Theory of Cryjlallifation. 379 



rhomboids, fimilar to the acute rhomboid, on the fix ob- 

 lique ridges a b, ag, ae,sd, sf, .p. This decrement pro- 

 duces two faces, one on each fide of each of thefe ndges, which 

 makes in all twelve faces. But as the two faces, winch have 

 the fame ridge for their line of departure, are on the lame 

 plane by the nature of the decrement, the twelve faces will 

 be reduced to fix, which are fquares ; fo that the fecondary 

 folid is a cube. This remit is analogous to that of the very 

 obtufe calcareous fpar before mentioned. 



Let us now fuppofe that the cube {Jig. 60.) admits, m 

 • regard to itsTummits a, s, two new divifions fimilar to the 

 preceding fix, that is to fay, one of which panes through 

 the points c, i, 0, and the other through the points h, n, r. 

 The firft will pafs alfo through the points b, g) e, and the 

 fecond through the points d,f, p, (fg.6i and 62.) of the 

 rhomboid; from which it follows, that thefe two divifions 

 will detach each a regular tctracdron bage or dsfp {Jg. 62.) , 

 fo that the rhomboid will be found converted into a regular 

 oftaedron ,/ {Jg. 6 3 .), which will be the real nucleus of 

 ' the cube; fince it is produced by divifions fimilarly made, 

 iii regard to the eight folid angles of the cv.be. 



If we fuppofe the fame cube to be divifible, throughout its 

 whole extent, by feclions analogous to the preceding, it is 

 clear that each of the fmall rhomboids of which it is the af- 

 femblage, will be found, in like manner, fubdivided into an 

 qaaedron, with two regular tetraedra applied on the two op. 

 polite faces of the oclaedron. 



By taking the oftaedron for nucleus, we may conftruft 

 around this nucleus a cube by regular fubtraclions of fmall 

 complete rhomboids. For example, if we fuppofe decre r 

 meats by a fingle range of thefe rhomboids, having b for 

 their point of departure, and made in a direction parallel to 

 the inferior edges gf, eg, de, df, of the four triangles, 

 which unite to form the folid angle b y there will refult four 

 faces, which will be found on a level, and, like the oftaedron 

 with fa folid angles, fimilar decrements around the other 



five 



