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 44
... quadrangle or quadrilateral . Thus ABCD is a quadrangle . 2. The line - segments AC and BD which join opposite vertices are the diagonals of the quadrangle . 3. The quadrangle formed when two parallel lines intersect two 44 SYNTHETIC ...
... quadrangle or quadrilateral . Thus ABCD is a quadrangle . 2. The line - segments AC and BD which join opposite vertices are the diagonals of the quadrangle . 3. The quadrangle formed when two parallel lines intersect two 44 SYNTHETIC ...
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 ...
Page 46
... .. ABDG AFDH , ( 64 ° ) and BD = DF . q.e.d. Def . — The figure ABFE is a trapezoid . Therefore a trapezoid is a quadrangle having only two sides parallel . The parallel sides are the major and 46 SYNTHETIC GEOMETRY .
... .. ABDG AFDH , ( 64 ° ) and BD = DF . q.e.d. Def . — The figure ABFE is a trapezoid . Therefore a trapezoid is a quadrangle having only two sides parallel . The parallel sides are the major and 46 SYNTHETIC GEOMETRY .
Page 50
... quadrangle will mean this figure . 2. The quadrangle ( 2 ) in which one of the internal angles , as at D , is greater than a straight angle . Such an angle in a closed figure is called a re - entrant angle . We will call this an ...
... quadrangle will mean this figure . 2. The quadrangle ( 2 ) in which one of the internal angles , as at D , is greater than a straight angle . Such an angle in a closed figure is called a re - entrant angle . We will call this an ...
Page 51
... quadrangle , and the D ( hyp . ) ( 90 ° ) But LBCD is supplementary to LECD ; and the ( BC . CD ) is either the angle BCD or DCE . 4 ( BC . CD ) is or supplementary to BAD . q.e.d. = ( 39 ° ) or LBCD is supplementary to BAD . EXERCISES ...
... quadrangle , and the D ( hyp . ) ( 90 ° ) But LBCD is supplementary to LECD ; and the ( BC . CD ) is either the angle BCD or DCE . 4 ( BC . CD ) is or supplementary to BAD . q.e.d. = ( 39 ° ) or LBCD is supplementary to BAD . EXERCISES ...
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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