Let us now suppose a glass plate placed in front of the Block in its first position. On this plate let the axes X and Z be drawn. They divide the surface into four parts, to which we give the following names (Fig. 17):-- Z X = that quarter defined by the positive Z and positive X axis. Z [=X] = that quarter defined by the positive Z and negative X axis (which is called “Z negative X”). [=Z] [=X] = that quarter defined by the negative Z and negative X axis. [=Z] X = that quarter defined by the negative Z and positive X axis. The Block appears in these different quarters or quadrants, as it is turned round the different axes. In Z X the Moenas appear, in Z [=X] the Alvus faces, in [=Z] X the Syces. In each quadrant are drawn nine squares, to receive the faces of the cubes when they enter. For instance, in Z X we have the Moenas of:-- Z | Comes Tibicen Vestis | Ostrum Bidens Scena | Urna Moles Saltus +--------------------------------------X And in Z [=X] we have the Alvus of:-- Z Mars Spicula Comes | Ala Uncus Ostrum | Sector Frenum Urna | -X-------------------------------------+ And in the [=Z] X we have the Syces of:-- +-----------------------------------X | Urna Moles Saltus | Frenum Plebs Sypho | Sector Hama Remus -Z Now, if the shape taken at the beginning of this chapter be looked at through the glass, and the distance of the second and third walls of the shape behind the glass be considered of no account--that is, if they be treated as close up to the glass--we get a plane outline, which occupies the squares Urna Moena, Moles Moena, Bidens Moena, Tibicen Moena. This outline is called a projection of the figure. To see it like a plane-being, we should have to look down on it along the Z axis. It is obvious that one projection does not give the shape. For instance, the square Bidens Moena might be filled by either Pallor or Cortis. All that a square in the room of Bidens Moena denotes, is that there is a cube somewhere in the Y, or unknown, direction from Bidens Moena. This view, just taken, we should call the front view in our space; we are then looking at it along the negative Y axis. When the same shape is turned round on the Z axis, so as to be projected on the Z [=X] quadrant, we have the squares--Urna Alvus, Frenum Alvus, Uncus Alvus, Spicula Alvus. When it is turned round the X axis, and projected on [=Z] X, we have the squares, Urna Syce, Moles Syce, Plebs Syce, and no more. This is what is ordinarily called the ground plan; but we have set it in a different position from that in which it is usually drawn. [Illustration: Fig. 19.]