When I saw my poor brother led away to imprisonment, I attempted to leap down into the
Council Chamber, desiring to intercede on his behalf, or at least bid him farewell. But I
found that I had no motion of my own. I absolutely depended on the volition of my
Guide, who said in gloomy tones, "Heed not thy brother; haply thou shalt have ample
time hereafter to condole with him. Follow me."
Illustration 10
(1) (2)
__________ __________
|\ |\ | \
| \ | \ | \
| \ ____|____\ | \
| | | | | |
|_____|____| | | |
\ | \ | \ |
\ | \ | \ |
\|_________\| \ __________|
Once more we ascended into space. "Hitherto," said the Sphere, "I have shewn you
naught save Plane Figures and their interiors. Now I must introduce you to Solids, and
reveal to you the plan upon which they are constructed. Behold this multitude of
moveable square cards. See, I put one on another, not, as you supposed, Northward of the
other, but ON the other. Now a second, now a third. See, I am building up a Solid by a
multitude of Squares parallel to one another. Now the Solid is complete, being as high as
it is long and broad, and we call it a Cube."
"Pardon me, my Lord," replied I; "but to my eye the appearance is as of an Irregular
Figure whose inside is laid open to the view; in other words, methinks I see no Solid, but
a Plane such as we infer in Flatland; only of an Irregularity which betokens some
monstrous criminal, so that the very sight of it is painful to my eyes."
"True," said the Sphere, "it appears to you a Plane, because you are not accustomed to
light and shade and perspective; just as in Flatland a Hexagon would appear a Straight
Line to one who has not the Art of Sight Recognition. But in reality it is a Solid, as you
shall learn by the sense of Feeling."
He then introduced me to the Cube, and I found that this marvellous Being was indeed no
Plane, but a Solid; and that he was endowed with six plane sides and eight terminal points
called solid angles; and I remembered the saying of the Sphere that just such a Creature
as this would be formed by a Square moving, in Space, parallel to himself: and I rejoiced
to think that so insignificant a Creature as I could in some sense be called the Progenitor
of so illustrious an offspring.
