Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 15
... describes the angle between OP and OP ' . Hence we have the following : - : - Def . 1. - The angle between two lines is the rotation neces- sary to bring one of the lines into the direction of the other . The word " rotation , " as ...
... describes the angle between OP and OP ' . Hence we have the following : - : - Def . 1. - The angle between two lines is the rotation neces- sary to bring one of the lines into the direction of the other . The word " rotation , " as ...
Page 16
... describes the two angles , or their equals , in succession . O op Thus if a radius vector starts from co- incidence with OA and rotates into direction OP it describes the LAOP . If it next rotates into direction OP ' it A describes the ...
... describes the two angles , or their equals , in succession . O op Thus if a radius vector starts from co- incidence with OA and rotates into direction OP it describes the LAOP . If it next rotates into direction OP ' it A describes the ...
Page 17
... describes in succession the angles AOB , BOC , .. EOF , FOA . .. .... But in its complete rotation it describes a circumangle ( 36 ° ) . LAOB + LBOC + + LFOA = a circumangle . Cor . The result may be thus stated : - q.e.d. The sum of ...
... describes in succession the angles AOB , BOC , .. EOF , FOA . .. .... But in its complete rotation it describes a circumangle ( 36 ° ) . LAOB + LBOC + + LFOA = a circumangle . Cor . The result may be thus stated : - q.e.d. The sum of ...
Page 18
... describes a straight angle . And conversely , if a radius vector describes a straight angle its original direction is reversed . Thus , if OA rotates through a straight angle it comes into the direction OB . And conversely , if it ...
... describes a straight angle . And conversely , if a radius vector describes a straight angle its original direction is reversed . Thus , if OA rotates through a straight angle it comes into the direction OB . And conversely , if it ...
Page 53
... unvarying distance B A A B from one another . Then , if one of the points A is fixed , while the other B moves over the paper or other plane surface , the moving point describes a physical circle . PARALLELS , ETC. 53.
... unvarying distance B A A B from one another . Then , if one of the points A is fixed , while the other B moves over the paper or other plane surface , the moving point describes a physical circle . PARALLELS , ETC. 53.
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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