B4 TERMINOLOGY. . 95. 



lene four-sided pyramids, derived according to the above 

 mentioned process. 



. 95. SERIES OF DERIVED PYRAMIDS OF A DIS- 

 SIMILAR TRANSVERSE SECTION, WITH THAT OF P. 

 OTHER METHOD OF DERIVING PYRAMIDS OF THE 

 SAME KIND. 



The pairs of scalene four-sided pyramids, deriv- 

 ed after one and the same m, from the members of 

 the series . 90. form two series, which proceed ac- 

 cording to the law of the series . 90., and are 

 similarly limited. 



The same method which from P produces (P) m and (P)'", 

 if applied to P + n, yields (P + n) m and (P 4- n) m . 

 The axis of (P) m is therefore to that of (P 4- n) m in the ra- 

 tio of the axis of P to the axis of P + n, or in that of 1 : 2". 

 Hence 2 is the fundamental number, 2^ the law of pro- 

 gression of the series. 



If the positive and negative value of n becomes infinite, 

 (P + n) m and ( + n) m are changed into (P + cc) m , 

 (P ^c) m and (P + cc) in , (P co ). According to . 91. 

 these farms are oblique-angular four-sided prisms, whose 

 transverse sections are equal and similar to the bases of 

 (P + n) m and (P + n) ra . Their plane angles are obtained by 

 the algebraic expressions in the preceding paragraph, if n is 

 supposed = 03 . The signs (P ec ) ra and (P co ) m re- 

 fer to the face perpendicular to the axis, already expressed ; 

 which face, however, more generally is designated by 

 P CD, the S'gn obtained in . 91. The complete designa- 

 tion of the two series between their limits, is therefore 

 P _ co ... (P + n) m ... (P + 03 )m ; 

 P co ... (P + n) m ... (P + co ) m . 



There exists, however, still another method of deriving 

 pyramids of dissimilar bases from the fundamental form ; 

 and although this method does not produce any new forms, 



