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.

INDEX.

ADJOINT points, 193.
Anharmonic Section, 126.
------- ratio, 127.
~ --- — pencil, 128.
Antiparallel, 169.
Artzt, 191.
Associated figures, 221.
Aubel E. Van, theorem by, 2I5.
Axis of perspective, 77.
- radical of two circles, 43.
- of similitude of three circles, 84.
- of three figures directly similar,
I85.
- of similitude of associated
figures, 222.
Brianchon, theorem by, 147.
Brocard, theorems by, I91, I95.
Brocard's circle of a triangle, I90.
- circle of a harmonic polygon, I99.
angle of a triangle, I72.
- angle of a harmonic polygon, 203.
- angle of Tarry's polygon,
222.
* ------ points of a triangle, 177.
---- points of a harmonic polygon, 205.
----- points of Tarry's polygon,
222.
----- - first triangle, 19I
-- econd triangle, I92.
---- first quadrilateral, 209.
------ second quadrilateral, 209.

Carnot, theorem by, 160.
Centre of perspective, 77.
- - of inversion, 41.
-- of inversion of-harmonic polygon, 219.
-- of involution, 133.
-- of mean position, I2.
-- of reciprocation, 144.
-- radical, of three circles, 43.
o- f similitude of two circles, 82.
- of two figures directly similar,.
I75.
Chasles, preface, I33.
Circle of inversion, 41, 96.
-- of similitude of two circles,.
86.
-- of similitude of three figures.
directly similar, 189.
- of similitude of associated
figures, 224.
-- cutting another circle orthogonally, 42.
- nine-points, 58, 104, Io5, I99.
-- touching three given circles,.
I2I, 123, 139.
-- Brocard's, I94, 205.
- - the cosine, 183, 216.
- - Lemoine's, I79, 2i6.
-- Longchamps' 247.
- - Tucker's system of, 179.
- - Taylor's, I84.
-- Neuberg's, 231.
- - M'Cay's, 237.
- four mutually orthogonal, Iio'
-- coaxal, 43, II3.