Unformatted text preview: Book IV of the Elements contains the following implicit proof of Theorem 1.3.3 (see Figure 1.26 ). This was proved by vector methods in Exercise 8 . (a) The lines bisecting ∠ B and ∠ C intersect at a point D above BC , because of Book I, Postulate 5 (known as the Parallel Postulate ): That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced 8 The “M¨obius band” was independently formulated by Johann Listing (18081882) at about the same time—in 1858, when M¨ obius was 68 years old. These two are often credited with beginning the study of topology. [ 31 , p. 1165]...
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 Fall '08
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 Calculus, Vectors, Vector Space, Euclidean geometry, Barycentric Coordinates

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