Proposition I.29 — A straight line falling on parallel straight lines makes the…

Proof

The first use of Postulate 5: any contrary supposition contradicts the parallel postulate via I.13.

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Depends on (2)

I.13Proposition I.13If a straight line set up on a straight line make angles, it will make either two right angles or angles equal to two…
5Postulate 5That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right…

Required by (dependents) (14)

I.30Proposition I.30Straight lines parallel to the same straight line are also parallel to one another.
I.32Proposition I.32In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles,…
I.33Proposition I.33The straight lines joining equal and parallel straight lines (at the extremities which are in the same directions) are…
I.34Proposition I.34In parallelogrammic areas the opposite sides and angles are equal to one another, and the diameter bisects the areas.
I.46Proposition I.46On a given straight line to describe a square.
II.4Proposition II.4If a straight line be cut at random, the square on the whole is equal to the squares on the segments and twice the…
II.9Proposition II.9If a straight line be cut into equal and unequal segments, the squares on the unequal segments of the whole are double…
II.10Proposition II.10If a straight line be bisected and a straight line be added to it in a straight line, the square on the whole with the…
IV.7Proposition IV.7About a given circle to circumscribe a square.
VI.2Proposition VI.2If a straight line be drawn parallel to one of the sides of a triangle, it will cut the sides of the triangle…
VI.3Proposition VI.3If an angle of a triangle be bisected and the straight line cutting the angle cut the base also, the segments of the…
VI.24Proposition VI.24In any parallelogram the parallelograms about the diameter are similar both to the whole and to one another.
VI.32Proposition VI.32If two triangles having two sides proportional to two sides be placed together at one angle so that their corresponding…
XI.8Proposition XI.8If two straight lines be parallel, and one of them be at right angles to any plane, the remaining one will also be at…

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