Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 15
... 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 . Let an ...
... 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 . Let an ...
Page 53
... fixed point in the plane . The compasses , whatever be their form , furnish us with two points , A and B , which , from the rigidity of the instrument , are supposed to preserve an unvarying distance B A A B from one another . Then , if ...
... fixed point in the plane . The compasses , whatever be their form , furnish us with two points , A and B , which , from the rigidity of the instrument , are supposed to preserve an unvarying distance B A A B from one another . Then , if ...
Page 54
... fixed point is the centre of the circle , and the distance between the fixed and moveable points is the radius of the circle . The curve itself , and especially where its length is under consideration , is commonly called the ...
... fixed point is the centre of the circle , and the distance between the fixed and moveable points is the radius of the circle . The curve itself , and especially where its length is under consideration , is commonly called the ...
Page 67
... fixed point on the OS and Q a variable one . The position of the secant L , cut- ting the circle in P and Q , depends upon the position of Q. T T ' As Q moves along the the secant rotates about P as pole . While Q makes one complete ...
... fixed point on the OS and Q a variable one . The position of the secant L , cut- ting the circle in P and Q , depends upon the position of Q. T T ' As Q moves along the the secant rotates about P as pole . While Q makes one complete ...
Page 71
... fixed , and the tangent at B is variable , we have the following theorem : - The segment of a variable tangent intercepted by two fixed tangents , all to the same circle , subtends a fixed angle at the centre . Ex . 2. If four circles ...
... fixed , and the tangent at B is variable , we have the following theorem : - The segment of a variable tangent intercepted by two fixed tangents , all to the same circle , subtends a fixed angle at the centre . Ex . 2. If four circles ...
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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