SCIENCE: ABSOLUTE OP SPACE. 



41 



on the plane in 2. 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 2&quot;. 



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

 NBQ^J^ rt.^, and make (by 

 35), in S, AMI ray BQ and I 

 - Q BN, and determine (by 37) 



we shall have, if IA 



FIG. 34. =#,(28), X=l :sin j rt. ^=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 III to the 

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

 perpendiculars to MN; manifestly ADEC= 

 ABEA; and so the angles 

 (perhaps mixtilinear) ECP, 

 EAT will fit, and EC=EA. 

 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 



