Excerpt from First Principles of the Differential and Integral Calculus, and Their Applications, According to the Course of Study of Coopers Hill College Another good illustration of the meaning of the word limit is given by considering what is meant by saying that a railway train, which may be continually varying its speed, is at any given moment moving at the rate of so many miles per hour. Every one, I believe, has a very clear conception that this is so - that at any one moment the train is going at one particular speed; but if we try to see how this is to be defined we are led at once to that par ticular kind of limit which is called a differential coefficient. 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.