Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. In this third edition, the two volumes have been compressed into one; the whole has.been very carefully revised and corrected; the Notes will be found at the foot of the pages, to which they respectively belong; the Questions for Practice, which were omitted in the last edition, have been restored; and though it is scarcely possible to print a mathematical work, of any extent, without some errata; yet it is hoped, that few can be named, which will be found more correct than the present.