Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 144
... 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 148
... regular inscribed pentagon . Scholium 1. If the arcs subtended by the sides of any regular inscribed polygon are bisected , and chords of the semi - arcs drawn , the resulting figure is a regular inscribed polygon of double the number ...
... regular inscribed pentagon . Scholium 1. If the arcs subtended by the sides of any regular inscribed polygon are bisected , and chords of the semi - arcs drawn , the resulting figure is a regular inscribed polygon of double the number ...
Page 149
... polygon which shall be similar to a given regular inscribed polygon . Let TNQ be a circle , O its centre , and ABCDEF a regu- lar inscribed polygon . At the middle points T , N , P , & c . , of the arcs sub- tended by the sides of the ...
... polygon which shall be similar to a given regular inscribed polygon . Let TNQ be a circle , O its centre , and ABCDEF a regu- lar inscribed polygon . At the middle points T , N , P , & c . , of the arcs sub- tended by the sides of the ...
Page 150
... polygon is equilateral . The circumscribed poly- gon being both equiangular and equilateral , is regular ; H T B D S and since it has the same number of ... polygon is greater than that of a regular circumscribed polygon of 150 GEOMETRY .
... polygon is equilateral . The circumscribed poly- gon being both equiangular and equilateral , is regular ; H T B D S and since it has the same number of ... polygon is greater than that of a regular circumscribed polygon of 150 GEOMETRY .
Page 151
... regular circumscribed polygon of double the number of sides , because the whole is greater than any of its parts . Sch . 2. By means of a circumscribed and inscribed square , we may construct , in succession , regular circum- scribed ...
... regular circumscribed polygon of double the number of sides , because the whole is greater than any of its parts . Sch . 2. By means of a circumscribed and inscribed square , we may construct , in succession , regular circum- scribed ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence