Kitap 1
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For, since the straight line AE stands on the straight line CD, making the angles CEA, AED, the angles CEA, AED are equal to two right angles [I. 13]
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Again, since the straight line DE stands on the straight line AB, making the angles AED, DEB, the angles AED, DEB are equal to two right angles. [I. 13]
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But the angles CEA, AED were also proved equal to two right angles; therefore the angles CEA, AED are equal to the angles AED DEB. [Post. 4 and C. N. 1] Let the angle AED be subtracted from each; therefore the remaining angle CEA is equal to the remaining angle BED. [C. N. 3]
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Similarly it can be proved that the angles CEB, DEA are also equal.
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Therefore etc. Q. E. D.
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[Porism. From this it is manifest that, if two straight lines cut one another, they will make the angles at the point of section equal to four right angles.
Proposition 16.
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Enunciation In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles.
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Proof. Let ABC be a triangle, and let one side of it BC be produced to D;
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I say that the exterior angle ACD is greater than either of the interior and opposite angles CBA, BAC.
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Let AC be bisected at E [I. 10], and let BE be joined and produced in a straight line to F;
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let EF be made equal to BE[I. 3], let FC be joined [Post. 1], and let AC be drawn through to G [Post. 2].
