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 . 1. Then AB = CD and AC = BD . B Proof.— ' . ' AD is a transversal to the parallels AB and CD , LCDA = LDAB . and · . · AD is a ...
... diagonals bisect one another . AB is || to CD , and AC is || to BD , and AD and BC are diagonals . 1. Then AB = CD and AC = BD . B Proof.— ' . ' AD is a transversal to the parallels AB and CD , LCDA = LDAB . and · . · AD is a ...
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
A. W. VERRALL ABCD algebraic altitude Assistant Master bisects BOOK Cambridge centre of similitude centre-line circles touch circumcircle co-axal coincide collinear common concurrent concurrent lines concyclic congruent cuts denote diagonals diameter divided Edited ELEMENTARY end-points equal angles equianharmonic equilateral triangle excircles EXERCISES external bisector FASNACHT Fcap fixed point G. E. FASNACHT geometric given circles given line given point GREEK harmonic range Hence HISTORY homographic Illustrated inverse points ISAAC TODHUNTER isosceles LAOB line-segment LL.D Mathematical median middle point orthogonally Owens College pair parallel parallelogram passes pencil perpendicular plane point of contact point of intersection Prof Professor Proof quadrangle radical axis radii radius rectangle regular polygon respect revised right angle right bisector rotation School secant Similarly square straight angle symbol tangent theorem Theorem.-The three circles Translated Trinity College vertex vertices
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References to this book
The Classification of Quadrilaterals: A Study of Definition Zalman Usiskin,Jennifer Griffin,David Witonsky,Edwin Willmore No preview available - 2008 |
The Classification of Quadrilaterals: A Study of Definition Zalman Usiskin,Jennifer Griffin,David Witonsky,Edwin Willmore No preview available - 2008 |