The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 174
Triangles and parallelograms of the same altitude are to one another as their bases . ... namely , the perpendicular drawn from the point A to BD : as the base BC is to the base CD , so shall the triangle ABC be to the triangle ACD ...
Triangles and parallelograms of the same altitude are to one another as their bases . ... namely , the perpendicular drawn from the point A to BD : as the base BC is to the base CD , so shall the triangle ABC be to the triangle ACD ...
Página 175
and since it has been shewn that if the base HC be greater than the base CL , the triangle AHC is greater than the triangle ACL ; and if equal , equal ; and if less , less ; therefore as the base BC is to the base CD , so is the ...
and since it has been shewn that if the base HC be greater than the base CL , the triangle AHC is greater than the triangle ACL ; and if equal , equal ; and if less , less ; therefore as the base BC is to the base CD , so is the ...
Página 225
2 Then , because the two sides AE , ED are equal to the two sides BE , EC , each to each , [ Construction , and that they contain equal angles AED , BEC ; [ I. 15 . therefore the base AD is equal to the base BC , and the angle DAE is ...
2 Then , because the two sides AE , ED are equal to the two sides BE , EC , each to each , [ Construction , and that they contain equal angles AED , BEC ; [ I. 15 . therefore the base AD is equal to the base BC , and the angle DAE is ...
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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