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
... inverse figures , of pole and polar , of harmonic division , etc. , as applied to the line and circle ; and it is believed that a student who becomes acquainted with these geometric extensions in this their simpler form will be greatly ...
... inverse figures , of pole and polar , of harmonic division , etc. , as applied to the line and circle ; and it is believed that a student who becomes acquainted with these geometric extensions in this their simpler form will be greatly ...
Page x
... Inverse Figures . SECTION V. - Pole and Polar . SECTION VI . - The Radical Axis .. SEC- TION VII . - Centres and Axes of Perspective or Similitude , PART V. SECTION I. - Anharmonic Division . SECTION II.— Harmonic Ratio . SECTION III ...
... Inverse Figures . SECTION V. - Pole and Polar . SECTION VI . - The Radical Axis .. SEC- TION VII . - Centres and Axes of Perspective or Similitude , PART V. SECTION I. - Anharmonic Division . SECTION II.— Harmonic Ratio . SECTION III ...
Page 137
... inverse points with respect to the circle . Ex . 2. Let PQ be a common direct tangent to the circles having O and O ' as centres . Let OP and O'Q be radii P R to the points of contact , and let QR be || to 00 ' . Denote A D B C the ...
... inverse points with respect to the circle . Ex . 2. Let PQ be a common direct tangent to the circles having O and O ' as centres . Let OP and O'Q be radii P R to the points of contact , and let QR be || to 00 ' . Denote A D B C the ...
Page 207
... INVERSE FIGURES . 256 ° . Def . - Two points so situated upon a centre - line of a circle that the radius is a geometric mean ( 169 ° , Def . ) between their distances from the centre are called inverse points with respect to the circle ...
... INVERSE FIGURES . 256 ° . Def . - Two points so situated upon a centre - line of a circle that the radius is a geometric mean ( 169 ° , Def . ) between their distances from the centre are called inverse points with respect to the circle ...
Page 208
... inverse . 6. When P comes to C , Q goes to ∞ ; so that the inverse of the centre of inversion is any point at infinity . 257 ° . Problem . To find the circle to which two pairs of collinear points may be inverse points . S T U P , Q ...
... inverse . 6. When P comes to C , Q goes to ∞ ; so that the inverse of the centre of inversion is any point at infinity . 257 ° . Problem . To find the circle to which two pairs of collinear points may be inverse points . S T U P , Q ...
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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