74 TERMINOLOGY. . 90. 



lar to the base of the fundamental form, and draw the 

 lines BA, CA, &c. These lines BA, CA, &c. will be 

 terminal "edges ; the planes BAC, CAB', &c. faces, and 

 BCB'C' the base of the derived pyramid, which is repre- 

 sented by ABCB'C'X. 



The triangle BMC is equal to the triangle BFC = A 

 FCC = A BBF. Hence A BMC = 4. A BMC, and 

 BCB'C'" = 4. BCB'C'. Therefore BC = 2. BC, and BM 

 = 2. BM. 



In the plane BAM, draw the line BA' parallel to ISA ; 

 the triangle BA'M will be similar to the triangle 30AM, and 



BM:BM=MA:MA', 

 hence 



MA' = MA. 



If ABCB'C'X be now supposed the fundamental pyra- 

 mid, AFGIHX will be the inscribed auxiliary form, and 

 ABCB'C'X the more acute derived pyramid, to which the 

 auxiliary form belongs (. 80.). 



In the bases of both these pyramids, the triangle BMC 

 is = J A BMC; therefore BC = BC, and BM = ^ BM. 



Lengthen now the axis MA to the point 3, and draw the 

 line B2t in the plane B9LM. This is the terminal edge of 

 the more acute derived pyramid, if its horizontal projection 

 be supposed equal to that of the fundamental form. 



But on account of the similarity of the triangles BAM 

 and B&M, the following proportion takes place : 



BM : BM = MA : M3, 

 and therefore, 



Ma = 2. MA. 



. 90. SERIES OF SCALENE FOUR-SIDED PYRAMIDS, 

 WHOSE BASES ARE SIMILAR TO THE BASE OF THE 

 FUNDAMENTAL FORM. 



If the derivation (. 88.) be continued, a series 

 of scalene four-sided pyramids of similar bases will 

 arise, whose axes increase and decrease, like the 



