Proposition Replicated

Proposition V.2

If a first magnitude be the same multiple of a second that a third is of a fourth, and a fifth also be the same multiple of the second that a sixth is of the fourth, then the sum of the first and fifth will also be the same multiple of the second that the sum of the third and sixth is of the fourth.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:V.2

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.1

PropositionProposition V.2

Outgoing (2)

V.12 V.18

Full neighborhood

Depends on (1)

V.1Proposition V.1If there be any number of magnitudes whatever which are, respectively, equimultiples of any magnitudes equal in…

Required by (dependents) (2)

V.12Proposition V.12If any number of magnitudes be proportional, as one of the antecedents is to one of the consequents, so will all the…
V.18Proposition V.18If magnitudes separated be proportional, they will also be proportional componendo.

Discussion

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