Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 70
... tangents at the point of intersection . Def . 2. When two circles intersect at right angles they are said to cut each other orthogonally , The same term is conveniently applied to the intersection of 70 SYNTHETIC GEOMETRY .
... tangents at the point of intersection . Def . 2. When two circles intersect at right angles they are said to cut each other orthogonally , The same term is conveniently applied to the intersection of 70 SYNTHETIC GEOMETRY .
Page 71
... orthogonally by any circle having its centre at a point without S and its radius the tangent from the point to the circle S. 116 ° . The following examples furnish theorems of some importance . Ex . 1. Three tangents touch the circle S ...
... orthogonally by any circle having its centre at a point without S and its radius the tangent from the point to the circle S. 116 ° . The following examples furnish theorems of some importance . Ex . 1. Three tangents touch the circle S ...
Page 119
... orthogonal projection , or simply the projec- tion , of the point upon the line . 3. Length being considered , the join of the projection of two points is the projection of the join of the points . Thus if L be a given line and P , Q ...
... orthogonal projection , or simply the projec- tion , of the point upon the line . 3. Length being considered , the join of the projection of two points is the projection of the join of the points . Thus if L be a given line and P , Q ...
Page 180
... orthogonal to that of the line . Hence any line can be brought into coincidence with any other line in its plane by rotation about the point of intersection . 223 ° . If a line rotates about a finite point while the point simultaneously ...
... orthogonal to that of the line . Hence any line can be brought into coincidence with any other line in its plane by rotation about the point of intersection . 223 ° . If a line rotates about a finite point while the point simultaneously ...
Page 183
... ORTHOGONAL PROJECTION . 229 ° . The orthogonal projection ( 167 ° , 2 ) of PQ on L is P'Q ' , the segment intercepted between the feet of the perpendiculars PP ' and QQ ' . - Now P'Q ' PQ cos ( PQ . P'Q ' ) . P P ' L O .. the projection ...
... ORTHOGONAL PROJECTION . 229 ° . The orthogonal projection ( 167 ° , 2 ) of PQ on L is P'Q ' , the segment intercepted between the feet of the perpendiculars PP ' and QQ ' . - Now P'Q ' PQ cos ( PQ . P'Q ' ) . P P ' L O .. the projection ...
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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