Excerpt from The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Two Books and Portions of the Eleventh and Twelfth Books; With Notes and Exercises

Polars, Orthogonal Circles, Pedal Triangles, The Pedal Line, The nine-point Circle, Co-axal Circles, Harmonic Ranges, Inversion, and the Properties of a Complete Quadrilateral.

Out of the large number of Propositions on these subjects it is clear that only a selection could be made, but I have endeavoured within the range chosen to omit no important Proposition. Without unduly increasing the size of_ the book it was impossible to prove all such important Proposi tions in the text. It is hoped, however, that the hints attached to those given as Exercises will be sufficient or any fairly intelligent student.

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