Elementary Synthetic Geometry of the Point, Line and Circle in the PlaneElementary Synthetic Geometry of the Point, Line and Circle in the Plane by Nathan Fellowes Dupuis, first published in 1889, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it. |
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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 + 2BOC + ... + LFOA = a circumangle . Cor . The result may be ... rotated until RELATIONS OF TWO LINES.- 17 - -ANGLES .
... rotation it describes a circumangle ( 36 ° ) . LAOB + 2BOC + ... + LFOA = a circumangle . Cor . The result may be ... rotated until RELATIONS OF TWO LINES.- 17 - -ANGLES .
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 algebraic altitude apothem bisects c.p.-circles centre of similitude centre-line chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent corresponding cut the circle denote diagonals diameter divided 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