e into mysteries yet higher than those I had
witnessed, shewing me how to construct Extra-Solids by the motion of
Solids, and Double Extra-Solids by the motion of Extra-Solids, and all
"strictly according to Analogy", all by methods so simple, so easy, as
to be patent even to the Female Sex.

Section 21. How I tried to teach the Theory of Three Dimensions
to my Grandson, and with what success

I awoke rejoicing, and began to reflect on the glorious career before
me. I would go forth, methought, at once, and evangelize the whole of
Flatland. Even to Women and Soldiers should the Gospel of Three
Dimensions be proclaimed. I would begin with my Wife.

Just as I had decided on the plan of my operations, I heard the sound
of many voices in the street commanding silence. Then followed a
louder voice. It was a herald's proclamation. Listening attentively,
I recognized the words of the Resolution of the Council, enjoining the
arrest, imprisonment, or execution of any one who should pervert the
minds of the people by delusions, and by professing to have received
revelations from another World.

I reflected. This danger was not to be trifled with. It would be
better to avoid it by omitting all mention of my Revelation, and by
proceeding on the path of Demonstration--which after all, seemed so
simple and so conclusive that nothing would be lost by discarding the
former means. "Upward, not Northward"--was the clue to the whole
proof. It had seemed to me fairly clear before I fell asleep; and when
I first awoke, fresh from my dream, it had appeared as patent as
Arithmetic; but somehow it did not seem to me quite so obvious now.
Though my Wife entered the room opportunely just at that moment, I
decided, after we had exchanged a few words of commonplace
conversation, not to begin with her.

My Pentagonal Sons were men of character and standing, and physicians
of no mean reputation, but not great in mathematics, and, in that
respect, unfit for my purpose. But it occurred to me that a young and
docile Hexagon, with a mathematical turn, would be a most suitable
pupil. Why therefore not make my first experiment with my little
precocious Grandson, whose casual remarks on the meaning of 3^3 had met
with the approval of the Sphere? Discussing the matter with him, a
mere boy, I should be in perfect safety; for he would know nothing of
the Proclamation of the Council; whereas I could not feel sure tha