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 10
... externally in the same manner . 24 ° . Axiom . - Through a given point only one line can pass in a given direction . Let A be the given point , and let the segment AP mark the given direction . Then , of all the lines P that can pass ...
... externally in the same manner . 24 ° . Axiom . - Through a given point only one line can pass in a given direction . Let A be the given point , and let the segment AP mark the given direction . Then , of all the lines P that can pass ...
Page 13
... what becomes of C ' ? 5. In Art . 30 ° the internal point of bisection is spoken of . What meaning can you give to the " external point of bisection " ? SECTION II . RELATIONS OF TWO LINES . - ANGLES THE LINE AND POINT . 13.
... what becomes of C ' ? 5. In Art . 30 ° the internal point of bisection is spoken of . What meaning can you give to the " external point of bisection " ? SECTION II . RELATIONS OF TWO LINES . - ANGLES THE LINE AND POINT . 13.
Page 20
... external bisector . B Let AOC be a given angle ; and Elet EOF be so drawn that LAOE = LEOC . A EF is the internal bisector of the angle AOC . Also , let GOH be so drawn that LCOG = LHOA . HG is the external bisector of the angle AOC ...
... external bisector . B Let AOC be a given angle ; and Elet EOF be so drawn that LAOE = LEOC . A EF is the internal bisector of the angle AOC . Also , let GOH be so drawn that LCOG = LHOA . HG is the external bisector of the angle AOC ...
Page 21
Nathan Fellowes Dupuis. and the external bisector of AOC is the internal bisector of its supplementary angle , COB ... externally . Thus , if OE is so drawn that the LAOE is double the LEOC , some line OG may also be drawn so that the ...
Nathan Fellowes Dupuis. and the external bisector of AOC is the internal bisector of its supplementary angle , COB ... externally . Thus , if OE is so drawn that the LAOE is double the LEOC , some line OG may also be drawn so that the ...
Page 24
... external angles of the triangle . 3. In relation to the external angle DCB , the angle BCA is the adjacent internal angle , while the angles CAB and ABC are opposite internal angles . 4. Any side of a triangle may be taken as its base ...
... external angles of the triangle . 3. In relation to the external angle DCB , the angle BCA is the adjacent internal angle , while the angles CAB and ABC are opposite internal angles . 4. Any side of a triangle may be taken as its base ...
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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