Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page ix
... SECTION V. - Constructive Geometry , PART III . SECTION I. Proportion amongst Line - Segments . SECTION II . - Functions of Angles and their Applications in Geometry , 91 147 PART IV . SECTION 1. - Geometric Extensions . Centre ix.
... SECTION V. - Constructive Geometry , PART III . SECTION I. Proportion amongst Line - Segments . SECTION II . - Functions of Angles and their Applications in Geometry , 91 147 PART IV . SECTION 1. - Geometric Extensions . Centre ix.
Page x
Nathan Fellowes Dupuis. PART IV . SECTION 1. - Geometric Extensions . Centre of Mean Position . linearity and ... Centres and Axes of Perspective or Similitude , PART V. SECTION I. — Anharmonic Division . SECTION II.— Harmonic Ratio ...
Nathan Fellowes Dupuis. PART IV . SECTION 1. - Geometric Extensions . Centre of Mean Position . linearity and ... Centres and Axes of Perspective or Similitude , PART V. SECTION I. — Anharmonic Division . SECTION II.— Harmonic Ratio ...
Page 6
... centre the centre of the circle ; stretched cords become straight lines , etc. 13 ° . The Point . A point marks position , but has no size . The intersection of one line by another gives a point , called the point of intersection . If ...
... centre the centre of the circle ; stretched cords become straight lines , etc. 13 ° . The Point . A point marks position , but has no size . The intersection of one line by another gives a point , called the point of intersection . If ...
Page 49
... centre and orthocentre both lie within the triangle . 2. If a triangle is obtuse - angled , the circumcentre and orthocentre both lie without the triangle . 3. If a triangle is right - angled , the circumcentre is at the middle point of ...
... centre and orthocentre both lie within the triangle . 2. If a triangle is obtuse - angled , the circumcentre and orthocentre both lie without the triangle . 3. If a triangle is right - angled , the circumcentre is at the middle point of ...
Page 54
... centre is less , equal to , or greater than the radius . 4. Two Os which have equal radii are congruent ; for , if the centres coincide , the figures coincide throughout and form virtually but one figure . Def . - Circles which have ...
... centre is less , equal to , or greater than the radius . 4. Two Os which have equal radii are congruent ; for , if the centres coincide , the figures coincide throughout and form virtually but one figure . Def . - Circles which have ...
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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