Let us now draw a pair of lines on a piece of paper or cardboard like those in the diagram ([Fig. 10]). In this diagram the top of the page is supposed to rest on the table, and the bottom of the page to be raised and brought near the eye, so that the plane of the diagram slopes upwards to the reader. Let Z denote the upward direction, and X the direction from left to right. Let us turn the Block of cubes with its front upon this slope i.e. so that Urna fits upon the square marked Urna. Moles will be to the right and Ostrum above Urna, i.e. nearer the eye. We might leave the block as it stands and put the piece of cardboard against it; in this case our plane-world would be vertical. It is difficult to fix the cubes in this position on the plane, and therefore more convenient if the cardboard be so inclined that they will not slip off. But the upward direction must be identified with Z. Now, taking the slabs, let us compose what a plane-being would see of the Block. He would perceive just the front faces of the cubes of the Block, as it comes into his plane; these front faces we may call the Moenas of the cubes. Let each of the slabs represent the Moena of its corresponding cube, the Gold slab of the Gold cube and so on. They are thicker than they should be; but we must overlook this and suppose we simply see the thickness as a line. We thus build a square of nine slabs to represent the appearance to a plane-being of the front face of the Block. The middle one, Bidens Moena, would be completely hidden from him by the others on all its sides, and he would see the edges of the eight outer squares. If the Block now begin to move through the plane, that is, to cut through the piece of paper at right angles to it, it will not for some time appear any different. For the sections of Urna are all Gold like the front face Moena, so that the appearance of Urna at any point in its passage will be a Gold square exactly like Urna Moena, seen by the plane-being as a line. Thus, if the speed of the Block’s passage be one inch a minute, the plane-being will see no change for a minute. In other words, this set of slabs lasting one minute will represent what he sees.
When the Block has passed one inch, a different set of cubes appears. Remove the front layer of cubes. There will now be in contact with the paper nine new cubes, whose names we write in the order in which we should see them through a piece of glass standing upright in front of the Block:
| Spicula Mala | Mora Mala | Oliva Mala |
| Uncus Mala | Pallor Mala | Tergum Mala |
| Frenum Mala | Plebs Mala | Sypho Mala |
We pick out nine slabs to represent the Moenas of these cubes, and placed in order they show what the plane-being sees of the second set of cubes as they pass through. Similarly the third wall of the Block will come into the plane, and looking at them similarly, as it were through an upright piece of glass, we write their names:
| Mars Mala | Merces Mala | Tyro Mala |
| Ala Mala | Cortis Mala | Aer Mala |
| Sector Mala | Hama Mala | Remus Mala |
Now, it is evident that these slabs stand at different times for different parts of the cubes. We can imagine them to stand for the Moena of each cube as it passes through. In that case, the first set of slabs, which we put up, represents the Moenas of the front wall of cubes; the next set, the Moenas of the second wall. Thus, if all the three sets of slabs be together on the table, we have a representation of the sections of the cube. For some purposes it would be better to have four sets of slabs, the fourth set representing the Murex of the third wall; for the three sets only show the front faces of the cubes, and therefore would not indicate anything about the back faces of the Block. For instance, if a line passed through the Block diagonally from the point Corvus (Gold) to the point Lama (Deep-blue), it would be represented on the slabs by a point at the bottom left-hand corner of the Gold slab, a second point at the same corner of the Light-buff slab, and a third at the same corner of the Deep-blue slab. Thus, we should have the points mapped at which the line entered the fronts of the walls of cubes, but not the point in Lama at which it would leave the Block.
Let the Diagrams 1, 2, 3 ([Fig. 11]), be the three sets of slabs. To see the diagrams properly, the reader must set the top of the page on the table, and look along the page from the bottom of it. The line in question, which runs from the bottom left-hand near corner to the top right-hand far corner of the Block will be represented in the three sets of slabs by the points A, B, C. To complete the diagram of its course, we need a fourth set of slabs for the Murex of the third wall; the same object might be attained, if we had another Block of 27 cubes behind the first Block and represented its front or Moenas by a set of slabs. For the point, at which the line leaves the first Block is identical with that at which it enters the second Block.
Fig. 11.
If we suppose a sheet of glass to be the plane-world, the Diagrams 1, 2, 3 ([Fig. 11]), may be drawn more naturally to us as Diagrams α, β, γ ([Fig. 12]). Here α represents the Moenas of the first wall, β those of the second, γ those of the third. But to get the plane-being’s view we must look over the edge of the glass down the Z axis.