Excerpt from A New Analysis of a Plane Geometry, Finite and Differential: With Numerous ExamplesCases (5) and (7) are reduced in surd form and (6) by means of a point to measures of two elements. Thus we do away with the idea of reference elements.But this brings us to another matter. We know that taking four arbitrary points, there is a relation between the six pairs of measures of two elements. We have also such relations in the case of three points and a line, two points and two lines and in the case of three lines. We have called such relations eliminants, being eliminants of relative position. Suppose we have reduced all our complex measures and noted all our eliminants. The matter of proving a relation between the complex measures reduces to proving the relation between their reductions with the help of the eliminants.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis 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.