Identifier

etd-07132005-181504

Degree

Master of Science (MS)

Department

Mathematics

Document Type

Thesis

Abstract

Euclid’s Elements is the foundation for geometry. Book V of Euclid’s Elements, which is independent from the earlier books, focuses on multiples, ratios, and proportions. This paper presents a model of the conceptual content of Book V, but using carefully selected modern notation to represent Euclid’s ideas without changing them drastically. All of the propositions and proofs from Euclid have been restated using just enough modern language to make clear for a modern reader. We also present a modern theory that bears analogy, proposition by proposition, to Euclid’s theory, but uses rigorous modern methods of proof.

Date

2005

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

James J. Madden

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