Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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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 Р A that can ...
... 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 Р A that can ...
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 Ό F D A Let AOC be a given angle ; and let EOF be so drawn that LAOE = LEOC . 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 ...
... external bisector . B Ό F D A Let AOC be a given angle ; and let EOF be so drawn that LAOE = LEOC . 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 ...
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 Algebra altitude becomes bisects c.p.-circles centre of similitude chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent cut the circle denote diagonals diameter divided double points 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