Proposition Replicated

Proposition XIII.1

If a straight line be cut in extreme and mean ratio, the square on the greater segment added to the half of the whole is five times the square on the half.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:XIII.1

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)

II.6 II.11

PropositionProposition XIII.1

Outgoing (5+)

XIII.2 XIII.3 XIII.4 XIII.5 XIII.6

Full neighborhood

Depends on (2)

II.6Proposition II.6If a straight line be bisected and a straight line be added to it in a straight line, the rectangle contained by the…
II.11Proposition II.11To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the…

Required by (dependents) (5)

XIII.2Proposition XIII.2If the square on a straight line be five times the square on a segment of it, then, when the double of the said segment…
XIII.3Proposition XIII.3If a straight line be cut in extreme and mean ratio, the square on the lesser segment added to the half of the greater…
XIII.4Proposition XIII.4If a straight line be cut in extreme and mean ratio, the square on the whole and the square on the lesser segment…
XIII.5Proposition XIII.5If a straight line be cut in extreme and mean ratio, and there be added to it a straight line equal to the greater…
XIII.6Proposition XIII.6If a rational straight line be cut in extreme and mean ratio, each of the segments is the irrational straight line…

Discussion

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