Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page v
... 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.
... 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 23
... vertices of the triangle , and the line- segments which have the points as end - points are the sides . The remaining portions of the determined lines are usually spoken of as the " sides produced . " But in many cases generality ...
... vertices of the triangle , and the line- segments which have the points as end - points are the sides . The remaining portions of the determined lines are usually spoken of as the " sides produced . " But in many cases generality ...
Page 24
... vertices other than three . If the vertices be four in number , with the restriction that each vertex is determined by the intersection of two sides , any one of the figures in the margin will satisfy the conditions . Hence the giving ...
... vertices other than three . If the vertices be four in number , with the restriction that each vertex is determined by the intersection of two sides , any one of the figures in the margin will satisfy the conditions . Hence the giving ...
Page 44
... quadrilateral . Thus ABCD is a quadrangle . 2. The line - segments AC and BD which join opposite vertices are the diagonals of the quadrangle . 3. The quadrangle formed when two parallel lines intersect two 44 SYNTHETIC GEOMETRY .
... quadrilateral . Thus ABCD is a quadrangle . 2. The line - segments AC and BD which join opposite vertices are the diagonals of the quadrangle . 3. The quadrangle formed when two parallel lines intersect two 44 SYNTHETIC GEOMETRY .
Page 51
... vertices of equilateral As described outwards upon the sides BC , CA , and AB respectively . Then AA ' = BB ' = CC ' . ( Use 52 ° . ) 2. Is Ex . I true when the equilateral As are described " inwardly " or upon the other sides of their ...
... vertices of equilateral As described outwards upon the sides BC , CA , and AB respectively . Then AA ' = BB ' = CC ' . ( Use 52 ° . ) 2. Is Ex . I true when the equilateral As are described " inwardly " or upon the other sides of their ...
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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