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 48
Nathan Fellowes Dupuis. Def . - When three or more lines meet in a point they are said to be concurrent . Therefore the three medians of a triangle are concurrent . Def . 2. - The point of concurrence , O , of the medians of a triangle ...
Nathan Fellowes Dupuis. Def . - When three or more lines meet in a point they are said to be concurrent . Therefore the three medians of a triangle are concurrent . Def . 2. - The point of concurrence , O , of the medians of a triangle ...
Page 85
... lines L , M , or N. 3 Cor . 1. Let I , and E , be the bisectors of the LC . Then , since O is equidistant from L and M , I , passes through O. ( 68 ° ) .. the three internal bisectors of the angles of a triangle are concurrent . Cor . 2 ...
... lines L , M , or N. 3 Cor . 1. Let I , and E , be the bisectors of the LC . Then , since O is equidistant from L and M , I , passes through O. ( 68 ° ) .. the three internal bisectors of the angles of a triangle are concurrent . Cor . 2 ...
Page 86
... concurrent . Def . 1. — When three or more points are in line they are Isaid to be collinear . Cor . 3. The line through any two centres passes through a vertex of the AABC . .. any two centres are collinear with a vertex of the A. The ...
... concurrent . Def . 1. — When three or more points are in line they are Isaid to be collinear . Cor . 3. The line through any two centres passes through a vertex of the AABC . .. any two centres are collinear with a vertex of the A. The ...
Page 187
... concurrent lines , l , m , n the perpendiculars from any point P upon L , M , and N respectively , then / sin MN + m sin ÑL + n sin LM = o . where MN denotes the angle between M and N , etc. 236 ° . Ex . I. Let four rays be GEOMETRIC ...
... concurrent lines , l , m , n the perpendiculars from any point P upon L , M , and N respectively , then / sin MN + m sin ÑL + n sin LM = o . where MN denotes the angle between M and N , etc. 236 ° . Ex . I. Let four rays be GEOMETRIC ...
Page 197
... line are collinear , and three or more lines meeting in a point are concurrent . Def . 2. - A tetragram or general quadrangle is the figure formed by four lines no three of which are concurrent , and no two of which are parallel . Thus ...
... line are collinear , and three or more lines meeting in a point are concurrent . Def . 2. - A tetragram or general quadrangle is the figure formed by four lines no three of which are concurrent , and no two of which are parallel . Thus ...
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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