Elementary Synthetic Geometry of the Point, Line and Circle in the PlaneElementary Synthetic Geometry of the Point, Line and Circle in the Plane by Nathan Fellowes Dupuis, first published in 1889, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it. |
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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 A 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 A 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 ...
... 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 ...
Page 80
... construct it . B с 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 с 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 algebraic altitude apothem bisects c.p.-circles centre of similitude centre-line chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent corresponding cut the circle denote diagonals diameter divided 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