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
... perpendicular to one another , and each is perpendicular to the other . Perpendicularity is denoted by the symbol , to be read 18 SYNTHETIC GEOMETRY .
... perpendicular to one another , and each is perpendicular to the other . Perpendicularity is denoted by the symbol , to be read 18 SYNTHETIC GEOMETRY .
Page 19
Nathan Fellowes Dupuis. Perpendicularity is denoted by the symbol , to be read " perpendicular to or is perpendicular to . " 66 A right angle is denoted by the symbol The symbol also denotes two right angles or a straight angle . Def . 3 ...
Nathan Fellowes Dupuis. Perpendicularity is denoted by the symbol , to be read " perpendicular to or is perpendicular to . " 66 A right angle is denoted by the symbol The symbol also denotes two right angles or a straight angle . Def . 3 ...
Page 20
... perpendicular . q.ed. Def . The perpendicular to a line - segment through its middle point is the right bisector of the segment . Since a segment has but one middle point ( 30 ° , Ex 3 ) , and since but one perpendicular can be drawn to ...
... perpendicular . q.ed. Def . The perpendicular to a line - segment through its middle point is the right bisector of the segment . Since a segment has but one middle point ( 30 ° , Ex 3 ) , and since but one perpendicular can be drawn to ...
Page 21
... perpendicular to one another . EF and GH are 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 ) ...
... perpendicular to one another . EF and GH are 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 ) ...
Page 30
... perpendicular can be drawn to a line from a point not on the line . B Proof . - Let B be the point and AD the line ; and let BC be 1 to AD , and BA be any line other than BC . A C D Then BCD is > < BAC , ( 60 ° ) BAC is not a , and BA ...
... perpendicular can be drawn to a line from a point not on the line . B Proof . - Let B be the point and AD the line ; and let BC be 1 to AD , and BA be any line other than BC . A C D Then BCD is > < BAC , ( 60 ° ) BAC is not a , and BA ...
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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