Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page v
... sides , but the combination of the three points and three lines forming what are usually termed its vertices and its sides and sides produced . This mode of considering geometric figures leads naturally to the idea of a figure as a locus V.
... sides , but the combination of the three points and three lines forming what are usually termed its vertices and its sides and sides produced . This mode of considering geometric figures leads naturally to the idea of a figure as a locus V.
Page 3
... sides of a triangle only one can be the greater , and of the two angles opposite these sides only one can be the greater . Then , if it is proved that the greater side is opposite the greater angle it follows that the greater angle is ...
... sides of a triangle only one can be the greater , and of the two angles opposite these sides only one can be the greater . Then , if it is proved that the greater side is opposite the greater angle it follows that the greater angle is ...
Page 23
... sides . The remaining portions of the determined lines are usually spoken of as the " sides produced . " But in many cases generality requires us to extend the term " side " to the whole line . B Thus , the points A , B , C are the a ...
... sides . The remaining portions of the determined lines are usually spoken of as the " sides produced . " But in many cases generality requires us to extend the term " side " to the whole line . B Thus , the points A , B , C are the a ...
Page 24
... sides are given , the triangle is com- X pletely given . This is not the case with a rectilinear figure having any number of vertices other than three . If the vertices be four in number , with the restriction that each vertex is ...
... sides are given , the triangle is com- X pletely given . This is not the case with a rectilinear figure having any number of vertices other than three . If the vertices be four in number , with the restriction that each vertex is ...
Page 25
... sides and the included angle in the one are respectively equal to two sides and the included angle in the other . If AB A'B ' the triangles BC = B'C ' are congru- and LB LB ' ent . Proof . - Place ABC on A B C A C AA'B'C ' so that B ...
... sides and the included angle in the one are respectively equal to two sides and the included angle in the other . If AB A'B ' the triangles BC = B'C ' are congru- and LB LB ' ent . Proof . - Place ABC on A B C A C AA'B'C ' so that B ...
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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