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 x
... Centre of Mean Position . SECTION III . — Col- linearity and Concurrence . SECTION IV . — Inver- sion and Inverse Figures . SECTION V. - Pole and Polar . SECTION VI . - The Radical Axis .. SEC- TION VII . - Centres and Axes of ...
... Centre of Mean Position . SECTION III . — Col- linearity and Concurrence . SECTION IV . — Inver- sion and Inverse Figures . SECTION V. - Pole and Polar . SECTION VI . - The Radical Axis .. SEC- TION VII . - Centres and Axes of ...
Page 6
... centre the centre of the circle ; stretched cords become straight lines , etc. 13 ° . The Point . A point marks position , but has no size . The intersection of one line by another gives a point , called the point of intersection . If ...
... centre the centre of the circle ; stretched cords become straight lines , etc. 13 ° . The Point . A point marks position , but has no size . The intersection of one line by another gives a point , called the point of intersection . If ...
Page 54
... centre is less , equal to , or greater than the radius . 4. Two Os which have equal radii are congruent ; for , if the centres coincide , the figures coincide throughout and form virtually but one figure . Def . - Circles which have ...
... centre is less , equal to , or greater than the radius . 4. Two Os which have equal radii are congruent ; for , if the centres coincide , the figures coincide throughout and form virtually but one figure . Def . - Circles which have ...
Page 55
... centre of the O , to a given line . And this is impossible ( 63 ° , 3 ) . Therefore a line can cut a O only twice ... centre is a centre - line , and its chord is a diameter . Where length is not implied , the term diameter is some ...
... centre of the O , to a given line . And this is impossible ( 63 ° , 3 ) . Therefore a line can cut a O only twice ... centre is a centre - line , and its chord is a diameter . Where length is not implied , the term diameter is some ...
Page 56
... centre at O , and radius equal to OA , passes through B and C. q.e.d. 2. Any through A , B , and C must have its centre equally distant from these three points . But O is the only point in the plane equidistant from A , B , and C. And ...
... centre at O , and radius equal to OA , passes through B and C. q.e.d. 2. Any through A , B , and C must have its centre equally distant from these three points . But O is the only point in the plane equidistant from A , B , and C. And ...
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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