Elements of Geometry and Trigonometry |
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Page 136
... REGULAR POLYGON is a polygon which is both equilateral and equiangular . PROPOSITION I. THEOREM . Regular polygons of the same number of sides are similar . Let ABCDEF and abcdef be regular polygons of the same number of sides : then ...
... REGULAR POLYGON is a polygon which is both equilateral and equiangular . PROPOSITION I. THEOREM . Regular polygons of the same number of sides are similar . Let ABCDEF and abcdef be regular polygons of the same number of sides : then ...
Page 137
... regular polygon ; a circle may also be inscribed in it . 1 ° Let ABCF be a regular polygon : then can the circumference of a circle be circumscribed about it . For , through three consecutive ver- tices A , B , C , describe the circum ...
... regular polygon ; a circle may also be inscribed in it . 1 ° Let ABCF be a regular polygon : then can the circumference of a circle be circumscribed about it . For , through three consecutive ver- tices A , B , C , describe the circum ...
Page 138
... regular inscribed polygon . For , the sides are equal , because they are chords of equal arcs , and the angles are equal , because they are measured by halves of equal arcs . If the vertices A , B , C , & c . , of a regular inscribed ...
... regular inscribed polygon . For , the sides are equal , because they are chords of equal arcs , and the angles are equal , because they are measured by halves of equal arcs . If the vertices A , B , C , & c . , of a regular inscribed ...
Page 139
... regular hexagon be inscribed in a circle , any side will be equal to the radius of the circle . Let ABD be a circle , and ABCDEH a regular in- scribed hexagon : then will any side , as AB , be equal to the radius of the circle . Draw ...
... regular hexagon be inscribed in a circle , any side will be equal to the radius of the circle . Let ABD be a circle , and ABCDEH a regular in- scribed hexagon : then will any side , as AB , be equal to the radius of the circle . Draw ...
Page 140
... regular hexagon in a given circle . Let ABE be a circle , and O its centre . Beginning at any point of the circumference , as A , ap- ply the radius OA six times as a chord ; then will ABCDEF be the hexagon required ( P. IV . ) . Cor ...
... regular hexagon in a given circle . Let ABE be a circle , and O its centre . Beginning at any point of the circumference , as A , ap- ply the radius OA six times as a chord ; then will ABCDEF be the hexagon required ( P. IV . ) . Cor ...
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Common terms and phrases
ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence