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... Illustration of Theorem 1.1 17 1.3 Illustration of Theorem 1.2 24 1.4 Illustration of Corollaries 1.7 and 1.8 31 1.5 Illustration of Theorem 1.3... sequence of line segments is unique This is stated in the following theorem which is also the main result in this section Theorem 1.1 Let a, b ∈ E and let e1 , , ek be a sequence of line segments... ym−1 = x∗m−1 ) If ym ∈ [x∗m−1 , x∗m [ , by Theorem 1.1, there exists t¯m ∈ [t¯m−1 , t¯m [ for which γ0 (t¯m ) = ym Since γ0 is parametrized by arclength, Theorem 1.1 says that γ0 , is still affine