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 9
... denoted by a single letter where- ever practicable , as " the point A. ” An indefinite line is also denoted by a single letter as " the line L , " but in this case the letter has no reference to any point . 66 L A B A segment is denoted ...
... denoted by a single letter where- ever practicable , as " the point A. ” An indefinite line is also denoted by a single letter as " the line L , " but in this case the letter has no reference to any point . 66 L A B A segment is denoted ...
Page 12
... denotes equality in length , and + denotes the placing of the segments AB and DE in line so as to have one common point as an end - point for each . The interpretation of the whole is , that AC is equal in length to AB and DE together ...
... denotes equality in length , and + denotes the placing of the segments AB and DE in line so as to have one common point as an end - point for each . The interpretation of the whole is , that AC is equal in length to AB and DE together ...
Page 15
... denoted by a single letter B placed at the vertex , as the 40 , or by a letter with or without an arch of dots , as 48 ; or by three letters of which the A extreme ones denote points upon the arms of the angle and the middle one denotes ...
... denoted by a single letter B placed at the vertex , as the 40 , or by a letter with or without an arch of dots , as 48 ; or by three letters of which the A extreme ones denote points upon the arms of the angle and the middle one denotes ...
Page 16
... denote the lines in the one - letter notation ( 22 ° ) ; or ( AB , CD ) , where AB and CD denote the lines in the two - letter notation . 34 ° . Def . - Two angles are equal when the arms of the one may be made to coincide in direction ...
... denote the lines in the one - letter notation ( 22 ° ) ; or ( AB , CD ) , where AB and CD denote the lines in the two - letter notation . 34 ° . Def . - Two angles are equal when the arms of the one may be made to coincide in direction ...
Page 18
... a right angle at their point of intersection , they are said to be perpendicular to one another , and each is perpendicular to the other . Perpendicularity is denoted by the symbol , to be read 18 SYNTHETIC GEOMETRY .
... a right angle at their point of intersection , they are said to be perpendicular to one another , and each is perpendicular to the other . Perpendicularity is denoted by the symbol , to be read 18 SYNTHETIC GEOMETRY .
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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