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 15
... radius vector . Let an inextensible thread fixed at O be kept stretched by a pencil at P. Then , when P moves , keeping the thread straight , OP becomes a radius vector rotating about the pole O. When the vector rotates from direction ...
... radius vector . Let an inextensible thread fixed at O be kept stretched by a pencil at P. Then , when P moves , keeping the thread straight , OP becomes a radius vector rotating about the pole O. When the vector rotates from direction ...
Page 16
... radius vector which describes the two angles , or their equals , in succession . p ' P Thus if a radius vector starts from co- incidence with OA and rotates into direction OP it describes the LAOP . If it next rotates into direction OP ...
... radius vector which describes the two angles , or their equals , in succession . p ' P Thus if a radius vector starts from co- incidence with OA and rotates into direction OP it describes the LAOP . If it next rotates into direction OP ...
Page 17
... radius vector which starts from coincidence with OA and rotates into the successive directions , OB , OC , ... ... 9 E OF , OA describes in succession the angles AOB , BOC , ... , EOF , FOA . .. But in its complete rotation it describes ...
... radius vector which starts from coincidence with OA and rotates into the successive directions , OB , OC , ... ... 9 E OF , OA describes in succession the angles AOB , BOC , ... , EOF , FOA . .. But in its complete rotation it describes ...
Page 18
Nathan Fellowes Dupuis. Cor . 2. If a radius vector be rotated until its direction is reversed it describes a straight angle . And conversely , if a radius vector describes a straight angle its original direction is reversed . Thus , if ...
Nathan Fellowes Dupuis. Cor . 2. If a radius vector be rotated until its direction is reversed it describes a straight angle . And conversely , if a radius vector describes a straight angle its original direction is reversed . Thus , if ...
Page 54
... radius of the circle . The curve itself , and especially where its length is under consideration , is commonly called the circumference of the circle . The symbol employed for the circle is O. 93 ° From the definitions of 92 ° we deduce ...
... radius of the circle . The curve itself , and especially where its length is under consideration , is commonly called the circumference of the circle . The symbol employed for the circle is O. 93 ° From the definitions of 92 ° we deduce ...
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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