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 86
... ex - circles of the triangle . REGULAR POLYGONS . 132 ° . Def . I. A closed rectilinear figure without re - entrant angles ( 89 ° , 2 ) is in general called a polygon . They are named according to the number of their sides as follows ...
... ex - circles of the triangle . REGULAR POLYGONS . 132 ° . Def . I. A closed rectilinear figure without re - entrant angles ( 89 ° , 2 ) is in general called a polygon . They are named according to the number of their sides as follows ...
Page 88
... ex - circles . ( 131 ° ) Then AP AP ' , CP ' = CP " , and BP = BP " , ( 114 ° , Cor.1 ) .. AP ' + AP = AB + BC + AC = a + b + c , and , denoting the perimeter of the triangle by 2s , we have AP = AP ' = s , BP = s - c = BP " . AR 88 ...
... ex - circles . ( 131 ° ) Then AP AP ' , CP ' = CP " , and BP = BP " , ( 114 ° , Cor.1 ) .. AP ' + AP = AB + BC + AC = a + b + c , and , denoting the perimeter of the triangle by 2s , we have AP = AP ' = s , BP = s - c = BP " . AR 88 ...
Page 89
... ex - circles upon the sides b and c respectively , we have Ai = Bc = Cb = s - a , Bi = Ca = Ac = s - b , Ci Ab Ba = s - c . EXERCISES . 66 1. In testing the straightness of a rule " three rules are virtually tested . How ? 2. To ...
... ex - circles upon the sides b and c respectively , we have Ai = Bc = Cb = s - a , Bi = Ca = Ac = s - b , Ci Ab Ba = s - c . EXERCISES . 66 1. In testing the straightness of a rule " three rules are virtually tested . How ? 2. To ...
Page 193
... excircle to the side a . Cor . 2. If any line be drawn through the centre of the in- circle of a triangle , and a , ß , y be the perpendiculars from the vertices upon it , aa + bB + cy = 0 , and if the line passes through the centre of ...
... excircle to the side a . Cor . 2. If any line be drawn through the centre of the in- circle of a triangle , and a , ß , y be the perpendiculars from the vertices upon it , aa + bB + cy = 0 , and if the line passes through the centre of ...
Page 200
... excircles are concurrent with a perpendicular at a point of contact of the incircle . 250 ° . Theorem . - When three points X , Y , Z lying on the sides BC , CA , and AB of a triangle are collinear , they divide the sides into parts ...
... excircles are concurrent with a perpendicular at a point of contact of the incircle . 250 ° . Theorem . - When three points X , Y , Z lying on the sides BC , CA , and AB of a triangle are collinear , they divide the sides into parts ...
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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 |