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 4
... right bisector of that segment . SECTION I. THE LINE AND POINT . 9. Space may be defined to be that which admits of length or distance in every direction ; so that length and direction are fundamental ideas in studying the geometric ...
... right bisector of that segment . SECTION I. THE LINE AND POINT . 9. Space may be defined to be that which admits of length or distance in every direction ; so that length and direction are fundamental ideas in studying the geometric ...
Page 20
... right angles ( 40 ° , Def . 2 ) . Therefore BOD is not a right angle , and OD is not 1 AB . But OD is any line other than OC . Therefore OC is the only perpendicular . q.ed ... bisector of AOC is the internal bisector 20 SYNTHETIC GEOMETRY .
... right angles ( 40 ° , Def . 2 ) . Therefore BOD is not a right angle , and OD is not 1 AB . But OD is any line other than OC . Therefore OC is the only perpendicular . q.ed ... bisector of AOC is the internal bisector 20 SYNTHETIC GEOMETRY .
Page 21
... bisectors of the LAOC ; then EF is 1 GH . Proof . LEOC = AOC , OE is a bisector ; and < COG = 14COB , OG is a bisector ; adding , LEOGLAOB . But LAOB is a straight angle , .. ( 38 ° , Cor . 1 ) ( 36 ° ) LEOG is a right angle . EXERCISES ...
... bisectors of the LAOC ; then EF is 1 GH . Proof . LEOC = AOC , OE is a bisector ; and < COG = 14COB , OG is a bisector ; adding , LEOGLAOB . But LAOB is a straight angle , .. ( 38 ° , Cor . 1 ) ( 36 ° ) LEOG is a right angle . EXERCISES ...
Page 26
... right bisector of a segment is equidistant from the end - points of the segment . A and .. B AB is a line - segment , and P is any point on its right bisector PC . Then PA = PB . Proof . In the As APC and BPC , - AC = CB , LACP LBCP ...
... right bisector of a segment is equidistant from the end - points of the segment . A and .. B AB is a line - segment , and P is any point on its right bisector PC . Then PA = PB . Proof . In the As APC and BPC , - AC = CB , LACP LBCP ...
Page 27
... right bisector of that segment . ( Converse of 53 ° . ) PA PB . Then P is on the right bisector of AB . Proof . If P is not on the right bisector of AB , let the right bisector cut AP in Q. Then but .. or which is not true . QA = QB ...
... right bisector of that segment . ( Converse of 53 ° . ) PA PB . Then P is on the right bisector of AB . Proof . If P is not on the right bisector of AB , let the right bisector cut AP in Q. Then but .. or which is not true . QA = QB ...
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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