Proposition XI.13 — From the same point two straight lines cannot be set up at r…

Proof

Two such perpendiculars would meet two lines in the plane at the same right angles; by XI.4 / XI.6 the two perpendiculars would have to be parallel; but parallels do not meet – contradicting their common origin.

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Depends on (2)

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…
XI.6Proposition XI.6If two straight lines be at right angles to the same plane, the straight lines will be parallel.

Required by (dependents) (2)

XI.14Proposition XI.14Planes to which the same straight line is at right angles will be parallel.
XI.19Proposition XI.19If two planes which cut one another be at right angles to any plane, their common section will also be at right angles…

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