Proposition Replicated

Proposition IX.9

If as many numbers as we please beginning from a unit be in continued proportion, and the number after the unit be square, all the rest will also be square; and if the number after the unit be cube, all the rest will also be cube.

type · theoreticalevidence · argumentextracted by · author

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

VIII.22 VIII.23 IX.8

PropositionProposition IX.9

Outgoing (1)

IX.10

Full neighborhood

Depends on (3)

VIII.22Proposition VIII.22If three numbers be in continued proportion, and the first be square, the third will also be square.
VIII.23Proposition VIII.23If four numbers be in continued proportion, and the first be cube, the fourth will also be cube.
IX.8Proposition IX.8If as many numbers as we please beginning from a unit be in continued proportion, the third from the unit will be…

Required by (dependents) (1)

IX.10Proposition IX.10If as many numbers as we please beginning from a unit be in continued proportion, and the number after the unit be not…

Discussion

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