Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 86
... 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 of collinearity are the six bisectors of the three angles A , B , and C. - Def ...
... 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 of collinearity are the six bisectors of the three angles A , B , and C. - Def ...
Page 197
... 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 L , M , N ...
... 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 L , M , N ...
Page 200
... collinear , they divide the sides into parts which fulfil the relation ( a ) BX.CY.AZ CX.AY.BZ = 1 ; and their joins with the opposite vertices divide the angles into parts which fulfil the relation A ( b ) sin BAX . sin CBY . sin ACZ ...
... collinear , they divide the sides into parts which fulfil the relation ( a ) BX.CY.AZ CX.AY.BZ = 1 ; and their joins with the opposite vertices divide the angles into parts which fulfil the relation A ( b ) sin BAX . sin CBY . sin ACZ ...
Page 201
... collinear only when an even number of sides or angles ( 2 or 0 ) are divided internally , and from 230 ° it is evident that the sign of the product is + in these two cases . Hence , in applying these criteria , the signs may be dis ...
... collinear only when an even number of sides or angles ( 2 or 0 ) are divided internally , and from 230 ° it is evident that the sign of the product is + in these two cases . Hence , in applying these criteria , the signs may be dis ...
Page 205
... collinear . The converse of this theorem is readily proved , and will be left as an exercise to the reader . Ex . A ' , B ' , C ' are points upon the sides BC , CA , AB re- spectively of the △ ABC , and ÁA ' , BB ' , CC ' are ...
... collinear . The converse of this theorem is readily proved , and will be left as an exercise to the reader . Ex . A ' , B ' , C ' are points upon the sides BC , CA , AB re- spectively of the △ ABC , and ÁA ' , BB ' , CC ' are ...
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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