Proposition VI.12 — To three given straight lines to find a fourth proportional.

Proof

Same construction as VI.11 but with three input segments: lay two on one transversal and one on the other, then drop a parallel from the last point. VI.2 yields the fourth proportional.

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Depends on (2)

I.31Proposition I.31Through a given point to draw a straight line parallel to a given straight line.
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…

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