Proposition Replicated

Proposition X.11

If four magnitudes be proportional, and the first be commensurable with the second, the third also will be commensurable with the fourth; and if the first be incommensurable with the second, the third also will be incommensurable with the fourth.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:X.11

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)

X.5 X.6

PropositionProposition X.11

Outgoing (2)

X.12 X.14

Full neighborhood

Depends on (2)

X.5Proposition X.5Commensurable magnitudes have to one another the ratio which a number has to a number.
X.6Proposition X.6If two magnitudes have to one another the ratio which a number has to a number, the magnitudes will be commensurable.

Required by (dependents) (2)

X.12Proposition X.12Magnitudes commensurable with the same magnitude are commensurable with one another.
X.14Proposition X.14If four straight lines be proportional, and the square on the first be greater than the square on the second by the…

Discussion

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