Proposition Replicated

Proposition X.71

If a rational and a medial area be added together, four irrational straight lines arise, namely either a binomial, a first bimedial, a major, or a side of a rational plus a medial area.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:X.71

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 (4)

X.36 X.37 X.39 X.40

PropositionProposition X.71

Outgoing (2)

X.72 X.108

Full neighborhood

Depends on (4)

X.36Proposition X.36If two rational straight lines commensurable in square only be added together, the whole is irrational; and let it be…
X.37Proposition X.37If two medial straight lines commensurable in square only and containing a rational rectangle be added together, the…
X.39Proposition X.39If two straight lines incommensurable in square which make the sum of the squares on them rational, but the rectangle…
X.40Proposition X.40If two straight lines incommensurable in square which make the sum of the squares on them medial, but the rectangle…

Required by (dependents) (2)

X.72Proposition X.72If two medial areas incommensurable with one another be added together, the remaining two irrational straight lines…
X.108Proposition X.108If from a rational area a medial area be subtracted, the side of the remaining area arises as one of four irrationals:…

Discussion

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