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Published online by Cambridge University Press: 03 November 2016
The textbook demonstrations of the well-known properties of two conics, the common self-polar triangle and the conic-envelope of lines cut in harmonic conjugates by them, usually suffer from the defects that the general case only is given and that the methods are not always adaptable to special cases. As the author feels the habit of contentment with general cases only a dangerous one and encouraging of loose thinking, he proposes to list the special cases, indicating for the sake of brevity proofs in outline only or, where very trivial, omitting them entirely. A third property—that of the conic-locus of points at which the conics subtend harmonic conjugates, as the immediate reciprocal of the second, has not been listed.
page no 2 note * An interesting alternative construction for the envelope is as follows: If p, the polar of P on S 1 with respect to S 2, meets S 1 at R, S, then PR, PS are the tangents to the envelope from P.