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 43
... constant , we deduce the following- 1. When two angles of a triangle are given the third is given also ; so that the giving of the third furnishes no new information . 2. As two parts of a triangle are not sufficient to deter- mine it ...
... constant , we deduce the following- 1. When two angles of a triangle are given the third is given also ; so that the giving of the third furnishes no new information . 2. As two parts of a triangle are not sufficient to deter- mine it ...
Page 53
... constant distance from a fixed point in the plane . The compasses , whatever be their form , furnish us with two points , A and B , which , from the rigidity of the instrument , are supposed to preserve an unvarying distance B A A B ...
... constant distance from a fixed point in the plane . The compasses , whatever be their form , furnish us with two points , A and B , which , from the rigidity of the instrument , are supposed to preserve an unvarying distance B A A B ...
Page 64
... constant . ( 105 ° , 4 ) Cor . 2. Since and LAPBLAOB minor , LAQB LAOB major , and . LAOB minor + LAOB major = 4 right angles LAPB + LAQB a straight angle . = And APBQ is a concyclic quadrangle . ( 37 ° ) Hence a concyclic quadrangle ...
... constant . ( 105 ° , 4 ) Cor . 2. Since and LAPBLAOB minor , LAQB LAOB major , and . LAOB minor + LAOB major = 4 right angles LAPB + LAQB a straight angle . = And APBQ is a concyclic quadrangle . ( 37 ° ) Hence a concyclic quadrangle ...
Page 65
... constant and its vertical angle APC constant . Therefore the locus of the vertex of a triangle which has a constant base and a constant vertical angle is an arc of a circle passing through the end - points of the base . This property is ...
... constant and its vertical angle APC constant . Therefore the locus of the vertex of a triangle which has a constant base and a constant vertical angle is an arc of a circle passing through the end - points of the base . This property is ...
Page 75
... constant length . Find the locus of the middle point of AB . 24. Two equal circles touch one another and each touches one of a pair of perpendicular lines . What is the locus of the point of contact of the circles ? 25. Two lines ...
... constant length . Find the locus of the middle point of AB . 24. Two equal circles touch one another and each touches one of a pair of perpendicular lines . What is the locus of the point of contact of the circles ? 25. Two lines ...
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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 |