Proposition: Prop. 11.05: Three Intersecting Lines Perpendicular to Another Line are in One Plane

(Proposition 5 from Book 11 of Euclid's “Elements”)

If a straight line is set up at right angles to three straight lines cutting one another, at the common point of section, then the three straight lines are in one plane. * For let some straight line $AB$ have been set up at right angles to three straight lines $BC$, $BD$, and $BE$, at the (common) point of section $B$. * I say that $BC$, $BD$, and $BE$ are in one plane.