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 3
... hence a theorem and its converse have in general to be proved separately . But on account of the peculiar relation existing between the two , a relation exists also between the modes of proof for the two . These are known as the direct ...
... hence a theorem and its converse have in general to be proved separately . But on account of the peculiar relation existing between the two , a relation exists also between the modes of proof for the two . These are known as the direct ...
Page 6
... hence arguments in regard to geometric lines may be replaced by arguments in regard to physical lines , if from such arguments we exclude everything that would involve the idea of breadth . The diagrams employed to direct and assist us ...
... hence arguments in regard to geometric lines may be replaced by arguments in regard to physical lines , if from such arguments we exclude everything that would involve the idea of breadth . The diagrams employed to direct and assist us ...
Page 9
... hence , in imagination , we may follow a line as far as we please without coming to any necessary termination . This property is conveniently expressed by saying that a line extends to infinity . 3. The hypothetical end - points of any ...
... hence , in imagination , we may follow a line as far as we please without coming to any necessary termination . This property is conveniently expressed by saying that a line extends to infinity . 3. The hypothetical end - points of any ...
Page 10
... hence the line through A and having the direction AP is given . Cor . 3. Two lines by their intersection determine one finite point . For , if they determined two , they would each pass through the same two points , which , from Cor . 2 ...
... hence the line through A and having the direction AP is given . Cor . 3. Two lines by their intersection determine one finite point . For , if they determined two , they would each pass through the same two points , which , from Cor . 2 ...
Page 11
... hence we assume that a figure may be supposed to be moved from place to place , and to be turned around or over in any way without undergoing any change whatever in its form or properties , or in the relations existing between its ...
... hence we assume that a figure may be supposed to be moved from place to place , and to be turned around or over in any way without undergoing any change whatever in its form or properties , or in the relations existing between its ...
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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