Now you can give yourself the answer to your own question: 1, 2, 4, are evidently in geometrical progression. What is the next number?

I. Eight.

Sphere. Exactly. The one Square produces a something-which-you-do-not-as-yet-know-a-name-for-but-which-we-call-a-cube with eight terminal Points. Now are you convinced?

I. And has this creature sides, as well as angles or what you call “terminal Points”?

Sphere. Of course; and all according to Analogy. But, by the way, not what you call sides, but what we call sides. You would call them solids .

I. And how many solids or sides will appertain to this being whom I am to generate by the motion of my inside in an “upward” direction, and whom you call a Cube?

Sphere. How can you ask? And you a mathematician! The side of anything is always, if I may so say, one Dimension behind the thing. Consequently, as there is no Dimension behind a Point, a Point has 0 sides; a Line, if I may say, has 2 sides (for the Points of a Line may be called by courtesy, its sides); a Square has 4 sides; 0, 2, 4; what progression do you call that?