134 GEOMETRICAL PORISMS. 



tangle MN, CG may be equal to that which is to be contained 

 by CG, DH. Let AN meet the circle in Fj join BF meeting 

 DE in H. 



The angle HDB is equal to LMK or AMN, and the angle 

 DBH is equal to MAN ; now BD 'is equal to AM ; therefore 

 the triangles BDH, AMN are in all refpedls equal, and DH is 

 equal to MN. Therefore the i'ed:angle DH, CG is equal to 

 MN, CG, that is, (by conflrudion), to the given fpace as requi- 

 red. 



It is eafy to fee, how, in like manner, by drawing AGN, fo 

 that CG may be to MN in a given ratio, (prop, ii.), the 

 lines BF, AF fliall cut off fegments DH, CG, having to each 

 other a given ratio. 



V. 



