Working Through Book I of Euclid’s Elements

Recently I re-worked my way through all forty-eight propositions of Book I of Euclid's Elements. In the book, Euclid offers a captivating introduction to classical geometry, which straddles the world of perfect abstraction on the one hand, yet also Euclidean geometry relies upon certain principles of the physical world around us. For example, in some … Continue reading Working Through Book I of Euclid’s Elements

On The Puzzling History of Euclid’s Fifth Postulate

At the outset of Euclid's Elements he offers twenty-three definitions, five postulates, and five common notions (sometimes translated as "axioms"). Of the five postulates, the fifth is the most troubling. It is known as the Parallel Postulate. The word postulate can be roughly translated to mean "request," "question," or "hypothesis" (postulat in Latin means "asked"). … Continue reading On The Puzzling History of Euclid’s Fifth Postulate