Mark STECHER - Academia.edu (original) (raw)
Uploads
Papers by Mark STECHER
Euclid’s Elements is the foundation for geometry. Book V of Euclid’s Elements, which is independe... more 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
Euclid’s Elements is the foundation for geometry. Book V of Euclid’s Elements, which is independe... more 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