Proposition Replicated

Proposition V.4

If a first magnitude have to a second the same ratio as a third to a fourth, any equimultiples whatever of the first and third will also have the same ratio to any equimultiples whatever of the second and fourth respectively, taken in corresponding order.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:V.4

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 (1)

V.3

PropositionProposition V.4

Outgoing (2)

V.16 V.18

Full neighborhood

Depends on (1)

V.3Proposition V.3If a first magnitude be the same multiple of a second that a third is of a fourth, and if equimultiples be taken of the…

Required by (dependents) (2)

V.16Proposition V.16If four magnitudes be proportional, they will also be proportional alternately.
V.18Proposition V.18If magnitudes separated be proportional, they will also be proportional componendo.

Discussion

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