Title page for ETD etd-07132005-181504


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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