Proposition Replicated

Proposition IX.35

If as many numbers as we please be in continued proportion, and there be subtracted from the second and the last numbers equal to the first, then, as the excess of the second is to the first, so will the excess of the last be to all those before it.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:IX.35

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 (3)

VII.11 VII.19 VIII.1

PropositionProposition IX.35

Outgoing (1)

IX.36

Full neighborhood

Depends on (3)

VII.11Proposition VII.11If, as whole is to whole, so is a number subtracted to a number subtracted, the remainder will also be to the remainder…
VII.19Proposition VII.19If four numbers be proportional, the number produced from the first and fourth will be equal to the number produced…
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…

Required by (dependents) (1)

IX.36Proposition IX.36If as many numbers as we please beginning from a unit be set out continuously in double proportion, until the sum of…

Discussion

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