Proposition Replicated

Proposition VII.27

If two numbers be prime to one another, and each by multiplying itself make a certain number, the products will be prime to one another; and if the original numbers by multiplying the products make certain numbers, these will be prime to one another.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:VII.27

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)

VII.25 VII.26

PropositionProposition VII.27

Outgoing (2)

VIII.2 VIII.13

Full neighborhood

Depends on (2)

VII.25Proposition VII.25If two numbers be prime to one another, the product of one of them into itself will be prime to the remaining one.
VII.26Proposition VII.26If two numbers be prime to two numbers, both to each, their products also will be prime to one another.

Required by (dependents) (2)

VIII.2Proposition VIII.2To find numbers in continued proportion, as many as may be prescribed, and the least that are in a given ratio.
VIII.13Proposition VIII.13If there be as many numbers as we please in continued proportion, and each by multiplying itself make some number, the…

Discussion

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