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.

238 A SEQUEL TO EUCLID.
triangle is the polar of the centroid of the first, with respect to
the Brocard circle.
44. Brocard's first triangle is triply in perspective with the
triangle ABC.
45. The centroid of the triangle, formed by the three centres
of perspective of Ex. 44, coincides with the centroid of ABC.
46-51. In the adjoining fig., ABCD is a harmonic quadrilateral,

E its symmedian point, M, N, P, Q its invariable points, &c.PQ NP OE
AC B PD ~ 2E'
2". NQ, GF, MP are parallel.
3~. The pairs of triangles MNP, FHG; MQP, GHF; NMQ,
FIG; NPQ, GIF are in perspective. The four centres of per