Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 23
Nathan Fellowes Dupuis. 47 ° . Theorem . - Four points determine at most six lines ; and four lines determine at most six points . Proof . - 1 . Let A , B , C , D be the four points . The groups of two are AB , AC , AD , BC , BD , and CD ...
Nathan Fellowes Dupuis. 47 ° . Theorem . - Four points determine at most six lines ; and four lines determine at most six points . Proof . - 1 . Let A , B , C , D be the four points . The groups of two are AB , AC , AD , BC , BD , and CD ...
Page 24
... 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 of the four vertices of such a figure is not ...
... 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 of the four vertices of such a figure is not ...
Page 44
... four lines as sides is in general called a quadrangle or 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 ...
... four lines as sides is in general called a quadrangle or 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 ...
Page 50
... four right angles , or a circumangle . Proof . The angles of the two △ s ABD and CBD make up the internal angles of the quadrangle . 1 + 1 ; ( 76 ° ) But these are therefore the internal angles of the quadrangle are together equal to four ...
... four right angles , or a circumangle . Proof . The angles of the two △ s ABD and CBD make up the internal angles of the quadrangle . 1 + 1 ; ( 76 ° ) But these are therefore the internal angles of the quadrangle are together equal to four ...
Page 52
... four congruent As . 13. From any point in a side of an equilateral △ lines are drawn parallel to the other sides . The perimeter of the so formed is equal to twice a side of the △ . 14. Examine Ex . 13 when the point is on a side pro ...
... four congruent As . 13. From any point in a side of an equilateral △ lines are drawn parallel to the other sides . The perimeter of the so formed is equal to twice a side of the △ . 14. Examine Ex . 13 when the point is on a side pro ...
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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