Excerpt from The Pythagorean Triangle: Or the Science of Numbers Accordingly, in tracing the science from the earliest period of its existence, we must prepare ourselves to meet with many changes which have periodically occurred in consequence Of improve ments and discoveries in the liberal arts, and the amelioration of manners and customs, as science progressed from ignorance to learning, and from a comparatively savage condition to its present palmy state of refinement and moral culture. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.