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. See now, I will rise; and the effect upon your eye
will be that my Circle will become smaller and smaller till it dwindles
to a point and finally vanishes.

There was no "rising" that I could see; but he diminished and finally
vanished. I winked once or twice to make sure that I was not dreaming.
But it was no dream. For from the depths of nowhere came forth a
hollow voice--close to my heart it seemed--"Am I quite gone? Are you
convinced now? Well, now I will gradually return to Flatland and you
shall see my section become larger and larger."

Every reader in Spaceland will easily understand that my mysterious
Guest was speaking the language of truth and even of simplicity. But
to me, proficient though I was in Flatland Mathematics, it was by no
means a simple matter. The rough diagram given above will make it
clear to any Spaceland child that the Sphere, ascending in the three
positions indicated there, must needs have manifested himself to me, or
to any Flatlander, as a Circle, at first of full size, then small, and
at last very small indeed, approaching to a Point. But to me, although
I saw the facts before me, the causes were as dark as ever. All that I
could comprehend was, that the Circle had made himself smaller and
vanished, and that he had now re-appeared and was rapidly making
himself larger.

When he regained his original size, he heaved a deep sigh; for he
perceived by my silence that I had altogether failed to comprehend him.
And indeed I was now