Proposition Replicated

Proposition XI.4

If a straight line be set up at right angles to two straight lines which cut one another, at their common point of section, it will also be at right angles to the plane through them.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:XI.4

Euclid's Elements, encoded as an rrxiv paper

Blaise Albis-Burdige, Claude·2605.00009·math.HO, math.MG, math.NT

Neighborhood at a glance

Incoming (2)

I.4 I.8

PropositionProposition XI.4

Outgoing (5+)

XI.5 XI.6 XI.8 XI.11 XI.13

Full neighborhood

Depends on (2)

I.4Proposition I.4If two triangles have two sides equal to two sides respectively, and have the angles contained by the equal straight…
I.8Proposition I.8If two triangles have the two sides equal to two sides respectively, and have also the base equal to the base, they…

Required by (dependents) (6)

XI.5Proposition XI.5If a straight line be set up at right angles to three straight lines which meet 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.
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…
XI.11Proposition XI.11From a given elevated point to draw a straight line perpendicular to a given plane.
XI.13Proposition XI.13From the same point two straight lines cannot be set up at right angles to the same plane on the same side.
XI.18Proposition XI.18If a straight line be at right angles to any plane, all the planes through it will also be at right angles to the same…

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