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 7
... pencil in drawing lines in Practical Geometry . 17 ° . A Plane is a surface such that the line joining any two arbitrary points in it coincides wholly with the surface . The planarity of a surface may be tested by applying the rule to ...
... pencil in drawing lines in Practical Geometry . 17 ° . A Plane is a surface such that the line joining any two arbitrary points in it coincides wholly with the surface . The planarity of a surface may be tested by applying the rule to ...
Page 15
... pencil at P. Then , when P moves , keeping the thread straight , OP becomes a radius vector rotating about the pole O. When the vector rotates from direction OP to direction OP ' it describes the angle between OP and OP ' . Hence we ...
... pencil at P. Then , when P moves , keeping the thread straight , OP becomes a radius vector rotating about the pole O. When the vector rotates from direction OP to direction OP ' it describes the angle between OP and OP ' . Hence we ...
Page 38
... pencil , the point of the pencil becomes a variable ( physical ) point , and the line or curve traced is its locus . In geometric applications the point , known as the generat- ing point , moves according to some law . The expression of ...
... pencil , the point of the pencil becomes a variable ( physical ) point , and the line or curve traced is its locus . In geometric applications the point , known as the generat- ing point , moves according to some law . The expression of ...
Page 66
... pencil at P traces through A and B. 108 ° . Theorem . - The angle between two intersecting se- cants is the sum of those angles in the circle which stand A B B A on the arcs intercepted between the secants , when the secants intersect ...
... pencil at P traces through A and B. 108 ° . Theorem . - The angle between two intersecting se- cants is the sum of those angles in the circle which stand A B B A on the arcs intercepted between the secants , when the secants intersect ...
Page 158
... pencil and the lines are rays . The point is the vertex or centre of the pencil . Cor . 1. Let the transversals meet in O , and let L denote any other transversal through O. Then AD , A'D ' , and L are all divided similarly by the ...
... pencil and the lines are rays . The point is the vertex or centre of the pencil . Cor . 1. Let the transversals meet in O , and let L denote any other transversal through O. Then AD , A'D ' , and L are all divided similarly by the ...
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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