The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 261
In the second case also the triangles are not necessarily equal , as may be shewn by an example ; in the figure of I. 11 , suppose the straight line FB drawn ; then in the two triangles FBE , PBD , the side PB and the angle FBC are ...
In the second case also the triangles are not necessarily equal , as may be shewn by an example ; in the figure of I. 11 , suppose the straight line FB drawn ; then in the two triangles FBE , PBD , the side PB and the angle FBC are ...
Página 285
For , one of the angles A BC , DEP must be greater than the other ; suppose A BC the greater ; and make the angle ABG equal to the angle DEF . Then it may be shewn , as in VI . 7 , that BG is equal to BC , and the angle BGA equal to the ...
For , one of the angles A BC , DEP must be greater than the other ; suppose A BC the greater ; and make the angle ABG equal to the angle DEF . Then it may be shewn , as in VI . 7 , that BG is equal to BC , and the angle BGA equal to the ...
Página 287
Suppose now that the angle DAE is greater than the angle DAP . Then the angle CAE is equal to the angle A ÉP , and therefore the angle CAE is equal to the angle A FE , and therefore the angle CA E is equal to the angle BAC . [ I. 29 .
Suppose now that the angle DAE is greater than the angle DAP . Then the angle CAE is equal to the angle A ÉP , and therefore the angle CAE is equal to the angle A FE , and therefore the angle CA E is equal to the angle BAC . [ I. 29 .
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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