Excerpt from Elementary Projective Geometry
The projective unit is the cross-ratio of four collinear points or of four concurrent lines in a plane: from this I proceed to the study of projective rows and pencils, and the involutions of six points or lines, which play an important part in the solution of problems. I then deduce the properties of the curve of the second degree, defined as the locus of the intersections of corresponding rays of two projective pencils, first proving an important harmonic property of the tangent.
The chief properties of polars follow; and of inscribed and circumscribed polygons, with the construction of conics to satisfy five given conditions, and solutions of other problems connected with the conic.
I conclude with the elements of polar reciprocation, and of plane homology, with brief notes on projection in space and the sections of a circular cone.
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