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Excerpt from A New Basis for the Metric Theory of Congruences: A Dissertation Submitted to the Faculty of the Ogden Graduate School of Science in Candidacy for the Degree of Doctor of Philosophy, Department of Mathematics In the third section we Obtain new proofs of some of the most important general theorems on congruences. These results are typical-of those Obtained by means of the Kummer theory. The fourth section takes up the axis and ray congruences and the cor responding curves on the focal surfaces, all of which were recently discovered by Wilczynski.1 A number of new theorems concerning these configurations, mainly metric in character, are proven in this section. In the final section we discuss the equations of the Darboux conics of a point on one of the focal surfaces and consider some special cases. 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.

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