Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |
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Page 41
... polygon . A circle is inscribed in a polygon when its circumference touches each side , and the polygon is said to be circumscribed ... polygon has all its sides equal , and all its angles equal . If all the sides are not equal , or all ...
... polygon . A circle is inscribed in a polygon when its circumference touches each side , and the polygon is said to be circumscribed ... polygon has all its sides equal , and all its angles equal . If all the sides are not equal , or all ...
Page 55
... polygon , which demonstrates the first part of the Theorem . As to the second part , we observe , that the sides AB , BC , CD , etc. , are equal chords , in reference to the circumscribed circle , and therefore they are equally distant ...
... polygon , which demonstrates the first part of the Theorem . As to the second part , we observe , that the sides AB , BC , CD , etc. , are equal chords , in reference to the circumscribed circle , and therefore they are equally distant ...
Page 56
... circumscribed polygon are equal . And since AA ' = A'B = BB ' = B'C = CC ' = etc. , we have A'B ' = B'C ' = C'D ' etc. That is , this circumscribed polygon has all its angles equal , and all its sides equal ; it is therefore regular ( D ...
... circumscribed polygon are equal . And since AA ' = A'B = BB ' = B'C = CC ' = etc. , we have A'B ' = B'C ' = C'D ' etc. That is , this circumscribed polygon has all its angles equal , and all its sides equal ; it is therefore regular ( D ...
Page 67
... polygon being given , to construct a regu- lar circumscribed polygon of the same number of sides ; and conversely . First construction . Through the vertices A , B , C , etc. , of the inscribed polygon , draw tangents to the ...
... polygon being given , to construct a regu- lar circumscribed polygon of the same number of sides ; and conversely . First construction . Through the vertices A , B , C , etc. , of the inscribed polygon , draw tangents to the ...
Page 68
... polygon re- quired . We have already shown that the two polygons thus obtained are equal ( T. XVI . , S. ) . E O c C D M E ' D " D ' Reciprocally . To obtain the inscribed polygon , when we al- ready know the circumscribed polygon A ...
... polygon re- quired . We have already shown that the two polygons thus obtained are equal ( T. XVI . , S. ) . E O c C D M E ' D " D ' Reciprocally . To obtain the inscribed polygon , when we al- ready know the circumscribed polygon A ...
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Common terms and phrases
ABē ABCD altitude angles equal apothem base bisecting centre chord circle circumference circumscribed circle circumscribed polygon cone consequently corresponding cosec Cosine Cotang cubic cylinder decimal denote diameter dicular distance divided draw drawn equally distant equation exterior angles feet figure frustum GEOMETRY given angle given line gives greater half hence homologous hypotenuse inches included angle intersection logarithm measure middle point multiplied number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant quadrilateral radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle Scholium secant similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang Tangent THEOREM three sides triangle ABC volume