Proposition I.27 — If a straight line falling on two straight lines make the al…

Proof

Suppose the lines meet; I.16 gives a contradiction. By Definition I.23 they are parallel.

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Depends on (2)

I.16Proposition I.16In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and…
I.23Definition I.23Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both…

Required by (dependents) (3)

I.28Proposition I.28If a straight line falling on two straight lines make the exterior angle equal to the interior and opposite angle on…
I.31Proposition I.31Through a given point to draw a straight line parallel to a given straight line.
I.33Proposition I.33The straight lines joining equal and parallel straight lines (at the extremities which are in the same directions) are…

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