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.

xlv

CONTENTS.

PAGE
Extension of Ptolemy's Theorem,. 103
Feuerbach's Theorem,.... 104, 105
*Dr. Hart's extension of Feuerbach's Theorem,. 106
Properties of inscribed and circumscribed circles to a
triangle,...... 107
Locus of pole of a chord of a circle which subtends a
right angle at a fixed point,... 108
*Relation between radii of inscribed and circumscribed
circles of a quadrilateral,..... 109
*Properties of four circles mutually orthogonal,. 111
SECTION V.
Coaxal Circles,... 113
Difference of squares of tangents from a variable point
to two fixed circles,...113
To describe a system of circles coaxal with two given
circles,... 114
If two circles cut orthogonally, the extremities of any
diameter of one are conjugate points with respect
to the other-Inferences,..... 115
Properties of radical axes of a circle, and a system of
coaxal circles,....... 116
The inverses of a system of concentric circles are
coaxal,... 117
Property of a variable circle touching two fixed
circles,....118
Property of angle subtended at limiting point of two
circles, by a chord of one which touches the other, 119
Properties of a coaxal system having real points of
intersection,....120
Solution of the Problem, to describe a circle touching
three circles,... 121
Modifications of Newton's Method,. 123
*Poncelet's Theorem,.... 125
*Dr. Hart's proof of Poncelet's Theorem,.. 126