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Excerpt from Three Dimensional Chains and the Classification of the Resulting Collineations in Space: Thesis If, however, the coefficients in the transformation are restricted to real numbers and if two such transformations are regarded as equivalents only if one can be transformed into the other by a transformation with real coefficients the number of types is increased. Thus in the one-dimensional case we have three well known types usually designated by the terms+, hyperbolic, elliptic, and, .parabolic. Here, furthermore, arises the important additional problem as to the conditions under which a collineation with complex coefficients can be transformed into one with real coefficients. In the one - dimensional case again these confiitions are well known: it is necessarv and sufficient that the projective transformation on the complex variable leave a circle in the Argand plane of the complex variable invariant. 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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