86 
Mr. glenie's Proportions on the 
the angles of one of thofe triangles , into which the origi- 
nal one is divided by the f aid line drawn from the vertex, 
will be equal to the parallelepiped contained by the fines of 
the angles of the other. 
cor. The two triangles, adjacent to the fegmentsof the 
hale, have to each other the proportion of the two adja- 
cent to the Tides containing the vertical angle, or the pro- 
portion of the two into which the original triangle is di- 
vided ; and any one of thefe pairs of triangles are as limi- 
lar figures delcribed on the fides, being as the fegments 
of the bale, which have to each other the duplicate pro- 
portion of the fides. 
PROPOSITION VIII. THEOREM III. 
If from the angles at the hypotenufe of any right angled 
right lined triangle , right lines be drawn to the alternate 
angles of fquares defer ibed on the fides containing the 
right angle , and from the point where the right line 
drazvn from the right angle , through their interfedlion , 
meets the hypotenufe , right lines be drawn to the points, 
where thefe lines meet the fides ; the lines fo drazvn will 
likewife be a third in proportion to lb, bc. Hence, fin. acl : fin. l = ac : N, 
and fin. L : fin. bcl ~ n : bc. Ex aquo perturb ate fin. acl : fin. bcl — ac : bc.. 
But fin. cbl : fin. c al = ac : bc. Therefore, fin. aci. :fin. bcl — cbl : fin. cal, 
and fin. acl x fin. cal = lin. bcl x fin. cbl. E. D. And hence, 
fin. l X fin. acl x fin. cal — fin. l x fin. bcl X fin. CBL, which is the feccnd 
branch of the proportion, s. horsley. 
make 
