t 73 ] 
III. Propoftions fele&ed from a Paper on the Divifon of 
Right Lines , Surfaces , and Solids. By James Glenie, 
A. M. of the Univerfity of Edinburgh. Communicated 
by the Aftronomer Royal. 
R. June, 1775. 
PROPOSITION I. THEOREM. 
If from the angles at the bafe of any right-lined triangle , 
right lines be drawn to the alternate angles of rhombi, 
defcribed upon the oppojite fides , and applied reciprocally 
to the fides produced ; and from the vertex , through the 
interfedlion of thefe lines , a right line be drawn to meet 
the bafe: the fegments of the bafe , made thereby , will 
have to each other the duplicate proportion of the fides. 
L ET acb be any right 
lined triangle. Let 
afec, cdgb be rhombi, 
on any two fides ac, cb 
of this triangle, applied 
refpe&ively to cb, ac, ^ 
produced : from the al- 
ternate angles ef a,dgb, 
of which let fa, ga, be 
right lines drawn to the 
angles at the bafe, or 
third fide, ab. Then, if through the interfecftion O of 
Vol. LX VI. L thefe 
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