Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 4
... chord in a circle . 3. Parallel lines never meet . 4. Every point equidistant from the end - points of a line- segment is on the right bisector of that segment . SECTION I. THE LINE AND POINT . 9 ° . Space may be defined to be that ...
... chord in a circle . 3. Parallel lines never meet . 4. Every point equidistant from the end - points of a line- segment is on the right bisector of that segment . SECTION I. THE LINE AND POINT . 9 ° . Space may be defined to be that ...
Page 55
... chord . ( 21 ° ) The term chord whenever involv- A B D M ing the idea of length means the segment having its end- points on the circle . But sometimes , when length is not involved , it is used to denote the whole secant of which it ...
... chord . ( 21 ° ) The term chord whenever involv- A B D M ing the idea of length means the segment having its end- points on the circle . But sometimes , when length is not involved , it is used to denote the whole secant of which it ...
Page 56
... chord is perpendicular to the chord . Cor . 5. From Cor . 4 by the Rule of Identity , A centre line which is perpendicular to a chord bisects the chord . .. the right bisector of a chord , the centre - line bisecting the chord , and the ...
... chord is perpendicular to the chord . Cor . 5. From Cor . 4 by the Rule of Identity , A centre line which is perpendicular to a chord bisects the chord . .. the right bisector of a chord , the centre - line bisecting the chord , and the ...
Page 57
... chords are equally distant from the centre ; and , conversely , chords equally dis- tant from the centre are equal . If ABCD and OE and OF are the per- pendiculars from the centre upon these chords , then OE = OF ; and conversely , if ...
... chords are equally distant from the centre ; and , conversely , chords equally dis- tant from the centre are equal . If ABCD and OE and OF are the per- pendiculars from the centre upon these chords , then OE = OF ; and conversely , if ...
Page 58
... chords B A E H P make equal angles with the centre - line through their point of intersection . AB = CD , and PO is a centre - line through the point of intersection of AB and CD . Then LAPO = LCPO . Proof . Let OE and OF be to AB and ...
... chords B A E H P make equal angles with the centre - line through their point of intersection . AB = CD , and PO is a centre - line through the point of intersection of AB and CD . Then LAPO = LCPO . Proof . Let OE and OF be to AB and ...
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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