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 27
... equilateral 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 ...
... equilateral 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 ...
Page 28
... equilateral triangle are the three right bisectors of the sides , and the three internal bisectors of the angles . 56 ° . Theorem . - If two angles of a triangle are equal to one another , the triangle is isosceles , and the equal sides ...
... equilateral triangle are the three right bisectors of the sides , and the three internal bisectors of the angles . 56 ° . Theorem . - If two angles of a triangle are equal to one another , the triangle is isosceles , and the equal sides ...
Page 51
... equilateral As described outwards upon the sides BC , CA , and AB respectively . Then AA ' = BB ' = CC ' . ( Use 52 ° . ) 2. Is Ex . I true when the equilateral As are described " inwardly " or upon the other sides of their bases ? 3 ...
... equilateral As described outwards upon the sides BC , CA , and AB respectively . Then AA ' = BB ' = CC ' . ( Use 52 ° . ) 2. Is Ex . I true when the equilateral As are described " inwardly " or upon the other sides of their bases ? 3 ...
Page 52
... equilateral lines are drawn parallel to the other sides . The perimeter of the so formed is equal to twice a side of the A. 14. Examine Ex . 13 when the point is on a side pro- duced . 15. The internal bisector of one angle of a △ and ...
... equilateral lines are drawn parallel to the other sides . The perimeter of the so formed is equal to twice a side of the A. 14. Examine Ex . 13 when the point is on a side pro- duced . 15. The internal bisector of one angle of a △ and ...
Page 61
... equilateral triangle ? Give all the axes where there are more than one . 12. When a rectilinear figure has more than one axis of symmetry , what relation in direction do they hold to one another ? 13. The vertices of an equilateral ...
... equilateral triangle ? Give all the axes where there are more than one . 12. When a rectilinear figure has more than one axis of symmetry , what relation in direction do they hold to one another ? 13. The vertices of an equilateral ...
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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