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 23
... triangle is the figure formed by three lines and the determined points , or by three points and the deter- mined lines . The points are the vertices of the triangle , and the line- segments which have the points as end - points are the ...
... triangle is the figure formed by three lines and the determined points , or by three points and the deter- mined lines . The points are the vertices of the triangle , and the line- segments which have the points as end - points are the ...
Page 24
... triangle is com- X pletely given . This is not the case with a rectilinear figure having any number of vertices ... triangle , or simply the angles of the triangle . 2. The angle DCB , and others of like kind , are external angles of the ...
... triangle is com- X pletely given . This is not the case with a rectilinear figure having any number of vertices ... triangle , or simply the angles of the triangle . 2. The angle DCB , and others of like kind , are external angles of the ...
Page 25
Nathan Fellowes Dupuis. The angles of the triangle are denoted usually by the capital letters A , B , C , and the ... triangles , admit of comparison in two ways . The first is as to their capability of perfect coinci- dence ; when this ...
Nathan Fellowes Dupuis. The angles of the triangle are denoted usually by the capital letters A , B , C , and the ... triangles , admit of comparison in two ways . The first is as to their capability of perfect coinci- dence ; when this ...
Page 26
... triangle . Thus the triangle APB is isosceles . The side AB , which is not one of the equal sides , is called the base . Cor . 1. Since the APC = BPC , :: LA = LB . Hence the basal angles of an isosceles triangle are equal to one ...
... triangle . Thus the triangle APB is isosceles . The side AB , which is not one of the equal sides , is called the base . Cor . 1. Since the APC = BPC , :: LA = LB . Hence the basal angles of an isosceles triangle are equal to one ...
Page 27
... triangle . Cor . 3. Since an equilateral triangle is isosceles with re- spect to each side as base , all the angles of an equilateral triangle are equal to one another ; or , an equilateral triangle is equiangular . 54 ° . Theorem ...
... triangle . Cor . 3. Since an equilateral triangle is isosceles with re- spect to each side as base , all the angles of an equilateral triangle are equal to one another ; or , an equilateral triangle is equiangular . 54 ° . Theorem ...
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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