And indeed I was now inclining to the belief
that he must be no Circle at all, but some extremely clever juggler;
or else that the old wives' tales were true, and that after all
there were such people as Enchanters and Magicians.
After a long pause he muttered to himself, "One resource alone remains,
if I am not to resort to action. I must try the method of Analogy."
Then followed a still longer silence, after which he continued
our dialogue.
SPHERE. Tell me, Mr. Mathematician; if a Point moves Northward,
and leaves a luminous wake, what name would you give to the wake?
I. A straight Line.
SPHERE. And a straight Line has how many extremities?
I. Two.
SPHERE. Now conceive the Northward straight Line moving parallel
to itself, East and West, so that every point in it leaves behind it
the wake of a straight Line. What name will you give to the Figure
thereby formed? We will suppose that it moves through a distance
equal to the original straight Line. -- What name, I say?
I. A Square.
SPHERE. And how many sides has a Square? How many angles?
I. Four sides and four angles.
SPHERE.
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