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 61
... range of Mathematics . Illustrations of its meaning and application in Geometry will occur frequently in the sequel , but the following are given by way of introduction . 1. A magnitude is continuous throughout its extent . Thus a line ...
... range of Mathematics . Illustrations of its meaning and application in Geometry will occur frequently in the sequel , but the following are given by way of introduction . 1. A magnitude is continuous throughout its extent . Thus a line ...
Page 63
... range of possibility . 105 ° . Let AB be a chord dividing the and let P and Q be any points upon the major and minor arcs respectively . ( 102 ° , Def . ) Let O be the centre . I. The radii OA and OB form two angles at the centre , a ...
... range of possibility . 105 ° . Let AB be a chord dividing the and let P and Q be any points upon the major and minor arcs respectively . ( 102 ° , Def . ) Let O be the centre . I. The radii OA and OB form two angles at the centre , a ...
Page 186
... direction is equal to that in a - direction . RANGES AND PENCILS OF FOUR . 233 ° . Let A , B , C , P be a range of four , then AB.CP + BC . AP + CA . BP = 0 . Proof.- AP AC + CP , and BP = BC 186 SYNTHETIC GEOMETRY .
... direction is equal to that in a - direction . RANGES AND PENCILS OF FOUR . 233 ° . Let A , B , C , P be a range of four , then AB.CP + BC . AP + CA . BP = 0 . Proof.- AP AC + CP , and BP = BC 186 SYNTHETIC GEOMETRY .
Page 189
Nathan Fellowes Dupuis. 237 ° . A , B , C being a range of three , and P any point not on the axis , AB . CP2 + BC . AP2 + CA . BP2 == - AB . BC . CA. Proof . - Let PQ be 1 to AC . Then AQ = AC + CQ , BQ = BC + CQ , and the expression ...
Nathan Fellowes Dupuis. 237 ° . A , B , C being a range of three , and P any point not on the axis , AB . CP2 + BC . AP2 + CA . BP2 == - AB . BC . CA. Proof . - Let PQ be 1 to AC . Then AQ = AC + CQ , BQ = BC + CQ , and the expression ...
Page 252
... reciprocals of one another , are called the two anharmonic ratios of the division of the segment AB by the points C and D , or the harmonoids of the range A , B , C , D. 252 J Either of the two anharmonic ratios expresses a relation ...
... reciprocals of one another , are called the two anharmonic ratios of the division of the segment AB by the points C and D , or the harmonoids of the range A , B , C , D. 252 J Either of the two anharmonic ratios expresses a relation ...
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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 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
Popular passages
Page 176 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 9 - BLACKIE— GREEK AND ENGLISH DIALOGUES FOR USE IN SCHOOLS AND COLLEGES. By JOHN STUART BLACKIE, Professor of Greek in the University of Edinburgh.
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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 |