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 70
... tangents at the point of intersection . Def . 2. When two circles intersect at right angles they are said to cut each other orthogonally . The same term is conveniently applied to the intersection of 70 SYNTHETIC GEOMETRY .
... tangents at the point of intersection . Def . 2. When two circles intersect at right angles they are said to cut each other orthogonally . The same term is conveniently applied to the intersection of 70 SYNTHETIC GEOMETRY .
Page 71
... orthogonally by any circle having its centre at a point without S and its radius the tangent from the point to the circle S. 116 ° . The following examples furnish theorems of some importance . Ex . 1. Three tangents touch the circle S ...
... orthogonally by any circle having its centre at a point without S and its radius the tangent from the point to the circle S. 116 ° . The following examples furnish theorems of some importance . Ex . 1. Three tangents touch the circle S ...
Page 119
... orthogonal projection , or simply the projec- tion , of the point upon the line . 3. Length being considered , the join of the projection of two points is the projection of the join of the points . P Thus if L be a given line and P , Q ...
... orthogonal projection , or simply the projec- tion , of the point upon the line . 3. Length being considered , the join of the projection of two points is the projection of the join of the points . P Thus if L be a given line and P , Q ...
Page 180
... orthogonal to that of the line . Hence any line can be brought into coincidence with any other line in its plane by rotation about the point of intersection . 223 ° . If a line rotates about a finite point while the point simultaneously ...
... orthogonal to that of the line . Hence any line can be brought into coincidence with any other line in its plane by rotation about the point of intersection . 223 ° . If a line rotates about a finite point while the point simultaneously ...
Page 183
... ORTHOGONAL PROJECTION . 229 ° . The orthogonal projection ( 167 ° , 2 ) of PQ on L is P'Q ' , the segment intercepted between the feet of the perpendiculars PP ' and QQ ' . Now P'Q ' = PQ cos ( PQ . P'Q ' ) . P P ' L .. the projection ...
... ORTHOGONAL PROJECTION . 229 ° . The orthogonal projection ( 167 ° , 2 ) of PQ on L is P'Q ' , the segment intercepted between the feet of the perpendiculars PP ' and QQ ' . Now P'Q ' = PQ cos ( PQ . P'Q ' ) . P P ' L .. the projection ...
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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.
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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 |