Smart, Edward Howard · London : Macmillian and Co. · leaf 97
ny pair of conjugate lines (with respect toa circle) through a point, together with the tangents to theI circle from that point, form a harmonic pencil. For let AB, AC be conjugate lines through A (Fig. 335).Then the pole of AB lies on AC. Also, since AB passes through A, the pole of AB lies on… … Fig. 336. Conversely, if four lines through a point form a liarmonicpencil, conjugate rays of which are tangents from the point,the other two are conjugate lines with respect to the circle. This follows easily : the proof is left as an exercise. HARMONIC PROPERTIES OF THE INSCRIBED QUAD-RANGLE AND…
Geometry, Projective
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