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 vii
... becomes acquainted with these geometric extensions in this their simpler form will be greatly assisted in the wider discussion of them in analytical conics . Through- out the whole work modern terminology and modern . processes have ...
... becomes acquainted with these geometric extensions in this their simpler form will be greatly assisted in the wider discussion of them in analytical conics . Through- out the whole work modern terminology and modern . processes have ...
Page 6
... become material or represent material objects . Thus in Mechanics we consider such things as levers , wedges , wheels , cords , etc. , and our diagrams become representations of these things . A pulley or wheel becomes a circle , its arms ...
... become material or represent material objects . Thus in Mechanics we consider such things as levers , wedges , wheels , cords , etc. , and our diagrams become representations of these things . A pulley or wheel becomes a circle , its arms ...
Page 11
... become virtually one figure by the superposition . 27 ° . Two line - segments can be compared with respect to length only . Hence a line is called a magnitude of one dimension . Two segments are equal when the end - points of one can be ...
... become virtually one figure by the superposition . 27 ° . Two line - segments can be compared with respect to length only . Hence a line is called a magnitude of one dimension . Two segments are equal when the end - points of one can be ...
Page 13
... becomes the middle point of AB , what becomes of C ' ? 5. In Art . 30 ° the internal point of bisection is spoken of . What meaning can you give to the " external point of bisection " ? SECTION II . RELATIONS OF TWO LINES . - ANGLES THE ...
... becomes the middle point of AB , what becomes of C ' ? 5. In Art . 30 ° the internal point of bisection is spoken of . What meaning can you give to the " external point of bisection " ? SECTION II . RELATIONS OF TWO LINES . - ANGLES THE ...
Page 14
... becomes smaller ; and if the stars become coinci- dent , or situated in the same line through E , the angle at E vanishes . Hence an angle is capable of continuous increase or diminution , and is therefore a magnitude . And , being ...
... becomes smaller ; and if the stars become coinci- dent , or situated in the same line through E , the angle at E vanishes . Hence an angle is capable of continuous increase or diminution , and is therefore a magnitude . And , being ...
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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