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 56
... three points . But O is the only point in the plane equidistant from A , B , and C. And we cannot have two separate centre and the same radius . ( 86 ° , Cor . ) having the same ( 93 ° , 4 ) .. only one circle ... Circles which coincide in ...
... three points . But O is the only point in the plane equidistant from A , B , and C. And we cannot have two separate centre and the same radius . ( 86 ° , Cor . ) having the same ( 93 ° , 4 ) .. only one circle ... Circles which coincide in ...
Page 69
... three points , two circles can be made to pass through the same three points . But this is not true . .. two circles can intersect in only two points . ( 96 ° ) Cor . Two circles can touch in only one point . For a point of contact is ...
... three points , two circles can be made to pass through the same three points . But this is not true . .. two circles can intersect in only two points . ( 96 ° ) Cor . Two circles can touch in only one point . For a point of contact is ...
Page 71
... circle S is cut orthogonally by any circle having its centre at a point without S and its radius the tangent from the point to the circle S. 116 ° . The following examples furnish theorems of some importance . Ex . I. Three tangents ...
... circle S is cut orthogonally by any circle having its centre at a point without S and its radius the tangent from the point to the circle S. 116 ° . The following examples furnish theorems of some importance . Ex . I. Three tangents ...
Page 74
... circles , and d the distance between them , the circles touch when d = r ± r . 8. Give the conditions under which ... three alternate sides is equal to that of the remaining three . 15. If two circles are concentric , any chord of the ...
... circles , and d the distance between them , the circles touch when d = r ± r . 8. Give the conditions under which ... three alternate sides is equal to that of the remaining three . 15. If two circles are concentric , any chord of the ...
Page 75
... circle is perpendicular to the centre - line through that point . 20. Three circles touch each other externally at A , B , and C. The chords AB and AC of two of the circles meet the third circle in D and E. Prove that DE is a diameter of ...
... circle is perpendicular to the centre - line through that point . 20. Three circles touch each other externally at A , B , and C. The chords AB and AC of two of the circles meet the third circle in D and E. Prove that DE is a diameter of ...
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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