Proposition Replicated
Proposition X.40
If two straight lines incommensurable in square which make the sum of the squares on them medial, but the rectangle contained by them rational, be added together, the whole straight line is irrational; and let it be called the side of a rational plus a medial area.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:X.40
Euclid's Elements, encoded as an rrxiv paper
Blaise Albis-Burdige, Claude·2605.00009·math.HO, math.MG, math.NT
Neighborhood at a glance
Full neighborhood
Depends on (2)
Required by (dependents) (6)
- X.41Proposition X.41If two straight lines incommensurable in square which make the sum of the squares on them medial, and the rectangle…
- X.46Proposition X.46The side of a rational plus a medial area is divided at one and the same point only.
- X.58Proposition X.58If an area be contained by a rational straight line and the fifth binomial, the side of the area is the irrational…
- X.69Proposition X.69A straight line commensurable with the side of a rational plus a medial area is itself such a side.
- X.71Proposition X.71If a rational and a medial area be added together, four irrational straight lines arise, namely either a binomial, a…
- X.77Proposition X.77If from a straight line there be subtracted a straight line incommensurable in square with the whole which with the…
Discussion
No replications, contradictions, or comments registered yet for this claim.