Proposition Replicated
Proposition X.41
If two straight lines incommensurable in square which make the sum of the squares on them medial, and the rectangle contained by them medial and also incommensurable with the sum of the squares on them, be added together, the remaining straight line is irrational; and let it be called the side of the sum of two medial areas.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:X.41
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) (5)
- X.47Proposition X.47The side of the sum of two medial areas is divided at one and the same point only.
- X.59Proposition X.59If an area be contained by a rational straight line and the sixth binomial, the side of the area is the irrational…
- X.70Proposition X.70A straight line commensurable with the side of the sum of two medial areas is itself such a side.
- X.72Proposition X.72If two medial areas incommensurable with one another be added together, the remaining two irrational straight lines…
- X.78Proposition X.78If from a straight line there be subtracted a straight line incommensurable in square with the whole which with the…
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