Excerpt from A Treatise on Some New Geometrical Methods, Vol. 1 of 2: Containing Essays on Tangential Coordinates, Pedal Coordinates, Reciprocal Polars, the Trigonometry of the Parabola, the Geometrical Origin of Logarithms, the Geometrical Properties of Elliptic Integrals, and Other Kindred Subjects Now, the reality of this distinction cannot justly be admitted. Man's triumphs in the sphere of intellect are as important in our own age as at any former period of this world's history. Let us limit our View to the progress of mathematical science alone; and it will suffice merely to mention the names of Euler, Lagrange, Laplace, Legendre, Jacobi, Abel, and a host of others to show the advance which this department of human knowledge has made in modern times, depending, as it does, neither on experiment nor observation, neither on the use of ingenious machinery nor of instruments of precision. 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.