The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 28
For if not , the angle BAC must be either equal to the angle EDF or less than the angle EDF . But the angle BAC is not equal to the angle EDF , for then the base BC would be equal to the base EF ; [ 1.
For if not , the angle BAC must be either equal to the angle EDF or less than the angle EDF . But the angle BAC is not equal to the angle EDF , for then the base BC would be equal to the base EF ; [ 1.
Página 103
But FAC , the exterior angle of the triangle ABC , is equal to the two angles ABC , ACB ; [ I. 32 . therefore the angle BAC is equal to the angle FAC , ( Ax . 1 . and therefore each of them is a right angle . [ I. Def . 10 .
But FAC , the exterior angle of the triangle ABC , is equal to the two angles ABC , ACB ; [ I. 32 . therefore the angle BAC is equal to the angle FAC , ( Ax . 1 . and therefore each of them is a right angle . [ I. Def . 10 .
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CA be to AD As AE is to AB : either the angle BAC shall be equal to the angle DA E , or the angles BAC and DAE shall be together equal to two right angles . [ The student can construct the figure for himself . ) ...
CA be to AD As AE is to AB : either the angle BAC shall be equal to the angle DA E , or the angles BAC and DAE shall be together equal to two right angles . [ The student can construct the figure for himself . ) ...
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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