Further nonsense verse and prose

(A Mathematical Courtship)

It was a lovely Autumn evening, and the glorious effects of chromatic aberration were beginning to show themselves in the atmosphere as the earth revolved away from the great western luminary, when two lines might have been observed wending their weary way across a plain superficies. The elder of the two had, by long practice, acquired the art, so painful to young and impulsive loci, of lying evenly between her extreme points; but the younger, in her girlish impetuosity, was ever longing to diverge and become an hyperbola or some such romantic and boundless curve.

“They had lived and loved: fate and the intervening superficies had hitherto kept them asunder, but this was no longer to be: a line had intersected them, making the two interior angles together less than two right angles. It was a moment never to be forgotten and they journeyed on, a whisper thrilled along the superficies in isochronous waves of sound, ‘Yes! We shall at length meet, if continually produced!’” (“Jacobi’s Course of Mathematics,” Chap. I.). We have commenced with the above quotation as a striking illustration of the advantage of introducing the human element into the hitherto barren region of Mathematics. Who shall say what germs of romance, hitherto not observed, may not underlie the subject? Who can tell whether the parallelogram, which in our ignorance we have defined and drawn, and the whole of whose properties we profess to know, may not be all the while panting for exterior angles, sympathetic with the interior, or sullenly repining at the fact that it cannot be inscribed in a circle?

What mathematician has ever pondered over an hyperbola, mangling the unfortunate curve with lines of intersection here and there, in his efforts to prove some property that perhaps after all is a mere calumny, who has not fancied at last that the ill-used locus was spreading out its asymptotes as a silent rebuke, or winking one focus at him in contemptuous pity?