Mr. glenie’s Proportions . 91 
the triangles bqg, bpc (15. and 29. E. 1.); the propor- 
tions of CQ_to qb, and of ap to pc, are relpedtively equal 
to the proportions of ac to bg or cd, and of ae or ce to 
cb. Wherefore the proportion of ch to ic is equal to the 
proportion compounded of the proportions of ac to cd 
and of ce to cb, or of ac to cb and of ce to cd. But 
lince the triangles coh, coi, are refpedtively equiangular 
to the triangles aol, lob, the proportion of ch to ic is 
equal to the proportion of al to lb (4. E. 6.). There- 
fore the proportion of al to lb is equal to the propor- 
tion compounded of the proportions of ac to cb and of 
ce to cd. E.D . 
scholium. If ce, cd, be equal to each other, al hath 
to lb the proportion of ac to cb, and cl bifedts the an- 
gle acb ; if ce have to cd the inverfe proportion of ac to 
cb, al is equal to lb ; if ce have to cd the proportion of 
ac to cb, al hath to lb the duplicate proportion of ac to 
cb; and univerfally, if ce have to cd any multiplicate 
proportion, of ac to cb, al hath to lb fuch a multipli- 
cate proportion of ac to cb as is expreffed by the num- 
ber n+ 1. And if ce have to cd any multiplicate pro- 
portion m of cb to ac, al will have to lb fuch a multi- 
plicate proportion of cb to ac, as is expreffed by the num- 
ber m-i. 
N 2 
IV. A 
