Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 10
... pass in a given direction . Let A be the given point , and let the segment AP mark the given direction . Then , of all the lines P Р A that can pass through the point A , only one can have the direction AP , and this one must lie along ...
... pass in a given direction . Let A be the given point , and let the segment AP mark the given direction . Then , of all the lines P Р A that can pass through the point A , only one can have the direction AP , and this one must lie along ...
Page 15
... passing through a fixed point in the plane is said to rotate about the point . The point about which the rotation takes place is the pole , and any segment of the rotating line , having the pole as an end - point , is a radius vector ...
... passing through a fixed point in the plane is said to rotate about the point . The point about which the rotation takes place is the pole , and any segment of the rotating line , having the pole as an end - point , is a radius vector ...
Page 20
... pass through the vertex of an angle and make equal angles with the arms , are the bisectors of the angle . The one which lies within the angle is the internal bisector , and the one lying without is the external bisector . B Ό F D A Let ...
... pass through the vertex of an angle and make equal angles with the arms , are the bisectors of the angle . The one which lies within the angle is the internal bisector , and the one lying without is the external bisector . B Ό F D A Let ...
Page 21
... pass through a common point and divide the plane into 6 equal angles . Express the value of each angle in right angles , and in degrees . 2. OA and OB make an angle of 30 ° , how many degrees are there in the angle made by OA and the ...
... pass through a common point and divide the plane into 6 equal angles . Express the value of each angle in right angles , and in degrees . 2. OA and OB make an angle of 30 ° , how many degrees are there in the angle made by OA and the ...
Page 23
... pass by threes through the four points . And in the second case the six points determined lie by threes upon the four lines . This reciprocality of property is very suggestive , and in the higher Geometry is of special importance . Ex ...
... pass by threes through the four points . And in the second case the six points determined lie by threes upon the four lines . This reciprocality of property is very suggestive , and in the higher Geometry is of special importance . Ex ...
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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