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 it also relies upon certain physical principles found in the 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

On the Definitions, Postulates, and Common Notions of Euclid’s Elements

Euclid's Elements ("Stoikheîon") is the foundational text of classical, axiomatic, and deductive geometry ("earth-measurement"). The Elements is composed of thirteen books, each filled with propositions that beautifully unfold a theory of number, shape, proportion, and measurability. The Elements was the essential geomtery textbook for nearly 2,000 years thanks to the preservation efforts of the Byzantines, … Continue reading On the Definitions, Postulates, and Common Notions of Euclid’s Elements