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.

AX:~- CONTENTS.
PAGE
Rectangle contained by sum and difference of two
sides of a triangle,..... 23
Euler's theorem with respect to four collinear points, 23
Perpendiculars let fall from angular points of a square
on a line,... 24
Theorem on the squares of sides of a triangle whose
base is divided in a given ratio,. 24
*Properties of sum of multiples of squares of lines
drawn to a variable point from any number of
given points,.... 9 25
SECTION II.
Exercises,......- e v 27
BOOK II.
SECTION I.
Properties of two circles touching each other,. 29
Common tangent to two circles,.. 31
Rectangles of non-corresponding sides of two equiangular triangles,.. 33
Properties of perpendiculars from any point of a circle
on two tangents and chord of contact,... 33
Properties of perpendiculars from any point of a circle
on sides of an inscribed quadrilateral,.. 34
Feet of perpendiculars on sides of a triangle from any
point in circumscribed circle are collinear,.. 34
Intercepts of perpendiculars of a triangle between
point of concurrence and circumscribed circle are
bisected by the sides of the triangle,. 35
Property of line joining any point in circumference of
a circle to the intersection of perpendiculars of an
inscribed triangle,.. 36
*Problems on maxima and minima,. 37