Type of Document	Master's Thesis
Author	Stecher, Mark Robert
Author's Email Address	bstecher@math.lsu.edu
URN	etd-07132005-181504
Title	Modern Interpretation of Euclid's Theory of Ratio and Proportion
Degree	Master of Science (M.S.)
Department	Mathematics
Advisory Committee	Advisor Name Title James J. Madden Committee Chair Frank Neubrander Committee Member W. George Cochran Committee Member
Keywords	adding magnitudes adding squares modern restatement ekthesis proportion ratio adding line segments logical structrue of Euclid's Elements geometry
Date of Defense	2005-06-23
Availability	unrestricted
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.
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