The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 63
And because AC is equal to CE , [ Construction . the square on AC is equal to the square on CE ; therefore the squares on AC , CE are double of the square on AC . But the square on AE is equal to the squares on AC , CE , because the ...
And because AC is equal to CE , [ Construction . the square on AC is equal to the square on CE ; therefore the squares on AC , CE are double of the square on AC . But the square on AE is equal to the squares on AC , CE , because the ...
Página 65
And because EC is equal to CA , the square on EC is oqual to the square on CA ; therefore the squares on EC , CA are double of the square or CA. But the squareon AE is equal to the squares on EC , CA . [ I . 47 . Therefore the square on ...
And because EC is equal to CA , the square on EC is oqual to the square on CA ; therefore the squares on EC , CA are double of the square or CA. But the squareon AE is equal to the squares on EC , CA . [ I . 47 . Therefore the square on ...
Página 268
must express each of these dimensions in terms of the same unit ; we may say that the rectangle measures 36 inches by 18 inches , and contains 36 times 18 square inches , that is , 648 square inches . Thus universally , if one side of a ...
must express each of these dimensions in terms of the same unit ; we may say that the rectangle measures 36 inches by 18 inches , and contains 36 times 18 square inches , that is , 648 square inches . Thus universally , if one side of a ...
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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