Mr. glenie’s Proportions. 74 
tion of ac to cb (n. E. 5.). But, fince the triangles 
con, coi, are refpedtively equiangular to the triangles 
aol, lob, the proportion of ch to ic is equal to the pro- 
portion of al to lb (4. E. 6. and 16. E. 5.). Therefore 
the proportion of al to lb is equal to the duplicate pro- 
portion of ac to cb (1 1. E. 5.)* $UE»D. 
cor.. 1. If the triangle be ifofceles, the right line 
drawn from the vertex to the bafe is perpendicular 
thereto, and the fegments of the bafe are equal to each 
other. 
cor. 11. When the triangle is right-angled, the line 
drawn from the vertex to the bafe is always perpendicu- 
lar to it (as appears from 8. E. 6. and its cor.); and the 
rhombi become fquares on the fides comprehending the 
right angle. 
cor. hi. The fegments of the fides adjacent to the 
bafe, are refpedtively third proportionals to the fum of 
the fides, and the fides themfelves. 
cor. iv. The fegments of the fides adjacent to the 
vertex are equal to each other, and each of them is a 
fourth proportional to the fum of the fides, and the 
fides themfelves r-A 
COR. 
(a ) And it may be added, a mean in proportion between the two fegments 
adjacent to the bafe. For if a right line ab be any how divided in c, and from . 
, 1 1 the two fegments ca, cb, third propor- 
■A D C E B tionals to the whole line and each fegment 
refpe&ively, cd, ce, be taken away, the remainders ad, eb, are equal, and each 
ie a mean in proportion between the two cd, ce, For becaufe ab : ac = ac : cd; 
L 2, therefore, 
