﻿450 DEMONSTRATION OF THE !2TII AXIOM, &C. 



Tf the cingle eailht 



olitusc, cic'ct a pcrpen- 



jP/;j\ 10. V">.^ i \ dicular a .i\ make the 



angle e do:=:ea2\ then 

 ,v a d -^0 dizne a d :■ 

 J' a d + d i + ad i are 

 less than two right an- 

 gles : tlicrcfore o da is acute, and therefore ida still 

 more acute, th.eretbre d i must meet a .v (by the 1st 

 case) suppose in i, take du = ai let fall a perpendicu- 

 lar u/j, produce u h till it meet do (1st case) in o, 

 take a e —~ d and draw the right line i e : now in 

 the triangles cai and odu, ta — do. and a.i = du by con- 

 struction ; and these sides contain equal angles, eai 

 — odu dierefore (4, 1 ) ate — duo — (proposition 4) .rid: ■ 

 aie 4- aid are equal to tNVo right angles,:-^ i and i e 

 arc one right line,:- du and a e meet in e. Q E D. 



