Page:Carroll - Euclid and His Modern Rivals.djvu/247



[''Scene as before. Time, the early dawn.  slumbering uneasily, having fallen forwards upon the table, his forehead resting on the inkstand. To him enter  on tip-toe, followed by the phantasms of , &c., who have come to see fair play.'']

§ 1. Treatment of Pairs of Lines.

Euc. Are all gone?

Min. 'Be cheerful, sir:
 * Our revels now are ended: these our actors,
 * As I foretold you, were all spirits, and
 * Are melted into air, into thin air!'

Euc. Good. Let us to business. And first, have you found any method of treating Parallels to supersede mine?

Min. No! A thousand times, no! The infinitesimal method, so gracefully employed by M. Legendre, is unsuited to beginners: the method by transversals, and the method by revolving Lines, have not yet been offered in a logical form: the 'equidistant' method is too cumbrous: