Theorem 3. Suppose moreover, that the chord in K x which connects the intersection points of K x with K2K 2 and K3K 3 respectively which are différent from the triple intersection, is not a chord whose endpoint tangents are parallel. Let K4K 4 be the unique translate of K différent from K x which also contains this segment as a chord. By the conditions of Theorem 4, K4K 4 passes through the remaining double intersection point of K2K 2 and K 3 . However, the above mentioned chord in K x is never of the " degenerate parallelogram " type, since if it were, we could fînd the desired translate K4K 4 passing through the intersection points of K1?K 1? K2K 2 and K3K 3 outside of K x fl K2K 2 f| K3K 3 by a passage to the limit. Hence Theorem 3is applicable and we hâve proved Theorem 4.
