Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 48
Nathan Fellowes Dupuis. Def . - When three or more lines meet in a point they are said to be concurrent . Therefore the three medians of a triangle are concurrent . Def . 2.- -The point of concurrence , O , of the medians of a triangle ...
Nathan Fellowes Dupuis. Def . - When three or more lines meet in a point they are said to be concurrent . Therefore the three medians of a triangle are concurrent . Def . 2.- -The point of concurrence , O , of the medians of a triangle ...
Page 85
... lines L , M , or N. Cor . 1. Let I , and E , be the bisectors of the C. Then , since O is equidistant from L and M , I , passes through O. ( 68 ° ) .. the three internal bisectors of the angles of a triangle are concurrent . 3 Cor . 2 ...
... lines L , M , or N. Cor . 1. Let I , and E , be the bisectors of the C. Then , since O is equidistant from L and M , I , passes through O. ( 68 ° ) .. the three internal bisectors of the angles of a triangle are concurrent . 3 Cor . 2 ...
Page 86
... concurrent . Def . 1. - When three or more points are in line they are said to be collinear . Cor . 3. The line through any two centres passes through a vertex of the ABC . .. any two centres are collinear with a vertex of the . The lines ...
... concurrent . Def . 1. - When three or more points are in line they are said to be collinear . Cor . 3. The line through any two centres passes through a vertex of the ABC . .. any two centres are collinear with a vertex of the . The lines ...
Page 197
... line are collinear , and three or more lines meeting in a point are concurrent . Def . 2. — A tetragram or general quadrangle is the figure formed by four lines no three of which are concurrent , and no two of which are parallel . Thus ...
... line are collinear , and three or more lines meeting in a point are concurrent . Def . 2. — A tetragram or general quadrangle is the figure formed by four lines no three of which are concurrent , and no two of which are parallel . Thus ...
Page 201
... line of collinearity of X , Y , Z is known as " Simson's line for the point O. ” 251 ° . Theorem . - When three lines through the vertices of a triangle are concurrent , they divide the angles into parts which fulfil the relation ( a ) ...
... line of collinearity of X , Y , Z is known as " Simson's line for the point O. ” 251 ° . Theorem . - When three lines through the vertices of a triangle are concurrent , they divide the angles into parts which fulfil the relation ( a ) ...
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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