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.

CONTENTS. xi
PAGE
Philo's line,....39
Centre of instantaneous rotation,.. 39
Inversions and orthogonal circles defined,.. 41
Easy Propositions on coaxal circles,... 42
Easy Propositions on poles and polars, o * 44
Problems on construction of triangles,.. 47
SECTION II.
Exercise,....... 48
BOOK IV.
SECTION I.
Intercepts between angular points of a triangle and
points of contact of inscribed and escribed circles
in terms of sides,.. 53
Area of triangle in terms of sides,. 55
Sum of perpendiculars from any point on the sides of
a regular polygon,...... 55
Sum of perpendiculars on any line from angular points
of a regular polygon,...... 56
*Sum of squares of distances from any point to angular
points of a regular polygon,. 56
'" Nine-points Circle" of a triangle,.. 57
Propositions relating to circumscribed circle to a
triangle,... 61
'Special multiples for mean centres of angular points
of a triangle,.... 62
SECTION II.

Exercises,

64