Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 4
... square of an odd number is an odd number . " EXERCISES . State the contrapositives and the converses of the follow- ing theorems : - I. The sum of two odd numbers is an even number . 2. A diameter is the longest chord in a circle . 3 ...
... square of an odd number is an odd number . " EXERCISES . State the contrapositives and the converses of the follow- ing theorems : - I. The sum of two odd numbers is an even number . 2. A diameter is the longest chord in a circle . 3 ...
Page 5
... square , " ' circle , " etc. 29 66 11 ° . That part of mathematics which treats of the properties and relations of plane geometric figures is Plane Geometry . Such is the subject of this work . The plane upon which the figures are ...
... square , " ' circle , " etc. 29 66 11 ° . That part of mathematics which treats of the properties and relations of plane geometric figures is Plane Geometry . Such is the subject of this work . The plane upon which the figures are ...
Page 46
... square , denoted by the symbol ☐ . Cor . 5. Since the square is a particular form of the rhombus and a particular form of the rectangle , Therefore all the sides of a square are equal to one another ; all the angles of a square are ...
... square , denoted by the symbol ☐ . Cor . 5. Since the square is a particular form of the rhombus and a particular form of the rectangle , Therefore all the sides of a square are equal to one another ; all the angles of a square are ...
Page 61
... square , ( b ) a rectangle , ( c ) an isosceles triangle , ( d ) an 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 ...
... square , ( b ) a rectangle , ( c ) an isosceles triangle , ( d ) an 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 ...
Page 66
... are the vertices of a square , and A , E , F of an equilateral triangle inscribed in the same circle . What is the angle between the lines BE and DF ? between BF and ED ? SPECIAL SECANTS -- TANGENT . 109 ° . Let P 66 SYNTHETIC GEOMETRY .
... are the vertices of a square , and A , E , F of an equilateral triangle inscribed in the same circle . What is the angle between the lines BE and DF ? between BF and ED ? SPECIAL SECANTS -- TANGENT . 109 ° . Let P 66 SYNTHETIC GEOMETRY .
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Common terms and phrases
ABCD Algebra altitude becomes bisects c.p.-circles centre of similitude chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent cut the circle denote diagonals diameter divided double points 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