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 18
... intersect- ing lines are equal to each other , all four of the angles so formed are equal to one another , and each is a right angle . Def . 2.- --- When two intersecting lines form a right angle at their point of intersection , they ...
... intersect- ing lines are equal to each other , all four of the angles so formed are equal to one another , and each is a right angle . Def . 2.- --- When two intersecting lines form a right angle at their point of intersection , they ...
Page 22
... intersect at O , and through O , L ' and M ' are drawn respectively to L and M. The angle be- tween L ' and M ' is equal to that between L and M. SECTION III . THREE OR MORE POINTS AND LINES . THE TRIANGLE . 46 ° . Theorem . - Three ...
... intersect at O , and through O , L ' and M ' are drawn respectively to L and M. The angle be- tween L ' and M ' is equal to that between L and M. SECTION III . THREE OR MORE POINTS AND LINES . THE TRIANGLE . 46 ° . Theorem . - Three ...
Page 39
... intersect at any finite point are parallel . Next to perpendicularity , parallelism is the most important directional relation . It is denoted by the symbol || , which is to be read " parallel to " or " is parallel to " as occasion may ...
... intersect at any finite point are parallel . Next to perpendicularity , parallelism is the most important directional relation . It is denoted by the symbol || , which is to be read " parallel to " or " is parallel to " as occasion may ...
Page 44
... intersecting lines , intersect at some finite point . D B 80 ° . Def . — 1 . A closed figure having four lines as sides is in general called a quadrangle or quadrilateral . Thus ABCD is a quadrangle . 2. The line - segments AC and BD ...
... intersecting lines , intersect at some finite point . D B 80 ° . Def . — 1 . A closed figure having four lines as sides is in general called a quadrangle or quadrilateral . Thus ABCD is a quadrangle . 2. The line - segments AC and BD ...
Page 45
Nathan Fellowes Dupuis. 3. The quadrangle formed when two parallel lines intersect two other parallel lines is a parallelogram , and is usually denoted by the symbol C 81 ° . Theorem . - In any parallelogram- 1. The opposite sides are ...
Nathan Fellowes Dupuis. 3. The quadrangle formed when two parallel lines intersect two other parallel lines is a parallelogram , and is usually denoted by the symbol C 81 ° . Theorem . - In any parallelogram- 1. The opposite sides are ...
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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