92 TERMINOLOGY. . 97- 



section through the axis and the unchanged diagonal, and 

 these limits are attained when the increasing diagonal be- 

 comes infinite. The pyramid is thus transformed into a 

 prism, the axis of which is the infinite diagonal : its situa- 

 tion is horizontal, and on this account the whole form is 

 termed a Horizontal Prism. Since each of the diagonals 

 may thus be supposed to increase till it becomes infinite, 

 there will be two horizontal prisms belonging to every sca- 

 lene four-sided pyramid, and each of these prisms is refer- 

 red to that diagonal, which remains unchanged, while the 

 other increases to infinity. 



This mode of considering the matter will suffice for 

 giving a general idea of horizontal prisms. But it has no 

 connexion with the relations of forms developed in the 

 preceding paragraphs, where there exists nowhere an ab- 

 solute increment of a diagonal, this being always a conse- 

 quence of a simultaneous increment of the axis (. 93. 95.). 

 In the principal series, whose members also possess their 

 appropriate horizontal prisms, the diagonals do not change 

 at all, while the axes may be increased to infinity. 



There are, however, two methods of obtaining horizon- 

 tal prisms, in connexion with other forms : either the inter- 

 mediate form (. 90.) is resolved by enlarging its homolo- 

 gous faces, or tangent planes are laid, not on all, but only 

 on the homologous, terminal edges of the given scalene 

 four-sided pyramid. The result is the same in both pro- 

 cesses. 



The designation of horizontal prisms is in general 

 Pr + n ; it is Pr + n, if they belong to the longer, it is 

 Pr -f- n, if they belong to the shorter diagonal of P. If 

 the faces of Pr + n and those of Pr + n appear in combina- 

 tion with each other, and produce the intermediate form, 

 their relative breadth is in the ratio of those diagonals 

 to which their axes are parallel. This intermediate form, 

 in as far as it is a compound form, receives the com- 

 pound sign Pr + n. Pr + n; but in as far as it is em- 

 ployed in the derivation of other forms, as in . 95., the 

 sign Pr -f n is applied to it, because the reference to 

 the diagonals is only taken into consideration afterwards. 



