Based on the author's work in Egypt in the 1880s, this unusual volume addresses one of history's greatest puzzles -- how were the pyramids of Gizeh built? Before Petrie undertook this study, the Great Pyramid was a byword for paradox - something that was generally familiar, yet not accurately known. No measurements or detailed examination had been performed. Petrie set out to apply mathematical methods to the study of the pyramids and surrounding temples, with the objective of understanding the methods and abilities of the ancient workers. The result, presented in this volume, is a complete set of measurements of the pyramids, both inside and outside. These provide the foundation for the rest of the book, which deals with the architectural ideas of the pyramid builders, the mechanical methods they used, and a comparison of previous theories with the facts that Petrie had newly established.