Proposition Replicated
Proposition X.39
If two straight lines incommensurable in square which make the sum of the squares on them rational, but the rectangle contained by them medial, be added together, the whole straight line is irrational; and let it be called major.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:X.39
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.40Proposition X.40If two straight lines incommensurable in square which make the sum of the squares on them medial, but the rectangle…
- X.45Proposition X.45A major straight line is divided at one and the same point only.
- X.57Proposition X.57If an area be contained by a rational straight line and the fourth binomial, the side of the area is the irrational…
- X.68Proposition X.68A straight line commensurable with a major straight line is itself major.
- X.71Proposition X.71If a rational and a medial area be added together, four irrational straight lines arise, namely either a binomial, a…
- X.76Proposition X.76If from a straight line there be subtracted a straight line incommensurable in square with the whole, which with the…
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