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.