,
length and breadth (or thickness).
STRANGER. But the very fact that a Line is visible implies
that it possesses yet another Dimension.
I. My Lord, I have just acknowledged that a Woman is broad
as well as long. We see her length, we infer her breadth;
which, though very slight, is capable of measurement.
STRANGER. You do not understand me. I mean that when you see
a Woman, you ought -- besides inferring her breadth --
to see her length, and to SEE what we call her HEIGHT;
although that last Dimension is infinitesimal in your country.
If a Line were mere length without "height", it would cease to
occupy Space and would become invisible. Surely you must
recognize this?
I. I must indeed confess that I do not in the least
understand your Lordship. When we in Flatland see a Line,
we see length and BRIGHTNESS. If the brightness disappears,
the Line is extinguished, and, as you say, ceases to occupy Space.
But am I to suppose that your Lordship gives to brightness the title
of a Dimension, and that what we call "bright" you call "high"?
STRANGER. No, indeed. By "height" I mean a Dimension like
your length: only, with you, "height" is not so easily perceptible,
being extremely small.
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