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 74
... polygon of 2n sides is 2 ( n − 1 ) right angles . 5. If the angle of a trammel is 60 ° what arc of a circle will it describe ? what if its angle is n ° ? 6. Trisect a right angle and thence show how to draw a regular 12 - sided polygon ...
... polygon of 2n sides is 2 ( n − 1 ) right angles . 5. If the angle of a trammel is 60 ° what arc of a circle will it describe ? what if its angle is n ° ? 6. Trisect a right angle and thence show how to draw a regular 12 - sided polygon ...
Page 86
... REGULAR POLYGONS . 132 ° . Def . I. A closed rectilinear figure without re - entrant angles ( 89 ° , 2 ) is in general called a polygon . They are named according to the number of their sides as follows : - - 3 , triangle or trigon ; 4 ...
... REGULAR POLYGONS . 132 ° . Def . I. A closed rectilinear figure without re - entrant angles ( 89 ° , 2 ) is in general called a polygon . They are named according to the number of their sides as follows : - - 3 , triangle or trigon ; 4 ...
Page 87
Nathan Fellowes Dupuis. regular polygon , the magnitude of an internal angle is ( 2–4 ) right angles . Proof . Let AB , BC be two consecu- - tive sides of the polygon and O its centre . Then the triangles AOB , BOC are isosceles and ...
Nathan Fellowes Dupuis. regular polygon , the magnitude of an internal angle is ( 2–4 ) right angles . Proof . Let AB , BC be two consecu- - tive sides of the polygon and O its centre . Then the triangles AOB , BOC are isosceles and ...
Page 88
... regular hexagon . Cor . Since AOB is an equilateral triangle , AB = AO ... polygon of any species may be capable of filling the plane , the number of ... regular polygons which can fill the plane , the hexagon includes the greatest area ...
... regular hexagon . Cor . Since AOB is an equilateral triangle , AB = AO ... polygon of any species may be capable of filling the plane , the number of ... regular polygons which can fill the plane , the hexagon includes the greatest area ...
Page 99
... polygon is regular every side is at the same distance from the centre . This distance is the apothem of the polygon . Thus if ABCD ... LA be a regu- lar polygon and O the centre ( 132 ° , Def . 2 ) , the triangles OAB , OBC , are all ...
... polygon is regular every side is at the same distance from the centre . This distance is the apothem of the polygon . Thus if ABCD ... LA be a regu- lar polygon and O the centre ( 132 ° , Def . 2 ) , the triangles OAB , OBC , are all ...
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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