SCIENCE ABSOLUTE OP SPACE. 



41 



on the plane in I. Thus e. g. a perigon can 

 be geometrically divided into any special num- 

 ber of equal parts, if it is permitted to make 

 this special partition in Z. 



38. If we construct (by 37] for example, 

 NBQ-^ rt.Z, and make (by 

 35), in S, AMI ray BQ and I 

 BN, and determine (by 37) 

 IM^BN; we shall have, if I A 

 FIG. 34. =*,( 28), X=l : sin # rt. Z=2, 



and x will be constructed geometrically. 



And NBQ may be so computed, that IA dif- 

 fers from i less than by anything given, which 

 happens for sin NBQ=V0. 



39. If (in a plane) PQ and ST are I! to the 

 straight MN (27), and AB, CD are equal 

 perpendiculars to MN; manifestly ADEC= 

 c A BE A; and so the angles 

 Q (perhaps mixtilinear) ECP, 

 EAT will fit, and EOEA. 

 If, moreover, CF= AG, then 

 AACF^ACAG, and each 

 is half of the quadrilateral 

 FAGC. 



If FAGC, HAGK are two quadrilaterals of 

 this sort on AG, between PQ and ST; their 

 equivalence (as in Euclid) is evident, as also 



