* 
336 A. C. Twining—Euclid's Doctrine of Parallels. 
angles are right angles, the angles ACO, BDL, are equal 
(4.1. Cor.), and COB, DLG, are equal. And in like manner it 
may be shown that BO P equals G LM, also that G P Q equals 
Z, and so on,—also that OPG equals LMI, and PQI 
equal to two right angles,—consequently their equals CO 
a are the same, and (14. P is one straight line— 
Prop. XXVIII 3. THEOREM. 
Through a given point there can be but one parallel to a given 
straight line. : 
. Let AB be the given line, and C a given point. Drop cA 
perpendicular to A B, and through C draw the straight line 
CR at right angles to AC; then CR is the only parallel © 
A B through C. 
es As above assumed. The demonstration of this proposition in the Proceedings 
the American Association, before alluded to, is by a different proess. 
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