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Chapter 1 gives a brief historical introduction to di erential geometry and explains the extrinsic versus the intrinsic viewpoint of the subject.2 This chapter was not included in the lecture course at ETH. The mathematical treatment of the eld begins in earnest in Chapter 2, which introduces the foundational concepts used in di erential geometry

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Book 11 deals with the fundamental propositions of three-dimensional geometry. Book 12 calculates the relative volumes of cones, pyramids, cylinders, and spheres using the method of exhaustion.

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