For even a Sphere --
which is my proper name in my own country -- if he manifest himself
at all to an inhabitant of Flatland -- must needs manifest himself
as a Circle.
Do you not remember -- for I, who see all things, discerned last night
the phantasmal vision of Lineland written upon your brain --
do you not remember, I say, how, when you entered the realm
of Lineland, you were compelled to manifest yourself to the King,
not as a Square, but as a Line, because that Linear Realm had not
Dimensions enough to represent the whole of you, but only a slice
or section of you? In precisely the same way, your country
of Two Dimensions is not spacious enough to represent me,
a being of Three, but can only exhibit a slice or section of me,
which is what you call a Circle.
The diminished brightness of your eye indicates incredulity. But now
prepare to receive proof positive of the truth of my assertions.
You cannot indeed see more than one of my sections, or Circles,
at a time; for you have no power to raise your eye out of the plane
of Flatland; but you can at least see that, as I rise in Space,
so my sections become smaller.
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