Euclid's Elements Book One with Questions for Discussion

Euclid's Elements has for thousands of years stood as the preeminent example of a self-contained rational system. From a small number of definitions, and only five postulates, Euclid constructs a sequence of proofs whose interconnectedness and remarkable conclusions raise deep questions about the nature of human reason and its relation to the world. Yet because the subject of this work is ostensibly mathematics, it is generally viewed as a technical treatise, full of useful conclusions and fine material for school geometry, but hardly leading to any genuine inquiry. The present book is an attempt to reclaim the Elements for serious students of the humanities. Book One is a beautiful and coherent composition, moving in sometimes surprising ways to a very satisfying end. It is deeply rewarding to readers who are ready to go beyond merely following step by step, who are interested in why this step here, how learning and discovery happen, and what a particular proof shows us about what it means for things to be the same or different. Rather than serving as commentary or explanation of the text, Dana Densmore's accompanying Questions for Discussion are intended as examples, to urge students to think more deeply and carefully about what they are watching unfold, and to help them find their own questions in a genuine and exhilarating inquiry. Book jacket.