Conics and Cubics

Extract

I am sorry that Professor Watson (this volume, p. 261) has been so puzzled by the last sentence in a recent note of mine “Query! What is the envelope of the principal axes of conics touching any four lines? ” By “Query ” I did not mean that I was delivering a seventeenth-century challenge to the learned world, but that I should be interested to see a really elementary investigation, provided it was short, though I was disinclined to seek one myself. For from a slightly higher standpoint the question is very simple. Consider the envelope of lines perpendicular to their conjugates with respect to all conics of a pencil of conic envelopes touching four lines.