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 44
... . Thus ABCD is a quadrangle . 2. The line - segments AC and BD which join opposite vertices are the diagonals of the quadrangle . 3. The quadrangle formed when two parallel lines intersect two 44 SYNTHETIC GEOMETRY .
... . Thus ABCD is a quadrangle . 2. The line - segments AC and BD which join opposite vertices are the diagonals of the quadrangle . 3. The quadrangle formed when two parallel lines intersect two 44 SYNTHETIC GEOMETRY .
Page 45
... diagonals bisect one another . AB is to CD , and AC is || to BD , and AD and BC are diagonals . I. Then AB = CD and AC = BD . C D B Proof .. AD is a transversal to the parallels AB and CD , .. LCDA = LDAB . and AD is a transversal to ...
... diagonals bisect one another . AB is to CD , and AC is || to BD , and AD and BC are diagonals . I. Then AB = CD and AC = BD . C D B Proof .. AD is a transversal to the parallels AB and CD , .. LCDA = LDAB . and AD is a transversal to ...
Page 46
... diagonals of a rectangle are equal to one another . Def . 3. — A rectangle with two adjacent sides equal is a square , denoted by the symbol . Cor . 5. Since the square is a particular form of the rhombus and a particular form of the ...
... diagonals of a rectangle are equal to one another . Def . 3. — A rectangle with two adjacent sides equal is a square , denoted by the symbol . Cor . 5. Since the square is a particular form of the rhombus and a particular form of the ...
Page 50
... diagonals ; so that both diagonals are within in the normal quadrangle , one is within and one without in the inverted quadrangle , and both are without in the crossed quadrangle . The general properties of the quadrangle are common to ...
... diagonals ; so that both diagonals are within in the normal quadrangle , one is within and one without in the inverted quadrangle , and both are without in the crossed quadrangle . The general properties of the quadrangle are common to ...
Page 52
... diagonal is greater than any side . 21. If any point other than the point of intersection of the diagonals be taken in a quadrangle , the sum of the line - segments joining it with the vertices is greater than the sum of the diagonals ...
... diagonal is greater than any side . 21. If any point other than the point of intersection of the diagonals be taken in a quadrangle , the sum of the line - segments joining it with the vertices is greater than the sum of the diagonals ...
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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