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. |
From inside the book
Results 1-5 of 35
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 = LAPB LAOB 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 ...
... constant . ( 105 ° , 4 ) Cor . 2. Since and = LAPB LAOB 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 ...
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 ...
Other editions - View all
Common terms and phrases
ABCD algebraic altitude apothem bisects c.p.-circles centre of similitude centre-line chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent corresponding cut the circle denote diagonals diameter divided end-points equal angles equianharmonic equilateral triangle excircles external bisector fixed point geometric given circles given line given point harmonic range Hence hexagram homographic homologous hypothenuse incircle internal angles inverse points isosceles joins LAOB line-segment locus median middle point nine-points circle opposite sides orthogonally pair parallel parallelogram passes pencil perpendicular perspective plane point of contact point of intersection polar reciprocal Proof quadrangle radical axis radical centre radii radius rectangle rectilinear figure regular polygon rhombus right angle right bisector rotation secant similar Similarly square straight angle symbol tangent tensor theorem Theorem.-The three circles transversal vertex vertices