Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 15
... rotate about the point . The point about which the rotation takes place is the pole , and any segment of the rotating line , having the pole as an end - point , is a radius vector . Let an inextensible thread fixed at O be kept ...
... rotate about the point . The point about which the rotation takes place is the pole , and any segment of the rotating line , having the pole as an end - point , is a radius vector . Let an inextensible thread fixed at O be kept ...
Page 16
... rotation . Thus , if , when O ' is placed upon O , and O'A ' is made to lie along OA , O'B ' can also be made to lie along OB , the LA'O'B ' is equal to LAOB . This equality is symbolized thus : LA'O'B ' LAOB . B B ' A ' Where the sign ...
... rotation . Thus , if , when O ' is placed upon O , and O'A ' is made to lie along OA , O'B ' can also be made to lie along OB , the LA'O'B ' is equal to LAOB . This equality is symbolized thus : LA'O'B ' LAOB . B B ' A ' Where the sign ...
Page 17
... rotation it describes a circumangle ( 36 ° ) . LAOB + LBOC + + LFOA = a circumangle . Cor . The result may be thus ... rotated until RELATIONS OF TWO LINES . - ANGLES . 17.
... rotation it describes a circumangle ( 36 ° ) . LAOB + LBOC + + LFOA = a circumangle . Cor . The result may be thus ... rotated until RELATIONS OF TWO LINES . - ANGLES . 17.
Page 18
Nathan Fellowes Dupuis. Cor . 2. If a radius vector be rotated until its direction is reversed it describes a straight angle . And conversely , if a radius vector describes a straight angle its original direction is reversed . Thus , if ...
Nathan Fellowes Dupuis. Cor . 2. If a radius vector be rotated until its direction is reversed it describes a straight angle . And conversely , if a radius vector describes a straight angle its original direction is reversed . Thus , if ...
Page 53
... rotate ? 27. The angle required in Ex . 26 is an external angle of the triangle . Show in this way that the sum of the ... rotation , and that AB rotates to CB , and finally CB rotates to CA in like manner . SECTION V. THE CIRCLE . 92 ...
... rotate ? 27. The angle required in Ex . 26 is an external angle of the triangle . Show in this way that the sum of the ... rotation , and that AB rotates to CB , and finally CB rotates to CA in like manner . SECTION V. THE CIRCLE . 92 ...
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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