Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 7
... pencil in drawing lines in Practical Geometry . 17 ° . A Plane is a surface such that the line joining any two arbitrary points in it coincides wholly with the surface . The planarity of a surface may be tested by applying the rule to ...
... pencil in drawing lines in Practical Geometry . 17 ° . A Plane is a surface such that the line joining any two arbitrary points in it coincides wholly with the surface . The planarity of a surface may be tested by applying the rule to ...
Page 15
... pencil at P. Then , when P moves , keeping the thread straight , OP becomes a radius vector rotating about the pole O. P A When the vector rotates from direction OP to direction OP ' it describes the angle between OP and OP ' . Hence we ...
... pencil at P. Then , when P moves , keeping the thread straight , OP becomes a radius vector rotating about the pole O. P A When the vector rotates from direction OP to direction OP ' it describes the angle between OP and OP ' . Hence we ...
Page 38
... pencil , the point of the pencil becomes a variable ( physical ) point , and the line or curve traced is its locus . In geometric applications the point , known as the generat- ing point , moves according to some law . The expression of ...
... pencil , the point of the pencil becomes a variable ( physical ) point , and the line or curve traced is its locus . In geometric applications the point , known as the generat- ing point , moves according to some law . The expression of ...
Page 66
... pencil at P traces through A and B. When it is made pins A and B , a an arc passing 108 ° . Theorem . - The angle between two intersecting se- cants is the sum of those angles in the circle which stand A B B A on the arcs intercepted ...
... pencil at P traces through A and B. When it is made pins A and B , a an arc passing 108 ° . Theorem . - The angle between two intersecting se- cants is the sum of those angles in the circle which stand A B B A on the arcs intercepted ...
Page 186
... pencil , when we consider both sign and mag- nitude , the sum LAOB + LBOC + 4COD + 4DOA = 0 . For we start from the ... PENCILS OF FOUR . 233 ° . Let A , B , C , P be a range of four , then AB.CP + BC . AP + CA . BP = 0 . Proof- AP - AC ...
... pencil , when we consider both sign and mag- nitude , the sum LAOB + LBOC + 4COD + 4DOA = 0 . For we start from the ... PENCILS OF FOUR . 233 ° . Let A , B , C , P be a range of four , then AB.CP + BC . AP + CA . BP = 0 . Proof- AP - AC ...
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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