Introduction

Summary

Through the ostensibly infallible process of logical deduction, Euclid of Alexandria (ca. 300 B.C.) derived a colossal body of geometric facts from a bare minimum of genetic material: five postulates—five simple geometric assumptions that he listed at the beginning of his masterpiece, the Elements. That Euclid could produce hundreds of unintuitive theorems from five patently obvious assumptions about space, and, still more impressively, that he could do so in a manner that precluded doubt, sufficed to establish the Elements as mankind's greatest monument to the power of rational organized thought. As a logically impeccable, tighty wrought description of space itself, the Elements offered humanity a unique anchor of definite knowledge, guaranteed to remain eternally secure amidst the perpetual flux of existence—a rock of certainty, whose truth,by its very nature, was unquestionable.

This universal, even transcendent, aspect of the Elements has profoundly impressed Euclid's readers for over two millennia. In contrast to all explicitly advertised sources of transcendent knowledge, Euclid never cites a single authority and he never asks his readers to trust his own ineffably mystical wisdom. Instead, we, his readers, need not accept anything on faith; we are free and even encouraged to remain skeptical throughout. Should one doubt the validity of the Pythagorean Theorem (Elements I.47), for example, one need not defer to the reputation of “the great Pythagoras. Instead, one may satisfy oneself in the manner of Thomas Hobbes, whose first experience with Euclid was described by John Aubrey, in his Brief Lives, in the following words.