Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 143
... circumscribed polygon is equal to the corresponding angle of the inscribed polygon : hence , the circumscribed polygon is equiangular . 2o . Draw the lines OG , OT , OH , ON , and OI . Then , because the lines HT and HN are tangent to ...
... circumscribed polygon is equal to the corresponding angle of the inscribed polygon : hence , the circumscribed polygon is equiangular . 2o . Draw the lines OG , OT , OH , ON , and OI . Then , because the lines HT and HN are tangent to ...
Page 144
... circumscribed polygon is equilateral . The circumscribed poly- K gon being both equiangular and equilateral , is regular ; and since it has ... circumscribed polygon is greater than that of a regular circumscribed polygon of 144 GEOMETRY .
... circumscribed polygon is equilateral . The circumscribed poly- K gon being both equiangular and equilateral , is regular ; and since it has ... circumscribed polygon is greater than that of a regular circumscribed polygon of 144 GEOMETRY .
Page 145
... circumscribed polygon of double the number of sides , because the whole is greater than any of its parts . Scholium . By means of a circumscribed and inscribed square , we may construct , in succession , regular circumscribed and ...
... circumscribed polygon of double the number of sides , because the whole is greater than any of its parts . Scholium . By means of a circumscribed and inscribed square , we may construct , in succession , regular circumscribed and ...
Page 146
... circumscribed or inscribed circles ; and their areas are to each other as the squares of those radii . 1o . Let ABC and KLM be similar regular polygons . Let OA and QK be the radii of their circumscribed , OD and QR be the radii of ...
... circumscribed or inscribed circles ; and their areas are to each other as the squares of those radii . 1o . Let ABC and KLM be similar regular polygons . Let OA and QK be the radii of their circumscribed , OD and QR be the radii of ...
Page 147
... circumscribed about a circle and the other inscribed in it , which shall differ from each other by less than any given surface . Let ABCE be a circle , O its centre , and the side of a square which is less than the given surface ; then ...
... circumscribed about a circle and the other inscribed in it , which shall differ from each other by less than any given surface . Let ABCE be a circle , O its centre , and the side of a square which is less than the given surface ; then ...
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Common terms and phrases
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following