Proposition XI.5 — If a straight line be set up at right angles to three straig…

Proof

Two of the three meeting lines determine a plane (XI.2); if the third were out of that plane, the perpendicular relation combined with XI.4 would force two distinct planes through the same set of perpendicular lines, contradiction.

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Depends on (2)

XI.2Proposition XI.2If two straight lines cut one another, they are in one plane, and every triangle is in one plane.
XI.4Proposition XI.4If a straight line be set up at right angles to two straight lines which cut one another, at their common point of…

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