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 70
... tangents at the point of intersection . Def . 2. When two circles intersect at right angles they are said to cut each other orthogonally . The same term is conveniently applied to the intersection of 70 SYNTHETIC GEOMETRY .
... tangents at the point of intersection . Def . 2. When two circles intersect at right angles they are said to cut each other orthogonally . The same term is conveniently applied to the intersection of 70 SYNTHETIC GEOMETRY .
Page 71
... 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 touch the circle S ...
... 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 touch the circle S ...
Page 119
... orthogonal projection , or simply the projec- tion , of the point upon the line . 3. Length being considered , the join of the projection of two points is the projection of the join of the points . P Thus if L be a given line and P , Q ...
... orthogonal projection , or simply the projec- tion , of the point upon the line . 3. Length being considered , the join of the projection of two points is the projection of the join of the points . P Thus if L be a given line and P , Q ...
Page 180
... orthogonal to that of the line . Hence any line can be brought into coincidence with any other line in its plane by rotation about the point of intersection . 223 ° . If a line rotates about a finite point while the point simultaneously ...
... orthogonal to that of the line . Hence any line can be brought into coincidence with any other line in its plane by rotation about the point of intersection . 223 ° . If a line rotates about a finite point while the point simultaneously ...
Page 183
... ORTHOGONAL PROJECTION . 229 ° . The orthogonal projection ( 167 ° , 2 ) of PQ on L is P'Q ' , the segment intercepted between the feet of the perpendiculars PP ' and QQ ' . P P ' Q Now P'Q ' PQ cos ( PQ . P'Q ' ) . .. the projection of ...
... ORTHOGONAL PROJECTION . 229 ° . The orthogonal projection ( 167 ° , 2 ) of PQ on L is P'Q ' , the segment intercepted between the feet of the perpendiculars PP ' and QQ ' . P P ' Q Now P'Q ' PQ cos ( PQ . P'Q ' ) . .. the projection 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