90 
Mr. glenie’s Proportions . 
;e 
t 
Let the triangle be acb, the bafe ab, the rhomboids 
acef, ccdg; and let the right lines bf, ag, be drawn. 
Then, if from the vertex c through their i liter fe£tion O r 
a right line col be drawn to meet the bafe, the fegments 
al, lb, thereof will have to each other the proportion 
compounded of the proportions of ac to cb, and of ce. 
to cd. For through the vertex c let a right line ich be 
drawn parallel to ab, to meet bf, ag, produced, if necef- 
fary. Then, fince the triangles cqh, cpi, are refpedtively 
equiangular to the triangles aqb, apb (i 5. and 29. E. 1.); 
the proportions of ch to ab, and of ab to ic are reflec- 
tively equal to the proportions of cq^to qb, and of ap to- 
pc (4. E. 6.). But the proportion of ch to ic is com- 
pounded of the proportions of ch to ab and of ab to ic ; 
and confequently is equal to a proportion compounded of 
the proportions of cc^to qb and of ap to pc. And fince 
the triangles acq^, apf, are refpe&ively equiangular to 
the 
