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 86
... collinear . Cor . 3. The line through any two centres passes through a vertex of the AABC . .. any two centres are collinear with a vertex of the A. The lines of collinearity are the six bisectors of the three angles A , B , and C. Def ...
... collinear . Cor . 3. The line through any two centres passes through a vertex of the AABC . .. any two centres are collinear with a vertex of the A. The lines of collinearity are the six bisectors of the three angles A , B , and C. Def ...
Page 197
... collinear , and three or more lines meeting in a point are concurrent . Def . 2. - A tetragram or general quadrangle is the figure formed by four lines no three of which are concurrent , and no two of which are parallel . Thus L , M , N ...
... collinear , and three or more lines meeting in a point are concurrent . Def . 2. - A tetragram or general quadrangle is the figure formed by four lines no three of which are concurrent , and no two of which are parallel . Thus L , M , N ...
Page 198
... collinear . ( 84 ° , Cor . 2 ) But these are the middle points of AC , BD , and EF re- spectively . .. P , Q , R are collinear . A Ex . 3. Theorem . - The circumcentre , the centroid , and the orthocentre of a triangle are col- linear ...
... collinear . ( 84 ° , Cor . 2 ) But these are the middle points of AC , BD , and EF re- spectively . .. P , Q , R are collinear . A Ex . 3. Theorem . - The circumcentre , the centroid , and the orthocentre of a triangle are col- linear ...
Page 200
... collinear , they divide the sides into parts which fulfil the relation ( a ) BX.CY.AZ CX.AY.BZ = 1 ; and their joins with the opposite vertices divide the angles into parts which fulfil the relation ( b ) sin BAX . sin CBY . sin ACZ = 1 ...
... collinear , they divide the sides into parts which fulfil the relation ( a ) BX.CY.AZ CX.AY.BZ = 1 ; and their joins with the opposite vertices divide the angles into parts which fulfil the relation ( b ) sin BAX . sin CBY . sin ACZ = 1 ...
Page 201
... collinear only when an even number of sides or angles ( 2 or 0 ) are divided internally , and from 230 ° it is evident that the sign of the product is + in these two cases . Hence , in applying these criteria , the signs may be dis ...
... collinear only when an even number of sides or angles ( 2 or 0 ) are divided internally , and from 230 ° it is evident that the sign of the product is + in these two cases . Hence , in applying these criteria , the signs may be dis ...
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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