272 



EECEEATIVE SCIENCE. 



bare those hidden and concealed heauties 

 which are the spirits of its form." 



To follow with advantage the description 

 of the anatomy of the cube, it will be neces- 

 sary for the reader to provide himself with 

 the means of reproducing the forms de- 

 scribed. Fortunately the modes of illustra- 

 tion are equally accessible and economical. 



A bar of hard, firm soap cut into equal- 

 sided blocks ; or, failing these, a few cubes 

 cut out of some good-sized turnips, or even 

 potatoes (although the latter are rather small 

 for our purpose) ; several pieces of thin 

 straight wire — slender knitting-needles an- 

 swer very well — and some pieces of card, or 

 pasteboard, furnish all the requisites. 



Before proceeding any further, let the 

 reader draw, upon a sheet of cardboard, six 

 squares, arranged as in the annexed figure 

 (Fig. 4), but much larger in size. Let him 



Fig. 4. 



now, with a sharp-pointed knife, cut quite 

 through the dark external lines, and half 

 through the light ones, when the cardboard 

 can be readily folded up into the form of a 

 cube, of which it is in fact the envelope. 



Availing ourselves of any one of these 

 cubes, let us proceed to examine its external 

 structure before we investigate its internal 

 anatomy. A cube is not, as it is often igno- 

 rantly termed, a square, but f^ eolid figure 



bounded by sia; equal square faces, and hence 

 often termed by geometers the hexahedron. 

 Each face has four right angles, consequently 

 there are twenty-four such angles in the 

 whole. It has twelve edges or boundary 

 lines of equal length, each one formed by 

 the meeting of two faces. It possesses 

 eight corners, or, as they are more correctly 

 termed, solid angles, each formed by the 

 meeting of three faces. 



The cube is, in fact, one of those remark- 

 able solid forms (of which only five exist) in 

 which all the parts are equal. Its faces, its 

 angles, its edges, its solid angles, are uni- 

 form. Hence "it is said to be one of the five 

 regular solids ; or, as they were termed by 

 the ancients, the Platonic bodies — which were 

 believed by them to possess mysterious 

 properties on which the explanation of the 

 most secret phenomena of Nature depended. 



Let us now consider what are the longest 

 straight or right lines that we can draw upon 

 the faces of the cube. It is evident, upon the 

 first trial, that such lines are those which run 

 through the opposite angles of eachface; hence 

 they are termed diagonals, from 5ja through, 

 and ycena an angle. If we draw all the dia- 

 gonals on the faces of the cube, as repre- 

 sented by Fig. 5, it will be seen that they 



Fig. 5. 



cross or intersect one another at the centre 

 of each face. Let us now imagine lines pass- 

 ing from the centre of each face to the centre 

 of the opposite face ; it is obvious that these 

 lines will pass through the centre of the solid ; 



