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 v
... points and three lines forming what are usually termed its vertices and its sides and sides produced . This mode of considering geometric figures leads MAR 2019/7383714 .315 81631 ( RECAP ) naturally to the idea of a figure as a locus.
... points and three lines forming what are usually termed its vertices and its sides and sides produced . This mode of considering geometric figures leads MAR 2019/7383714 .315 81631 ( RECAP ) naturally to the idea of a figure as a locus.
Page vi
Nathan Fellowes Dupuis. naturally to the idea of a figure as a locus , and con- sequently prepares the way for the study of Cartesian Geometry . It requires , however , that a careful distinction be drawn between figures which are ...
Nathan Fellowes Dupuis. naturally to the idea of a figure as a locus , and con- sequently prepares the way for the study of Cartesian Geometry . It requires , however , that a careful distinction be drawn between figures which are ...
Page 38
... LOCUS . 69 ° . A locus is the figure traced by a variable point , which takes all possible positions subject to some constraining condition . If the point is confined to the plane the locus is one or more lines , or some form of curve ...
... LOCUS . 69 ° . A locus is the figure traced by a variable point , which takes all possible positions subject to some constraining condition . If the point is confined to the plane the locus is one or more lines , or some form of curve ...
Page 39
... locus of a point equidistant from two sides of a triangle ? 12. Find the locus of a point which is twice as far from one of two given lines as from the other . 13. Find the locus of a point equidistant from a given line and a given ...
... locus of a point equidistant from two sides of a triangle ? 12. Find the locus of a point which is twice as far from one of two given lines as from the other . 13. Find the locus of a point equidistant from a given line and a given ...
Page 53
... locus of a point which , moving in the plane , keeps at a constant distance from a fixed point in the plane . The compasses , whatever be their form , furnish us with two points , A and B , which , from the rigidity of the instrument ...
... locus of a point which , moving in the plane , keeps at a constant distance from a fixed point in the plane . The compasses , whatever be their form , furnish us with two points , A and B , which , from the rigidity of the instrument ...
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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