"Supposing we divide that line which has no reality into two parts at its origin in the sun or star, shall we get two infinities?—or shall we say, two halves of the infinite?"
"We conceive of each as partaking the quality of infinity."
"Now, let us cut out the diameter of the sun; or rather—since this is what our successors in the school will do,—let us take a line of our earth's longitude which is equally unreal, and measure a degree of this thing which does not exist, and then divide it into equal parts which we will use as a measure or metre. This metre, which is still nothing, as I understand you, is infinitely divisible into points? and the point itself is infinitely small? Therefore we have the finite partaking the nature of the infinite?"
"Undoubtedly!"
"One step more, Mr. Abelard, if I do not weary you! Let me take three of these metres which do not exist, and place them so that the ends of one shall touch the ends of the others. May I ask what is that figure?"
"I presume you mean it to be a triangle."
"Precisely! and what sort of a triangle?"
"An equilateral triangle, the sides of which measure one metre each."
"Now let me take three more of these metres which do not exist, and construct another triangle which does not exist;—are these two triangles or one triangle?"
"They are most certainly one—a single concept of the only possible equilateral triangle measuring one metre on each face."