Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
From inside the book
Results 1-5 of 22
Page x
... Radical Axis . SEC- TION VII . - Centres and Axes of Perspective or Similitude , PART V. SECTION I. — Anharmonic Division . SECTION II.— Harmonic Ratio . SECTION III . —Anharmonic Properties . SECTION IV . — Polar Reciprocals and ...
... Radical Axis . SEC- TION VII . - Centres and Axes of Perspective or Similitude , PART V. SECTION I. — Anharmonic Division . SECTION II.— Harmonic Ratio . SECTION III . —Anharmonic Properties . SECTION IV . — Polar Reciprocals and ...
Page 137
... radical axis of the circles , and is a line of great importance in studying the relations of two or more circles . Cor . I. The radical axis of two circles bisects their com- mon tangents . Cor . 2. When two circles intersect , their ...
... radical axis of the circles , and is a line of great importance in studying the relations of two or more circles . Cor . I. The radical axis of two circles bisects their com- mon tangents . Cor . 2. When two circles intersect , their ...
Page 210
... radical axis . Cor . 4. A having its centre on the radical axis of two given Os , and cutting one of them orthogonally , cuts the other orthogonally also . 259 ° . Let P , Q be inverse points to circle S and D any S P'P B Q point on it ...
... radical axis . Cor . 4. A having its centre on the radical axis of two given Os , and cutting one of them orthogonally , cuts the other orthogonally also . 259 ° . Let P , Q be inverse points to circle S and D any S P'P B Q point on it ...
Page 213
... radical axis of the two circles . ( 178 ° , Def . ) Cor . 3. If a circle passes through the centre OF INVERSION AND INVERSE FIGURES . 213.
... radical axis of the two circles . ( 178 ° , Def . ) Cor . 3. If a circle passes through the centre OF INVERSION AND INVERSE FIGURES . 213.
Page 214
... axis of S and S ' , and the circle with centre at D and radius DT cuts S and S ' orthogonally . But this circle also cuts circle I orthogonally ( 258 ° ) ... D is on the radical axes of I , S and S ' . Similarly D ' , the middle point ...
... axis of S and S ' , and the circle with centre at D and radius DT cuts S and S ' orthogonally . But this circle also cuts circle I orthogonally ( 258 ° ) ... D is on the radical axes of I , S and S ' . Similarly D ' , the middle point ...
Other editions - View all
Common terms and phrases
ABCD Algebra altitude becomes bisects c.p.-circles centre of similitude chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent cut the circle denote diagonals diameter divided double points end-points equal angles equianharmonic equilateral triangle excircles external bisector fixed point geometric given circles given line given point harmonic range Hence hexagram homographic homologous hypothenuse incircle internal angles inverse points isosceles joins LAOB line-segment locus median middle point nine-points circle opposite sides orthogonally pair parallel parallelogram passes pencil perpendicular perspective plane point of contact point of intersection polar reciprocal Proof quadrangle radical axis radical centre radii radius rectangle rectilinear figure regular polygon rhombus right angle right bisector rotation secant similar Similarly square straight angle symbol tangent tensor theorem Theorem.-The three circles transversal vertex vertices