Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 4
... 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 ...
... 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
... bisector of the segment . Since a segment has but one middle point ( 30 ° , Ex . 3 ) , and since but one perpendicular can be drawn to the segment through that point , .. a ... bisector of AOC is the internal bisector 20 SYNTHETIC GEOMETRY .
... bisector of the segment . Since a segment has but one middle point ( 30 ° , Ex . 3 ) , and since but one perpendicular can be drawn to the segment through that point , .. a ... bisector of AOC is the internal bisector 20 SYNTHETIC GEOMETRY .
Page 21
... bisectors of an angle are perpendicular to one another . EF and GH are bisectors of the LAOC ; then EF is 1 GH . Proof . LEOC = { 4AOC , and < COG = 34COB , OE is a bisector ; :: OG is a bisector ; adding , LEOG = AOB . But LAOB is a ...
... bisectors of an angle are perpendicular to one another . EF and GH are bisectors of the LAOC ; then EF is 1 GH . Proof . LEOC = { 4AOC , and < COG = 34COB , OE is a bisector ; :: OG is a bisector ; adding , LEOG = AOB . But LAOB is a ...
Page 22
... bisectors of the angle are drawn , and again the bisectors of the angle between these bisectors . What are the angles between these latter lines and the original ones ? 5. The lines L , M intersect at O , and through O , L ' and M ' are ...
... bisectors of the angle are drawn , and again the bisectors of the angle between these bisectors . What are the angles between these latter lines and the original ones ? 5. The lines L , M intersect at O , and through O , L ' and M ' are ...
Page 26
... bisector of the base of an isosceles tri- angle is the internal bisector of the vertical angle . And since these two bisectors are one and the same line the converse is true . Def . 2. -A triangle in which all the sides 26 SYNTHETIC ...
... bisector of the base of an isosceles tri- angle is the internal bisector of the vertical angle . And since these two bisectors are one and the same line the converse is true . Def . 2. -A triangle in which all the sides 26 SYNTHETIC ...
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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