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Unformatted text preview: the Metrica is an application of the Law of Cosines, as given in Book II, Propositions 12 and 13 in the Elements . Given ABC , we denote the (lengths of the) side opposite each vertex using the corresponding lower case letter (see igure 1.50 ). A B C D c b a A B C D c b a igure 1.50: Propositions II.12-13: c 2 = a 2 + b 2 2 c CD (a) Obtuse Case: Suppose the angle at C is obtuse. Extend BC to the foot of the perpendicular from A , at D . Prove Euclids Proposition 11.12: c 2 = a 2 + b 2 + 2 c CD....
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- Fall '08