This is all in accordance with Analogy;
surely it must be clear to you.
Restraining my impatience--for I was now under a strong temptation
to rush blindly at my Visitor and to precipitate him into Space,
or out of Flatland, anywhere, so that I could get rid of him--I replied:--
"And what may be the nature of the Figure which I am to shape out
by this motion which you are pleased to denote by the word `upward'?
I presume it is describable in the language of Flatland."
Sphere. Oh, certainly. It is all plain and simple, and in strict
accordance with Analogy--only, by the way, you must not speak of the
result as being a Figure, but as a Solid. But I will describe it to you.
Or rather not I, but Analogy.
We began with a single Point, which of course--being itself a Point--
has only ONE terminal Point.
One Point produces a Line with TWO terminal Points.
One Line produces a Square with FOUR terminal Points.
Now you can give yourself the answer to your own question: 1, 2,
4, are evidently in Geometrical Progression. What is the next number?
I. Eight.
Sphere. Exactly. The one Square produces a SOMETHING-WHICH-YOU-
DO-NOT-AS-YET-KNOW-A-NAME-FOR-BUT-WHICH-WE-CALL-A-CUBE with EIGHT
terminal Points.
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