Restraining my impatience—for I was now under a strong temptation to rush blindly at my Visitor and to precipitate him into Space, or out of Flatland, anywhere, so that I could get rid of him—I replied:— “And what may be the nature of the Figure which I am to shape out by this motion which you are pleased to denote by the word ‘upward’? I presume it is describable in the language of Flatland.” _Sphere._ Oh, certainly. It is all plain and simple, and in strict accordance with Analogy—only, by the way, you must not speak of the result as being a Figure, but as a Solid. But I will describe it to you. Or rather not I, but Analogy. We began with a single Point, which of course—being itself a Point—has only _one_ terminal Point. One Point produces a Line with _two_ terminal Points. One Line produces a Square with _four_ terminal Points. Now you can yourself give 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 so 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? _I._ Arithmetical. _Sphere._ And what is the next number? _I._ Six. _Sphere._ Exactly. Then you see you have answered your own question. The Cube which you will generate will be bounded by six sides, that is to say, six of your insides. You see it all now, eh? “Monster,” I shrieked, “be thou juggler, enchanter, dream, or devil, no more will I endure thy mockeries. Either thou or I must perish.” And saying these words I precipitated myself upon him. § 17.—_How the Sphere, having in vain tried words, resorted to deeds._ It was in vain. I brought my hardest right angle into violent collision with the Stranger, pressing on him with a force sufficient to have destroyed any ordinary Circle: but I could feel him slowly and unarrestably slipping from my contact; not edging to the right nor to the left, but moving somehow out of the world and vanishing to nothing. Soon there was a blank. But I still heard the Intruder’s voice.