The Reminiscences of an Astronomer (Boston and New York, 1903), p. 388.
[2114]. What distinguishes the straight line and circle more than anything else, and properly separates them for the purpose of elementary geometry? Their self-similarity. Every inch of a straight line coincides with every other inch, and off a circle with every other off the same circle. Where, then, did Euclid fail? In not introducing the third curve, which has the same property—the screw. The right line, the circle, the screw—the representations of translation, rotation, and the two combined—ought to have been the instruments of geometry. With a screw we should never have heard of the impossibility of trisecting an angle, squaring the circle, etc.—De Morgan, A.
Quoted in Graves’ Life of Sir W. R. Hamilton, Vol. 3 (New York, 1889), p. 342.
Mad Mathesis alone was unconfined,
Too mad for mere material chains to bind,
Now to pure space lifts her ecstatic stare,
Now, running round the circle, finds it square.
—Pope, Alexander.
The Dunciad, Bk. 4, lines 31-34.