Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
From inside the book
Results 1-5 of 21
Page 74
... polygon of 21 sides is 2 ( n − 1 ) right angles . - 5. If the angle of a trammel is 60 ° what arc of a circle will it describe ? what if its angle is n ° ? 6. Trisect a right angle and thence show how to draw a regular 12 - sided polygon ...
... polygon of 21 sides is 2 ( n − 1 ) right angles . - 5. If the angle of a trammel is 60 ° what arc of a circle will it describe ? what if its angle is n ° ? 6. Trisect a right angle and thence show how to draw a regular 12 - sided polygon ...
Page 86
... polygons higher than the quadrangle are regular polygons . Def . 2. - A regular polygon has its vertices concyclic , and all its sides equal to one another . The centre of the circumcircle is the centre of the polygon . 133 ° . Theorem ...
... polygons higher than the quadrangle are regular polygons . Def . 2. - A regular polygon has its vertices concyclic , and all its sides equal to one another . The centre of the circumcircle is the centre of the polygon . 133 ° . Theorem ...
Page 87
Nathan Fellowes Dupuis. regular polygon , the magnitude of an internal angle is ( 2-4 ) right angles . Proof . Let AB ... polygons expressed in right angles and in degrees are found , by putting proper values for n , to be as follows ...
Nathan Fellowes Dupuis. regular polygon , the magnitude of an internal angle is ( 2-4 ) right angles . Proof . Let AB ... polygons expressed in right angles and in degrees are found , by putting proper values for n , to be as follows ...
Page 88
... polygons , each taken alone , can fill the plane . That a regular polygon of any species may be capable of filling the plane , the number of right angles in its internal angle must be a divisor of 4. But as no internal angle can be so ...
... polygons , each taken alone , can fill the plane . That a regular polygon of any species may be capable of filling the plane , the number of right angles in its internal angle must be a divisor of 4. But as no internal angle can be so ...
Page 98
... polygon . 3. To bisect a triangle by a line drawn through a given point in one of the sides . 4. To construct a rhombus equal to a given parallelogram , and with one of the sides of the parallelogram as its side . 5. The three ...
... polygon . 3. To bisect a triangle by a line drawn through a given point in one of the sides . 4. To construct a rhombus equal to a given parallelogram , and with one of the sides of the parallelogram as its side . 5. The three ...
Other editions - View all
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