Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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... Harmonic Ratio . SECTION III . —Anharmonic Properties . SECTION IV . — Polar Reciprocals and Reciprocation . SECTION V. - Homography and Involution , PAGE 178 252 PART I. GENERAL CONSIDERATIONS . 1o . A statement which X CONTENTS .
... Harmonic Ratio . SECTION III . —Anharmonic Properties . SECTION IV . — Polar Reciprocals and Reciprocation . SECTION V. - Homography and Involution , PAGE 178 252 PART I. GENERAL CONSIDERATIONS . 1o . A statement which X CONTENTS .
Page 142
... reciprocals of one another with respect to the AC as unit . 185 ° . Problem . - To find the side of a square which is equal to a given rectangle . F A B D Constr . - Let AC be the rectangle . Make BE = BC and in line with BA . E On AE ...
... reciprocals of one another with respect to the AC as unit . 185 ° . Problem . - To find the side of a square which is equal to a given rectangle . F A B D Constr . - Let AC be the rectangle . Make BE = BC and in line with BA . E On AE ...
Page 213
... reciprocal process , the inverse of a line is a circle through the centre of inversion and so situated that the line is to the common centre- line of the two circles . Cor . 2. Let I be the circle of inversion , and let PT and PT ' be ...
... reciprocal process , the inverse of a line is a circle through the centre of inversion and so situated that the line is to the common centre- line of the two circles . Cor . 2. Let I be the circle of inversion , and let PT and PT ' be ...
Page 221
... reciprocal △ s become coincident , the resulting △ is self - reciprocal or self - conjugate , each vertex being the pole of the opposite side . Def . 3. - The centre of the O with respect to which a △ is self - reciprocal is the ...
... reciprocal △ s become coincident , the resulting △ is self - reciprocal or self - conjugate , each vertex being the pole of the opposite side . Def . 3. - The centre of the O with respect to which a △ is self - reciprocal is the ...
Page 222
... reciprocals , the inverse of a side of one passes through a vertex of the other . 2. A right - angled triangle has its right - angled vertex at the centre of a polar circle . What is its polar reciprocal ? 3. In Fig . of 269 ° , if the ...
... reciprocals , the inverse of a side of one passes through a vertex of the other . 2. A right - angled triangle has its right - angled vertex at the centre of a polar circle . What is its polar reciprocal ? 3. In Fig . of 269 ° , if the ...
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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