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 v
... points and three lines forming what are usually termed its vertices and its sides and sides produced . This mode of considering geometric figures leads MAR 2019/7383714 .315 81631 ( RECAP ) naturally to the idea of a figure as a locus.
... points and three lines forming what are usually termed its vertices and its sides and sides produced . This mode of considering geometric figures leads MAR 2019/7383714 .315 81631 ( RECAP ) naturally to the idea of a figure as a locus.
Page 15
... vertex . Cor . From 31 ° , 2 , an angle does not in any way depend upon the lengths of its arms , but only upon ... vertex the angle between them may be denoted by a single letter B placed at the vertex , as the 40 , or by a letter with ...
... vertex . Cor . From 31 ° , 2 , an angle does not in any way depend upon the lengths of its arms , but only upon ... vertex the angle between them may be denoted by a single letter B placed at the vertex , as the 40 , or by a letter with ...
Page 16
Nathan Fellowes Dupuis. 3. The angle between two lines , when the vertex is not pictured , or not referred to , is expressed by 4 ( L . M ) , or ĹM , where L and M denote the lines in the one - letter notation ( 22 ° ) ; or ( AB , CD ) ...
Nathan Fellowes Dupuis. 3. The angle between two lines , when the vertex is not pictured , or not referred to , is expressed by 4 ( L . M ) , or ĹM , where L and M denote the lines in the one - letter notation ( 22 ° ) ; or ( AB , CD ) ...
Page 20
... vertex of an angle and make equal angles with the arms , are the bisectors of the angle . The one which lies within the angle is the internal bisector , and the one lying without is the external bisector . B Let AOC be a given angle ...
... vertex of an angle and make equal angles with the arms , are the bisectors of the angle . The one which lies within the angle is the internal bisector , and the one lying without is the external bisector . B Let AOC be a given angle ...
Page 23
... vertices of the triangle , and the line- segments which have the points as end - points are the sides . The remaining portions of the determined lines are usually spoken of as the " sides produced . " But in many cases generality ...
... vertices of the triangle , and the line- segments which have the points as end - points are the sides . The remaining portions of the determined lines are usually spoken of as the " sides produced . " But in many cases generality ...
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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