Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 16
... remaining arms , the angles are adjacent angles . 36 ° . Def . — A radius vector which starts from any given direction and makes a complete rotation so as to return to its original direction describes a circumangle , or perigon . One ...
... remaining arms , the angles are adjacent angles . 36 ° . Def . — A radius vector which starts from any given direction and makes a complete rotation so as to return to its original direction describes a circumangle , or perigon . One ...
Page 23
... remaining portions of the determined lines are usually spoken of as the " sides produced . " But in many cases generality requires us to extend the term " side " to the whole line . B Thus , the points A , B , C are the a vertices of ...
... remaining portions of the determined lines are usually spoken of as the " sides produced . " But in many cases generality requires us to extend the term " side " to the whole line . B Thus , the points A , B , C are the a vertices of ...
Page 35
... remaining parts and hence the congruence of the triangles follow as a consequence . Thus it is sufficient that two sides and the included angle in one triangle shall be respectively equal to two sides and the included angle in another ...
... remaining parts and hence the congruence of the triangles follow as a consequence . Thus it is sufficient that two sides and the included angle in one triangle shall be respectively equal to two sides and the included angle in another ...
Page 41
... remaining alternate angles are equal . 2. LAEG = LCFE , etc. Proof.- and LAEG supplement of LAEF , = LCFE supplement of EFI ) . ( 72 ° ) ( 64 ° ) q.e.d. ( 40 ° , Def . 1 ) But ... LAEF = LEFD ; LAEG LCFE . ( PARALLELS , ETC. 4I.
... remaining alternate angles are equal . 2. LAEG = LCFE , etc. Proof.- and LAEG supplement of LAEF , = LCFE supplement of EFI ) . ( 72 ° ) ( 64 ° ) q.e.d. ( 40 ° , Def . 1 ) But ... LAEF = LEFD ; LAEG LCFE . ( PARALLELS , ETC. 4I.
Page 74
... equal to that of the remaining three . 15. If two circles are concentric , any chord of the outer which is tangent to the inner is bisected by the point of contact ; and the parts intercepted on any secant 74 SYNTHETIC GEOMETRY .
... equal to that of the remaining three . 15. If two circles are concentric , any chord of the outer which is tangent to the inner is bisected by the point of contact ; and the parts intercepted on any secant 74 SYNTHETIC GEOMETRY .
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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