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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INDEX.

Clebsch, 77.
Collinear points, 5.
Complete quadrilateral, 5.
Concurrent lines, 3.
Conjugate points, 45.
---- lines, 75.
Co-symmedian figures, I99.
Dewulf, theorem by, 240.
Director point, 192.
Double points of two figures directly
similar, I75.
- of a harmonic polygon,
205.
- - of a pencil in involution, I34.
of a system in involution, I33.
of a homographic
system, I36.
Envelope of a movable line or circle
defined, 120.
Escribed circles, 55.
--- square, II.
Feuerbach's theorem, 58, 104, I05,
201.
'Graham, theorems by, i60.
Harmonic conjugates, 87, 90.
-. —. mean, 88.
----- pencil, 90.
-— p olygon, I99.
-quadrilateral, 200.
-- section, 87.
-system of points on a
circle, 92.
---- triangle of quadrilateral,
94.
Hamilton, theorem by, I63.
Hart, theorems by, o06, I55.
Hexagon, Brianchon's, I47.
-— ' — Lemoine's, I80.
---- - Pascal's, 129.
Homographic division, I36.
Homothetic figures, 173.

Ingram, 95.
Invariable points of three figures,
i87.
-— 187 --- of a harmonic polygon, 205.
_- -- -- - of associated figures, 222.
Invariable triangle, I87.
Inverse points defined, 95.
- of a curve, 95.
Inversion defined, 49, 5I.
Involution, pencil in, I34.
points in, I33.
Isogonal conjugates with respect to
an angle, 165.
- points with respect to a
triangle, 167.
Isotomic conjugates with respect to
a side of a triangle, i68.
points with respect to a
triangle, 169.
Lemoine, i80, 181, i82, i87, 2II, 2I2.
Locus, 5.
Longchamps, theorems by, 247.
Malfatti's problem, I54.
Mathesis, 183, 205, 2o6.
Maximum and minimum defined, I3.
M'Cay, theorems by, II2, i58, 162,
i95, 206, 2II, 239, 240, 244.
Miquel's theorem, 15I.
Multiples, system of, I3.
Neuberg, theorems by, 189, 207, 209,
217, 219, 246, 247 -Newton, method of describing a
circle touching three given circles,
123.
Points, the adjoint points of similar
figures, I93.
-- the Brocard points of a
triangle, I77.
-- the Brocard points of a harmonic polygon, 205.
- the invariable points of three
figures directly similar, I9I.
--- the director points, I92.