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 x
... Similitude , PART V. SECTION I. - Anharmonic Division . SECTION II.— Harmonic Ratio . SECTION III . - Anharmonic Properties . SECTION IV . - Polar Reciprocals and Reciprocation . SECTION V. - Homography and Involution , 178 252 PART I ...
... Similitude , PART V. SECTION I. - Anharmonic Division . SECTION II.— Harmonic Ratio . SECTION III . - Anharmonic Properties . SECTION IV . - Polar Reciprocals and Reciprocation . SECTION V. - Homography and Involution , 178 252 PART I ...
Page 237
... contact . Cor . 5. When 0 = 4 = 22 , Z cuts S and S ' orthogonally , and OL = 0 , and the centre of the cutting circle is on the radical axis of the two . SECTION VII . CENTRE AND AXES OF SIMILITUDE OR PERSPECTIVE OF THE RADICAL AXIS . 237.
... contact . Cor . 5. When 0 = 4 = 22 , Z cuts S and S ' orthogonally , and OL = 0 , and the centre of the cutting circle is on the radical axis of the two . SECTION VII . CENTRE AND AXES OF SIMILITUDE OR PERSPECTIVE OF THE RADICAL AXIS . 237.
Page 238
... similitude ; while the polygons ABCD ... and a'b'c'd ' ... are oppositely placed , and O is their internal centre of similitude . Hence , when the lines joining any point to the vertices of a polygon are all divided in the same manner ...
... similitude ; while the polygons ABCD ... and a'b'c'd ' ... are oppositely placed , and O is their internal centre of similitude . Hence , when the lines joining any point to the vertices of a polygon are all divided in the same manner ...
Page 239
... similitude . Let ABCD ... , abcd ... be the polygons . Since they are similar , AB : ab = BC : bc = CD : cd ... ( 207 ° ) , and by hypothesis AB is || to ab , BC to bc , etc. Let Aa and Bb meet at some point O. Then OAB is a △ and ab ...
... similitude . Let ABCD ... , abcd ... be the polygons . Since they are similar , AB : ab = BC : bc = CD : cd ... ( 207 ° ) , and by hypothesis AB is || to ab , BC to bc , etc. Let Aa and Bb meet at some point O. Then OAB is a △ and ab ...
Page 240
... similitude . Cor . 1. In the limiting form of the polygons , the line BC becomes a tangent at B , and the line bc ... similitude . 285 ° . Let S and S ' be two circles with centres C , C ' and radii r , respectively , and let O and O ...
... similitude . Cor . 1. In the limiting form of the polygons , the line BC becomes a tangent at B , and the line bc ... similitude . 285 ° . Let S and S ' be two circles with centres C , C ' and radii r , respectively , and let O and O ...
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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