50 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
We then have— . 
(a.) These projections are circles whose diameters are, respect- 
ively, 2, $, and 4, the diameter of the circumcircle. 
(b.) The centers of the circles fF”, F’”, F all lie in EO and there- 
fore in HO joining circumcenter to orthocenter and are points of 
bisection of HO in both the ordinary and extended sense in such 
Wise that Fy Sih "Ol Sa = Bae 
(c.) The segments of the medians EA, EB, EC and EA’, EB’, 
EC’ are all bisected by each of the circles. In the case of the 
third circle F, the segments are bisected in the eatended sense, and 
since the segments of the medians, EA, EB, EC, are also bisected 
in the extended sense by the sides of the triangle the,cirele F bisects 
the sides of the triangle. 
The points of bisection on the medians determined by the circle 
F”’ are bisections in the ordinary sense. 
