First Step in Geometry

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. Geometrical deductions are problems which are intended to be solved by the application of recognised geometrical methods and propositions. They are divided into several classes. A geometrical deduction is termed a rider when it is given as an exercise on a particular proposition. It generally happens that the difficulty of a deduction is greatly diminished when it is given in this way, for we know in what direction to seek for a solution. When a deduction is presented as a rider, it is, of course, expected that the proposition to which the deduction is appended shall be made use of in the solution. It will occasionally happen, with carelessly constructed riders, that a simpler solution, not in volving this proposition, is available; but generally there can be no difficulty in so arranging the proof as to introduce the proposition on which the deduction is supposed to be founded.