A sequel to the first six books of the Elements of Euclid, containing an easy introduction to modern geometry, with numerous examples. By John Casey.

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A SEQUEL TO EUCLID.

tively equal to those into which A"A divides the angle
BAC. Hence A"a is a symmedian line of bac, and
similarly B"b, C"c are symmedian lines of the same triangle.
COR. 1.-The symmedian point of the triangle bac is
on the Brocard circle ofBAC.
a

Dem. —Because the triangle bac is formed by three
homologous lines, and A"B"C" is the triangle of similitude, and [Section Iv., Prop. 1] these are in perspective; therefore their centre of perspective, K', is a
point on the circle of similitude, that is, on the Brocard
circle.