The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 243
Therefore all the angles at the bases of the triangles are together greater than all the angles of the polygon . Now all the angles of the triangles are together equal to twice as many right angles as there are triangles , that is ...
Therefore all the angles at the bases of the triangles are together greater than all the angles of the polygon . Now all the angles of the triangles are together equal to twice as many right angles as there are triangles , that is ...
Página 248
Let then the segments EK , KF , FL , LG , GM , MH , HN , NE be those which remain , and which are together less than the excess of the circle above S ; therefore the rest of the circle , namely the polygon EKFLGMHN , is greater than the ...
Let then the segments EK , KF , FL , LG , GM , MH , HN , NE be those which remain , and which are together less than the excess of the circle above S ; therefore the rest of the circle , namely the polygon EKFLGMHN , is greater than the ...
Página 279
Hence also , regular polygons having as many sides as any of these numbers may be inscribed in a circle , or described about a circle . This however does not enable us to describe a regular polygon of any assigned number of sides ...
Hence also , regular polygons having as many sides as any of these numbers may be inscribed in a circle , or described about a circle . This however does not enable us to describe a regular polygon of any assigned number of sides ...
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ABCD angle ABC angle ACB angle BAC Axiom base BC is equal bisected Book centre circle circle ABC circumference common Construction contained Corollary Definition demonstration described diameter divided double draw drawn edition Elements equal equal angles equiangular equilateral equimultiples Euclid exterior angle extremities fall figure four fourth given straight line greater half Hypothesis impossible join less Let ABC magnitudes manner meet multiple namely parallel parallelogram pass perpendicular plane polygon PROBLEM produced proportionals Q.E.D. PROPOSITION ratio reason rectangle rectangle contained rectilineal figure right angles segment shewn sides similar Simson solid square straight line &c suppose Take taken THEOREM third touches the circle triangle ABC Wherefore whole