Proposition Replicated

Proposition VIII.9

If two numbers be prime to one another, and numbers fall between them in continued proportion, then, however many numbers fall between them in continued proportion, so many will also fall in continued proportion between each of them and a unit.

type · theoreticalevidence · argumentextracted by · author

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

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)

VIII.1 VIII.2

PropositionProposition VIII.9

Outgoing (1)

VIII.10

Full neighborhood

Depends on (2)

VIII.1Proposition VIII.1If there be as many numbers as we please in continued proportion, and the extremes of them be prime to one another, the…
VIII.2Proposition VIII.2To find numbers in continued proportion, as many as may be prescribed, and the least that are in a given ratio.

Required by (dependents) (1)

VIII.10Proposition VIII.10If numbers fall between each of two numbers and a unit in continued proportion, however many numbers fall between each…

Discussion

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