77 
Mr. glenie’s Proportions. 
LET ac, cb, be any two 
given right lines, and let cd 
in ac produced be equal to 
cb. On ad defcribe a femi- 
circle; draw cn at right an- 
gles to ad, and equal to cd 
(ii. E. i.); join a, n, and 
apply a right line am in the 
femi-circle equal to an (i. 
E. 4.). From the point m 
draw the right line ms at 
right angles to ad (1. E. 4.) 
ing its lides equal to ac, as, and cb (by 22. E. 1.); and 
acb is the angle required to be found; and the feg- 
ments al, lb, of the right line ab joining the extre- 
mities a and b of the given lines are refpedively equal 
to the fegments ap, bq ^, of the given lines, which are 
adjacent to them. For the fquare on bc hath to the fquare 
on ac the duplicate proportion of bc to ac (cor. 1. to 
20. E. 6.); that is, the proportion of bl to la (prop. 1.). 
Wherefore the lquares on ac, cb ; that is, the fquare on 
an or am (47. E. 1 .) hath to the fquare on ac the propor- 
tion of ab to al (18. E. 5.). But the fquare on an or 
am is equal to the redangle contained by ad, as (8. and 
17. E. 6.). Wherefore the redangle contained by ad, 
as, hath to the fquare on ac, the proportion of ab to al ; 
ithat is, the proportion of the rectangle contained by ab, 
as to the redangle contained by al, as (i. E. 6.). Con- 
fequently, the proportion of the rectangle ad, as, to the 
redangle 
Make a triangle acb, hav- 
