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 4
... which admits of length or distance in every direction ; so that length and direction are fundamental ideas in studying the geometric properties of space . Every material object exists in , and is surrounded by 4 SYNTHETIC GEOMETRY .
... which admits of length or distance in every direction ; so that length and direction are fundamental ideas in studying the geometric properties of space . Every material object exists in , and is surrounded by 4 SYNTHETIC GEOMETRY .
Page 11
... distance be- tween two given points . Although it is possible to give a reasonable proof of this axiom , no amount of proof could make its truth more apparent . The following will illustrate the axiom . Assume any two points on a thread ...
... distance be- tween two given points . Although it is possible to give a reasonable proof of this axiom , no amount of proof could make its truth more apparent . The following will illustrate the axiom . Assume any two points on a thread ...
Page 13
... distance between their other end - points ? 2. Obtain any relation between “ the sum and the differ- ence " of two segments and " the relative directions " of the two segments , they being in line . 3. A given line - segment has but one ...
... distance between their other end - points ? 2. Obtain any relation between “ the sum and the differ- ence " of two segments and " the relative directions " of the two segments , they being in line . 3. A given line - segment has but one ...
Page 33
... distance of the point from the line . 64 ° . Theorem . - If two triangles have two angles in the one respectively equal to two angles in the other , and a side opposite an equal angle in each equal , the triangles are congruent . the As ...
... distance of the point from the line . 64 ° . Theorem . - If two triangles have two angles in the one respectively equal to two angles in the other , and a side opposite an equal angle in each equal , the triangles are congruent . the As ...
Page 39
... distance between two given points . " 9. Show from 60 ° that a triangle cannot have two of its angles right angles . 10. If a triangle has a right angle , the side opposite that angle is greater than either of the other sides . II ...
... distance between two given points . " 9. Show from 60 ° that a triangle cannot have two of its angles right angles . 10. If a triangle has a right angle , the side opposite that angle is greater than either of the other sides . II ...
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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