Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 76
... constructing a line , and the " Compasses ” ( 92 ° ) of constructing a circle . In Theoretic Constructive Geometry we assume the ability to construct these two elements , and by means of these we are to determine the required elements ...
... constructing a line , and the " Compasses ” ( 92 ° ) of constructing a circle . In Theoretic Constructive Geometry we assume the ability to construct these two elements , and by means of these we are to determine the required elements ...
Page 77
... construct the right bisector of a given line segment . Let AB be the given segment . Construction . - With A and B as centres and with a radius AD greater than half of AB describe circles . Since AB is < the sum of the radii and > their ...
... construct the right bisector of a given line segment . Let AB be the given segment . Construction . - With A and B as centres and with a radius AD greater than half of AB describe circles . Since AB is < the sum of the radii and > their ...
Page 78
... construct a figure as given . Bisect PD in E ( 119 ° , Cor . 1 ) . Then CE is || to L. For C and E are the middle points of two sides of a triangle of which L is the base . ( 84 ° , Cor . 2 ) 121 ° . The Square . The square consists of ...
... construct a figure as given . Bisect PD in E ( 119 ° , Cor . 1 ) . Then CE is || to L. For C and E are the middle points of two sides of a triangle of which L is the base . ( 84 ° , Cor . 2 ) 121 ° . The Square . The square consists of ...
Page 80
... construct it . B C Constr . - Place the three sides of the triangle in line , as AB , BC , CD . With centre C and radius CD D describe a circle , and with centre B and radius BA describe a circle . Let E be one point of intersection of ...
... construct it . B C Constr . - Place the three sides of the triangle in line , as AB , BC , CD . With centre C and radius CD D describe a circle , and with centre B and radius BA describe a circle . Let E be one point of intersection of ...
Page 81
... construct a triangle when two sides and the median to the third side are given . Let a and b be two sides and n the ... constructed by 124 ° . Thence the triangle ACB is readily constructed . Cor . Since CC ' is twice the given median ...
... construct a triangle when two sides and the median to the third side are given . Let a and b be two sides and n the ... constructed by 124 ° . Thence the triangle ACB is readily constructed . Cor . Since CC ' is twice the given median ...
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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