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 41
... transversal . Thus EF is a transversal to the lines AB and CD . In general , the angles formed by a transversal to any two lines are distinguished as follows- E A b B c / d C e / f g h a and e , c and g , b and ƒ , d and h are pairs of ...
... transversal . Thus EF is a transversal to the lines AB and CD . In general , the angles formed by a transversal to any two lines are distinguished as follows- E A b B c / d C e / f g h a and e , c and g , b and ƒ , d and h are pairs of ...
Page 42
... transversal to two lines makes a pair of alternate angles equal , the two lines are parallel . ( Con- verse of 74 ° in part . ) If LAEF = LEFD , AB and CD are parallel . G A P B E O Proof - Draw PQ as in 74 ° , 1 to AB , ΔΟΡΕ = ΔΟQF ...
... transversal to two lines makes a pair of alternate angles equal , the two lines are parallel . ( Con- verse of 74 ° in part . ) If LAEF = LEFD , AB and CD are parallel . G A P B E O Proof - Draw PQ as in 74 ° , 1 to AB , ΔΟΡΕ = ΔΟQF ...
Page 43
Nathan Fellowes Dupuis. Then BC is a transversal to the parallels AB and CE ; LABC = LBCE . Also , AC is a transversal to the same parallels ; LBAC LECD . LABC + LBAC = ✩BCD ( 74 ° , 1 ) ( 74 ° , 2 ) = supplement of ¿ BCA . LA + LB + LC ...
Nathan Fellowes Dupuis. Then BC is a transversal to the parallels AB and CE ; LABC = LBCE . Also , AC is a transversal to the same parallels ; LBAC LECD . LABC + LBAC = ✩BCD ( 74 ° , 1 ) ( 74 ° , 2 ) = supplement of ¿ BCA . LA + LB + LC ...
Page 44
... transversal to two lines makes the sum of a pair of interadjacent angles less than a straight angle , the two lines meet upon that side L E K B F C / H of the transversal upon which these inter- adjacent angles lie . GH is a transversal ...
... transversal to two lines makes the sum of a pair of interadjacent angles less than a straight angle , the two lines meet upon that side L E K B F C / H of the transversal upon which these inter- adjacent angles lie . GH is a transversal ...
Page 45
... transversal to the parallels AB and CD , .. LCDA = LDAB . and AD is a transversal to the parallels AC and BD , Hence , LCAD = LADB . ACAD = ABDA . ( 74 ° , 1 ) ( 74 ° , 1 ) ( 59 ° ) q.e.d. ... AB CD and AC = BD . 2. ¿ CAB = 4BDC and ...
... transversal to the parallels AB and CD , .. LCDA = LDAB . and AD is a transversal to the parallels AC and BD , Hence , LCAD = LADB . ACAD = ABDA . ( 74 ° , 1 ) ( 74 ° , 1 ) ( 59 ° ) q.e.d. ... AB CD and AC = BD . 2. ¿ CAB = 4BDC and ...
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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